National Water

Quality Handbook

September 2003
(450–VI–NWQH, September 2003)

Issued September 2003

National Water Quality Handbook

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(450–VI–NWQH, September 2003) i

Contents:

National Water

Quality Handbook

Part 600 Introduction

Part 601 Resource Management Framework

Part 602 Introduction to Water Quality

Part 603 Water Quality Assessment

Part 604 Nutrients

Part 605 Pathogens

Part 606 Pesticides

Part 607 Temperature

Part 608 Sediment

Part 609 Dissolved Oxygen

Part 610 Salts

Part 611 Heavy Metals

Part 612 Other Contaminants of Surface and Groundwater

Part 613 Reserved

Part 614 Design of Water Quality Monitoring Systems

Part 615 Analysis of Water Quality Monitoring Data

Part 616 Reserved

Part 617 Examples and Case Studies

Part 618 Reserved

Part 619 Glossary
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National Water Quality Handbook

Part 600

Introduction

Part 600 Introduction
United States

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National Water Quality Handbook

Part 600 Introduction to

National Water

Quality Handbook
(450–VI–NWQH, September 2003) i

Contents:

Part 600 Introduction to National

Water Quality Handbook

600.0000 Purpose of handbook 1

600.0001 Scope of handbook 1

600.0002 Intended audience 1

600.0003 Structure 1

600.0004 Key handbook support references 1
(450–VI–NWQH, September 2003) 1

Part 600 Introduction to National Water

Quality Handbook

600.0000 Purpose of handbook

Water quality is an important natural resource concern

for the Nation. Being a lead natural resource technical

agency, the Natural Resources Conservation Service

(NRCS) has developed this handbook as a principal

reference pertaining to water quality as it relates to all

agricultural land uses. The handbook is the principal

NRCS reference document for technical information

and guidance in carrying out water quality responsibilities. This document consolidates pertinent procedures,

guidelines, and other materials to facilitate finding

relevant and reliable information. It provides clear

guidelines for filing and cross-referencing applicable

local, state, and national water quality related reference materials.

600.0001 Scope of handbook

The National Water Quality Handbook (NWQH) is

designed to provide guidance in all aspects of water

quality to NRCS personnel, Agency technical partners,

and those who provide technical services to clients for

NRCS. Guidance is provided to address water quality

issues within the NRCS planning and implementation

process. Agricultural related pollutants are addressed

within this document or through references to other

water quality technical materials.

Specific technical or procedural details for planning,

such as conservation practice design criteria, are

beyond the scope of this handbook. Detailed design

information is retained in other NRCS handbooks and

manuals and is referred to in appropriate sections of

the NWQH. Also, water quality issues related to industrial and municipal waste pollutants are not within the

scope of this document.

600.0002 Intended audience

The focus of this handbook is the NRCS field office,

NRCS technical partners, and those providing technical services for NRCS. The NWQH includes technical

and procedural guidance that is applicable at any

organizational or technical level in support of NRCS

water quality activities. This handbook is appropriate

for basic orientation of NRCS water quality activities

as well as advanced procedures for technical specialists.

600.0003 Structure

The National Water Quality Handbook consists of core

water quality information as well as extensive crossreferencing to NRCS documents and publications and

selected non-NRCS materials. Referenced documents

that support and contribute to the handbook are

referred to as Key References. The handbook leads the

user through a logical sequence beginning with basic

information and introductory material and progressing

through planning and implementation procedures for

more complex subjects. Key references are presented

to allow the user to pursue more in-depth information

than given in the handbook. A substantial part of the

handbook is available electronically on the NRCS

national Web page, (http://www.nrcs.usda.gov) which

reflects updates, revisions, and the status of the document.

600.0004 Key handbook support

references

This document and its specified support references are

listed in section I of the Field Office Technical Guide

(FOTG). Hardcopy materials of the NRCS National

Water Quality Handbook and key references reside in

each NRCS field office.

Key references

Agricultural Waste Management Field Handbook,

Rev. 1

Field Office Technical Guide (FOTG) Sections I–V

Ground Water and Surface Water, A Single Resource

USGS Circular 1139

National Agronomy Manual

National Engineering Handbook, Part 652, National

Irrigation Guide

National Planning Procedures Handbook

Stream Corridor Restoration—Principles, Processes,

and Practices (NEH Part 653)
United States

Department of

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Natural

Resource

Conservation

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National Water Quality Handbook

Part 601

Resource Management

Part 601 Resource Management

Framework
United States

Department of

Agriculture

Natural

Resource

Conservation

Service

National Water Quality Handbook

Part 602

Intro to Water Quality

Part 602 Introduction to Water

Quality
United States

Department of

Agriculture

Natural

Resource

Conservation

Service

National Water Quality Handbook

Part 603

Water Quality Assessment

Part 603 Water Quality Assessment
United States

Department of

Agriculture

Natural

Resource

Conservation

Service

National Water Quality Handbook

Nutrients

Part 604

Part 604 Nutrients
United States

Department of

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Natural

Resource

Conservation

Service

National Water Quality Handbook

Pathogens

Part 605

Part 605 Pathogens
United States

Department of

Agriculture

Natural

Resource

Conservation

Service

National Water Quality Handbook

Part 606 Pesticides

Pesticides

Part 606
United States

Department of

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Natural

Resource

Conservation

Service

National Water Quality Handbook

Part 607

Temperature

Part 607 Temperature
United States

Department of

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Resource

Conservation

Service

National Water Quality Handbook

Sediment

Part 608

Part 608 Sediment
United States

Department of

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Natural

Resource

Conservation

Service

National Water Quality Handbook

Part 609

Dissolved Oxygen

Part 609 Dissolved Oxygen
United States

Department of

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Natural

Resource

Conservation

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National Water Quality Handbook

Part 610

Salts

Part 610 Salts
United States

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Natural

Resource

Conservation

Service

National Water Quality Handbook

Part 611

Part 611 Heavy Metals

Heavy Metals
United States

Department of

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Natural

Resource

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National Water Quality Handbook

Part 612

Other Contaminants

Part 612 Other Surface and Ground

Water Contaminants
United States

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Natural

Resource

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National Water Quality Handbook

Part 613

Part 613
United States

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Natural

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National Water Quality Handbook

Part 614

WQM System Design

Part 614 Water Quality Monitoring

System Design
United States

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National Water Quality Handbook

Part 614 Design of Water

Quality Monitoring

Systems
(450–VI–NWQH, September 2003) i

The purpose of part 614 of the National Water Quality Handbook (NWQH)

is to describe methods for monitoring the water quality response to land

use and land management activities and conservation practices. These

methods include how to design a monitoring study, how to set up a monitoring station, and how to analyze the water quality data. The information

presented assumes that the reader has a basic understanding of water

quality. A basic knowledge of statistical analysis also is useful, although

part 615 of this handbook provides guidance in statistical analysis of water

quality data.

Part 614 of the NWQH is needed at this time because:

• The effectiveness of programmatic activities needs to be determined.

Water quality managers are constantly asking for evidence of the

results of a program.

• Comprehensive guidance is needed. Many water quality managers are

placed in the role of overseeing or designing monitoring projects, but

a comprehensive guidance is lacking.

• Several water quality monitoring projects currently underway may

require modification to show the results anticipated.

It is intended to assist those with direct or supervisory responsibilities in

planning, implementing, and evaluating water quality monitoring projects.

This part of the NWQH is formatted to directly assist in designing a water

quality monitoring project. A 2-page worksheet using the steps in planning a

monitoring study is at the end of chapter 1. This worksheet was organized

to facilitate rapid and complete monitoring study design. Each step in the

worksheet corresponds to a separate chapter in part 614. Each chapter

includes examples to guide practice in applying the major concepts being

described.

Part 615 of the handbook is concerned with the statistical analysis of monitoring results. It may be useful to review the introductory chapter in part

615 to perform some of the statistical operations described in part 614.

Part 614 of the National Water Quality Handbook was written by John C.

Clausen, Ph.D., College of Agriculture and Natural Resources, University of

Connecticut. The concept for this project was developed by James N.

Krider, former national environmental engineer, Natural Resources Conservation Service (NRCS), Washington, DC. Technical leadership was

provided by Bruce J. Newton, limnologist, NRCS National Water and

Climate Center, Portland, Oregon, and by Frank Geter, agricultural engineer, formerly with the NRCS Information Technology Center, Fort Collins,

Colorado, and Douglas Holy, limnologist, Ecological Sciences Division,

Washington, DC.

Purpose

Preface

Structure of

part 614

Acknowledgments
ii (450–VI–NWQH, September 2003)

Many people contributed to this document. The following NRCS staff

served on teams that reviewed drafts of parts 614 and 615:

Stephanie Aschmann, agroecologist, Watershed Science Institute,

Lincoln, Nebraska

William H. Boyd, environmental engineer, National Water Management

Center, Little Rock, Arkansas

Richard Croft, water quality specialist, Watershed Science Institute,

Burlington, Vermont

Carl DuPoldt, agricultural engineer, Somerset, New Jersey

David C. Moffitt, envirnomental engineer, National Water Management

Center, Fort Worth, Texas

Gerald Montgomery, biologist, Northern Plains Regional Office, Lincoln,

Nebraska

James D. Rickman, (retired) agricultural engineer, Fort Worth, Texas

Lynn Sampson, biologist, East Lansing, Michigan

Ron Schierer, Northern Plains Regional Technical Team, Lakewood,

Colorado

Donald Stettler, (retired) agricultural engineer, National Water and Climate Center, Portland, Oregon

Howard Thomas, (retired) economist, Portland, Oregon

Barbara M. Vining, pesticide and nutrient specialist, formally of NRCS,

Indianapolis, Indiana

James Wood, water quality specialist, Burlington, Vermont

In addition, many attendees of a water quality monitoring workshop held in

1993 provided helpful input. They included Jerry M. Bernard, Denise A.

Tennessee, Gene Lindeman, and John Sutton. Other comments were

provided by Dana Chapman, Lyle J. Steffen, and Ivan Wilkinson.

Joseph A. Neafsey, water quality specialist, Storrs, Connecticut, was the

contract project officer. Mary R. Mattinson, editor, and Wendy R.

Pierce, illustrator, National Cartography and Geospatial Center, Fort

Worth, Texas, provided editorial and graphic support.

The National Water Quality Handbook is the result of a collaborative effort

of the NRCS Science and Technology Consortium. Special thanks to the

following individuals for their leadership and support in the development

and publishing of this essential technical reference:

Wil Fontenot, natural resource specialist, Lafayette, Louisianna

Jon Werner, national hydrologist, Conservation Engineering Division,

Washington, D.C.

Roy Mann, (retired) resource conservationist, Portland, Oregon

Ken Pfeiffer, pest management specialist, National Water and Climate

Center, Portland, Oregon

Bruce Newton, acting director, National Water and Climate Center, Portland, Oregon

Lynn Betts, communications director, Wildlife Habitat Management Institute, Des Moines, IA
(450–VI–NWQH, September 2003) iii

Part 614 National Water Quality

Handbook

Contents: Chapter 1 Introduction

Chapter 2 Water Quality Problem

Chapter 3 Objectives

Chapter 4 Statistical Designs

Chapter 5 Scale of Study

Chapter 6 Variable Selection

Chapter 7 Sample Type

Chapter 8 Sampling Location

Chapter 9 Sampling Frequency and Duration

Chapter 10 Station Type

Chapter 11 Sample Collection and Analysis

Chapter 12 Land Use and Management Monitoring

Chapter 13 Data Management

Appendixes

Index
(450–VI–NWQH, September 2003)

United States

Department of

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Service

Part 614

National Water Quality Handbook

Chapter 1 Introduction
(450–VI–NWQH, September 2003) 1–i

Chapter 1 Introduction

Contents: 614.0100 General 1–1

614.0101 Definitions 1–2

614.0102 Monitoring purposes 1–2

(a) Analyze trends ............................................................................................... 1–2

(b) Determine fate and transport of pollutants ............................................... 1–2

(c) Define critical areas...................................................................................... 1–3

(d) Assess compliance........................................................................................ 1–3

(e) Measure effectiveness of conservation practices ..................................... 1–3

(f) Evaluate program effectiveness .................................................................. 1–3

(g) Make wasteload allocations ........................................................................ 1–3

(h) Model validation and calibration ................................................................ 1–4

(i) Conduct research ......................................................................................... 1–4

(j) Define water quality problem ...................................................................... 1–4

614.0103 Monitoring study design 1–4

614.104 References 1–13

Steps in Planning a Water Quality Monitoring System 1–15

Tables Table 1–1 Variables monitored for the St. Albans Bay project 1–8

Table 1–2 Sample types for the St. Albans Bay Project 1–9

Table 1–3 St. Albans Bay monitoring frequency 1–11
Part 614

National Water Quality Handbook

Chapter 1 Introduction

1–ii (450–VI–NWQH, September 2003)

Figures Figure 1–1 Steps in decisionmaking for a water quality 1–4

monitoring system

Figure 1–2 Steps in water quality monitoring system design 1–5

Figure 1–3 St. Albans Bay watershed 1–6

Figure 1–4 Level 3 paired watershed 1–10

Figure 1–5 Wetland sampling locations 1–10

Example Example 1–1 Case study—St. Albans Bay RCWP 1–7
(450-VI-NWQH, September 2003) 1–1

Chapter 1 Introduction

614.0100 General

Recognition of agriculture’s contribution to nonpoint

source (NPS) pollutant loadings to streams, lakes,

estuaries, and ground water has led to increased

emphasis on water quality monitoring in rural watersheds. Conservation Districts and the Natural Resources Conservation Service (NRCS) are often sponsors and cooperators, respectively, of studies and

projects to reduce agricultural NPS loadings. The

primary purpose of this handbook is to provide these

entities and their partners with guidance for gathering

and using water quality information to support planning and implementation activities.

Although opinions vary about the value of water quality monitoring, there is consensus that monitoring is

relatively expensive. Therefore, it is imperative that

monitoring be well designed. As stated by Ward, et al.

(1986), appropriate designs of monitoring systems are

needed to prevent a "data rich, but information poor"

monitoring system. Part 614 of this handbook primarily addresses the design of intensive monitoring

programs. Part 615 addresses the analysis of monitoring data to enable us to refine our understanding of

water quality.

For most projects that involve water quality concerns,

the NRCS planning process requires information

obtained by monitoring to perform the planning steps.

Current and historical data are needed to perform

Phase I, which includes identifying problem areas,

determining objectives and setting goals, inventorying

resources, and analyzing resource data. The results of

Phase I work are used in Phase II to formulate and

evaluate alternatives and decide on a plan. Phase III,

implementation and evaluation, requires water quality

information collected through time to evaluate the

effectiveness of the implemented alternative.

The collection of water quality information is extremely important as we learn how to address water

quality resource concerns. Adaptive management

requires that we observe the effects of natural resources management decisions so we can maximize

learning and increase the knowledge base for future

natural resources management decisions. Even during

studies, data could be used to calibrate and refine

planning tools, such as computer models. The success

of such efforts should eventually reduce the need for

costly water quality monitoring in the future.

State water quality agencies are generally most active

in assisting local water quality monitoring. At the

Federal level, the Office of Management and Budget

has directed agencies to coordinate their data acquisition efforts with the U.S. Geological Survey

(USGS)(OMB Circular M-92-01). The local USGS office

should be involved in the design of project water

quality monitoring.
Part 614

National Water Quality Handbook

Chapter 1 Introduction

1–2 (450-VI-NWQH, September 2003)

614.0101 Definitions

The term water quality is used throughout this guide,

so a definition is appropriate. Although many definitions for this term exist (APHA, et al. 1969; Rechard

and McQuisten 1968; Veatch and Humphreys 1966),

water quality can be broadly defined as the physical,

chemical, and biological composition of water as

related to its intended use for such purposes as drinking, recreation, irrigation, and fisheries.

The term water quality has different meanings to

different users of the water, which can result in confusion among water quality managers. The term may be

applied to a single characteristic of the water or to a

group of characteristics combined into a water quality

index.

A few other terms related to water quality are important to define.

Water quality management can be defined as the

management of the physical, chemical, and biological

characteristics of water (Sanders, et al. 1983).

Water quality monitoring, one function of water

quality management, is the collection of information

on the physical, chemical, and biological characteristics of water (Sanders, et al. 1983).

Pollution refers to a condition of water within a

water body caused by the presence of undesirable

materials (APHA, et al. 1969).

Contamination is the introduction of substances into

water at a sufficient concentration to make the water

unfit for its intended use (APHA, et al. 1969).

Pollution control generally is associated with the

regulation of pollutants.

614.0102 Monitoring purposes

Monitoring of water quality can serve many purposes.

Each purpose is described using relevant examples.

(a) Analyze trends

Monitoring on a regular basis has been used to determine how water quality is changing over time. A

widely publicized example of trend analysis was that

published by Smith and Alexander (1983) on stream

chemistry trends at the USGS benchmark stations.

Trend analysis was also used in several of the Rural

Clean Water Program (RCWP) projects in the United

States, including those in Vermont, Idaho, and Florida.

Monitoring of so called "baseline" conditions also has

been used and is often recommended. Baseline generally is thought of as a pre-condition; that is, what the

water quality conditions are that currently exist.

Caution is recommended in using baseline monitoring.

Unless such data are used for reconnaissance purposes or actually are the beginning of trend analysis,

then baseline monitoring is not recommended except

where the effects caused by climate are controlled in

the design of the project. If, for example, the baseline

data were collected during an abnormal year, the data

could be biased.

(b) Determine fate and transport

of pollutants

Monitoring also is conducted to determine whether a

pollutant may move and where it may go. For such

projects, monitoring over a long period may not be

needed. For example, if the objective is to determine

whether a pesticide is leaving the root zone, a shortterm (<5 years) study of intensive sampling would be

sufficient.

Fate and transport studies typically require frequent

sampling of all possible transport pathways in a relatively small area. These studies also are subject to

climate influences and may require sophisticated

sampling equipment.
Part 614

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Chapter 1 Introduction

(450-VI-NWQH, September 2003) 1–3

(c) Define critical areas

Water quality monitoring has been used to locate areas

within watersheds exhibiting greater pollution potential than other areas. The results of such monitoring

can then be used to target Resource Management

Systems (RMSs). This type of monitoring has often

been termed reconnaissance monitoring.

Targeting critical areas also could occur following

interpretation of water quality data collected early in a

project. For example, monitoring in a particular watershed could indicate that one of the subwatersheds may

have the highest phosphorus concentrations and

export as compared to the other monitored sub-watersheds. Supplemental investigation may reveal the

source of the phosphorus, either natural or related to

management. Based on these early findings from

monitoring data, priority could be given to that

subwatershed for implementation of RMSs.

Reconnaissance monitoring however, is generally

conducted over a short time frame, and caution should

be exercised to assure that decisions regarding targeting are not biased by unusual climate conditions

during the period of monitoring.

(d) Assess compliance

Water quality monitoring frequently has been used to

determine compliance with water quality plans and

standards. For example, bacteria monitoring has been

used to determine the percentage of the time bacteria

levels exceed a standard, such as 200 organisms per

100 milliliter. Compliance monitoring should consider

climate conditions as well as the ability to link

instream levels with actual sources before taking

action.

(e) Measure effectiveness of

conservation practices

Monitoring to determine the effectiveness of individual

conservation practices is typically conducted on a plot

or field scale, or as close as possible to the practice.

Water quality studies of individual practices can be

conducted in a relatively short time frame (<5 years).

However, some practices may take many years to

show results.

An example of monitoring to assess the effectiveness

of a conservation practice would be sampling above

and below a filter strip being used to treat feedlot

runoff. Another example of a practice suitable for

monitoring would be field nutrient management, in

which case, sampling of both the field soils and the

field runoff would be conducted.

(f) Evaluate program effectiveness

Water quality monitoring used to evaluate the effectiveness of a program in a watershed (e.g., Hydrologic

Unit Areas, HUAs) is generally conducted on a watershed scale. Several land uses would probably be within

the watershed. RMSs, implemented as a result of a

water quality program, would most likely be staggered

over time and managed with varying vigor. Monitoring

for program effectiveness would be conducted over

the long-term (>5 years).

Monitoring the effectiveness of a program is difficult

because of the lack of control over exactly what

happens and when it happens. Also, the staggering of

events will most likely compensate each other. Finally,

water quality responses to changes in practices may

be gradual and take many years because of the buildup

of the pollutant of concern in the watershed.

(g) Make wasteload allocations

Monitoring of receiving water bodies would be needed

to perform wasteload allocations. Though typically

thought of for point sources, wasteload allocations are

used in some parts of the United States for both point

and nonpoint sources (e.g., Oregon). Monitoring could

be used to determine how much additional (or less)

agriculture or what conservation practice could be

allowed in a watershed without exceeding a certain

level or tropic state in a water body.

Monitoring to allocate loads from different sources

requires a good knowledge of the actual contributions

from the sources. For nonpoint sources, extensive

monitoring may be needed to determine the actual

source.
Part 614

National Water Quality Handbook

Chapter 1 Introduction

1–4 (450-VI-NWQH, September 2003)

(h) Model validation and

calibration

Water quality monitoring may be needed to validate or

calibrate models to local conditions. Also, it is used to

verify a model’s adequacy. In such tests, the values

predicted by the model are compared to values observed by monitoring.

A major difficulty in model validation is that many

models are developed to simulate long-term average

conditions; whereas, most monitoring data are collected on a relatively short-term basis. In addition,

many of the input variables used in a model, such as

the hydraulic conductivity or wind speed, typically are

not monitored.

(i) Conduct research

Water quality monitoring is necessary for addressing

specific research questions. An example would be a

comparison of nitrate concentrations obtained from

samples using various types of lysimeters including

suction plate, porous cup, and zero-tension types. Such

monitoring would normally be conducted by a research agency or university. The difference between

research monitoring and other purposes of monitoring

often is not great. However, research monitoring is not

the purpose of this handbook.

(j) Define water quality problem

Although discussed elsewhere in this guide, water

quality monitoring may be required to give adequate

definition to the water quality problem. For example, if

a fishery is impaired in a water body, water quality

monitoring will be needed to determine the cause of

the impairment. Possible causes might include sediment, toxins, reduced dissolved oxygen, or temperature problems, to name a few.

If monitoring to better define the water quality problem, the appropriate water quality characteristics must

be monitored.

614.0103 Monitoring

study design

Many outlines for developing a monitoring study have

been made (Canter 1985; Ponce 1980; Sanders, et al.

1983; Solomon and Avers 12987; Tinlin and Everett

1978; Ward, et al. 1990; Whitfield 1988).

Water quality monitoring, like other tasks, can be

viewed in a decisionmaking or planning context that

begins with a definition of the problem and ends with

an evaluation of the effectiveness of the plan (fig.

1–1).

Identify

problem

 Example:

Excess fecal coliform

in Long Lake

 

To determine the effect of implementing

conservation practices on fecal coliform

levels in Long Lake.

 • Extent of problem

 (time, space)

 • Source?

 • Effectiveness of conservation practices

Monitor bacteria in:

 • Long Lake, or

 • Tributaries, or

 • Plots or fields

Objectives

Objectives

tree

Attributes

Formulate

alternative

strategies

{

{

{

{

Inventory &

analyze

resource data

Decide

monitoring

plan

Conduct

monitoring

Evaluate

plan

Evaluate

alternatives

Figure 1–1 Steps in decisionmaking for a water quality

monitoring system
Part 614

National Water Quality Handbook

Chapter 1 Introduction

(450-VI-NWQH, September 2003) 1–5

This framework is similar to the 9-Step Planning Process (USDA-SCS 1993), although that process is primarily aimed at developing and implementing conservation practices. In some cases it may be desirable to

develop the water quality monitoring plan within the

context of the 9-Step Planning Process. The steps are:

Step 1 Identify problems

Step 2 Determine objectives

Step 3 Inventory resources

Step 4 Analyze resource data

Step 5 Formulate alternatives

Step 6 Evaluate alternatives

Step 7 Make decisions

Step 8 Implement plan

Step 9 Evaluate plan

This handbook uses 12 steps for developing a monitoring study (fig. 1–2). Chapters 2 through 13 describe

these steps in detail. The complexity of each step

varies with the type of system being designed; however, each step should be addressed for all monitoring

projects.

The first step, defining the water quality problem, is

necessary to assure that monitoring actually matches

the problem. Setting objectives for monitoring clarifies

the purposes of the project and keeps it on track.

Knowledge of the overall project objectives assures

that monitoring is consistent with the implementation

goals. The statistical design is needed as an overall

framework to ensure that the samples are being collected from the appropriate locations. The monitoring

design must also include the scale of the project (plot,

field, or watershed); the type of sample; the variables

and locations to sample; and the frequency and duration of sampling. The type of monitoring station and its

construction should be defined. The methods for

collecting land use and management data need to be

described, including how the water quality data and

land use data will be linked. Finally, a system for

managing the data should be described.

The 12 steps for developing a water quality monitoring

design are similar in some ways to the 9-Step Planning

Process. Water quality monitoring can be used to

identify resource problems (step 1), formulate alternatives (step 5), and evaluate the effectiveness of the

plan (step 9). In a side-by-side comparison, the first

two steps of each method are analogous. Step 1 identifies problems, and step 2 determines objectives. The

remaining steps in water quality monitoring design are

included in step 3 of the 9-step process, which is to

inventory resources. In actual practice, both frameworks would most likely be considered by the water

quality specialist.

Example 1–1 is a case study for developing a water

quality monitoring plan using the 12 water quality

monitoring design steps. This case study is of the St.

Albans Bay Rural Clean Water Program project in

Northwestern Vermont (fig. 1–3). This project was one

of 21 in the nation and one of 5 comprehensive monitoring and evaluation projects active from 1980 to 1990

(Cassell, et al. 1983). It contains physical, chemical,

and biological monitoring.

Figure 1–2 Steps in water quality monitoring system

design

 1. Identify problem

 2. Form objectives

 3. Design experiment

 4. Select scale

 5. Select variables

 6. Choose sample type

 7. Locate stations

 8. Determine frequency

 9. Design stations

10. Define collection/

analysis methods

11. Define land use

monitoring

12. Design data

management
Part 614

National Water Quality Handbook

Chapter 1 Introduction

1–6 (450-VI-NWQH, September 2003)

Figure 1–3 St. Albans Bay watershed

Legend

Level 1

Level 2

Level 3

Level 4

Precip.

ST. ALBANS BAY WATERSHED

FRANKLIN COUNTY, VERMONT

P-4

P-2

P-1

41

26

4

12 13

11

24 23

42

25

22

44

P-3

21

3132

N

ST. ALBANS BAY
Part 614

National Water Quality Handbook

Chapter 1 Introduction

(450-VI-NWQH, September 2003) 1–7

Step 1 Water quality problem Recreation within St. Albans Bay was impaired because of excessive

eutrophication. Also, a state park had closed because of reduced attendance associated with frequent beach closings resulting from coliform

bacteria standard violations. A 1-year reconnaissance monitoring project

by the state natural resource agency determined that both bacteria and

phosphorus were coming from both point (wastewater treatment plant)

and nonpoint (agricultural) sources.

Step 2 Objectives Several monitoring objectives were defined:

• To document changes in the water quality of specific tributaries

within the watershed resulting from implementation of manure management practices.

• To measure the changes in the amount of suspended sediment and

nutrients entering St. Albans Bay resulting from implementation of

water quality management programs within the watershed.

• To evaluate trends in the water quality of St. Albans Bay and the

surface water within the St. Albans Bay watershed during the period

of the RCWP Watershed Project.

Additional objectives were developed to address special projects in the

study area. They included:

• To determine the role of an existing wetland, located between the

point and nonpoint sources and the Bay, on the quality of water

entering St. Albans Bay.

• To determine the role of Bay and wetland sediment on the quality of

St. Albans Bay.

• To determine the effect of Bay circulation on the quality of St. Albans

Bay.

• To determine the effect of individual BMPs, especially manure management, on exports to the Bay.

• To determine the effect of implementation of BMPs on aquatic organisms in the Bay and tributaries.

Step 3 Statistical design Many statistical designs were used to meet the objectives. These designs

were associated with four levels of study:

Level 1: Bay monitoring

Level 2: Tributary monitoring

Level 3: BMP monitoring

Level 4: Supplemental tributary monitoring

The primary statistical approach for the level 1 and 2 monitoring was

trend analysis of data collected at each Bay (4) and tributary (4) station.

In addition, since BMPs were not implemented at the same rate or

intensity throughout the project area, paired regressions between

tributary and bay stations were also used. An above-and-below paired

Example 1–1 Case study—St. Albans Bay RCWP
Part 614

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Chapter 1 Introduction

1–8 (450-VI-NWQH, September 2003)

watershed study was used for the level 3 monitoring. These types of

statistical approaches are described in chapter 3 of this handbook. The

level 4 monitoring had no statistical basis and was later dropped. There

was no control watershed in the study area to serve as a hydrologic

comparison for the treated watersheds. This lack of a control was found

to be an important deficiency.

Step 4 Scale of study The scale varied with the level of monitoring. Level 1 Bay stations were

points along a nutrient gradient in the Bay. Level 2 and 4 tributary stations were of watershed scale ranging from 3,900 to 8,800 acres in area.

The level 3 BMP monitoring used a field scale. The wetland study used

point scale for samples within the wetland and a watershed scale for the

wetland outlet. Sediment and circulation monitoring used point scales.

Step 5 Variables selection The variable selected for study also varied with the level of study

(table 1–1).

Table 1–1 Variables monitored for the

St. Albans Bay project

Variable Levels

Turbidity 1, 2, 4

Total suspended solids 1 – 4

Volatile suspended solids 1 – 4

Total phosphorus 1 – 4

Ortho-phosphorus 1 – 4

Ammonia-nitrogen 1 – 4

Total Kjeldahl nitrogen 1 – 4

Nitrate-nitrogen 1 – 4

Chlorophyll a 1

Fecal coliform 1, 2, 4

Fecal streptococcus 1, 2, 4

Temperature 1, 2, 4

Dissolved oxygen 1, 2, 4

pH 1, 2, 4

Conductivity 1, 2, 4

Secchi disc 1

Flow 2, 3, 4

Chloride Wetland

Fish populations 2

Invertebrates 2

Periphyton 2

Precipitation

Example 1–1 Case study—St. Albans Bay RCWP—Continued
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Chapter 1 Introduction

(450-VI-NWQH, September 2003) 1–9

Step 6 Sample type The type of sample varied with the level of monitoring (table 1–2)

Table 1–2 Sample types for the

St. Albans Bay Project

Level Sample type

1 Grab - 2 depths

plankton - depth integrated

2, 3 time composite at point

grab - bacteria

4 grab

Wetland grab

time composite at outlet

Step 7 Sampling location Sampling locations for all levels are shown in figure 1–3. Originally,

three stations were located in St. Albans Bay. One station was associated with the closed beach; the other two represented an inner and outer

bay component. A fourth station was added in the fourth year of the

project to better characterize the nutrient gradient in the bay following

the procedures described by Potash and Henson (1978). At each bay

station, samples were taken at two points: one at the surface and one

near the bottom. In addition, the extent and type of macrophyte growth

were determined annually using aerial photography and a field survey.

Level 2 tributary stations were located along the four major tributaries

to the bay at the lowest possible accessible site that passed a site selection criteria test. Samples were automatically collected in a tube at a

single point at each cross section. Level 2 biological monitoring was

conducted at the level 2 stations.

Two level 3 BMP stations were located with a ditch that drained two

adjacent fields (fig. 1–4). The stations were located one up stream of the

other, with the upper station serving as the control. At each station,

samples were automatically collected in a tube at a point in the crosssection.

Level 4 stations were located at four tributaries as close to the bay as

possible, and 15 wetland samples were located along stream channels at

equal spacing. Additional wetland samples were located in the bay to

better define a gradient (fig. 1–5).

Example 1–1 Case study—St. Albans Bay RCWP—Continued
Part 614

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Chapter 1 Introduction

1–10 (450-VI-NWQH, September 2003)

Figure 1–4 Level 3 paired watershed

Example 1–1 Case study—St. Albans Bay RCWP—Continued

Figure 1–5 Wetland sampling locations

Legend

Wetland boundary

Stream boundary

Paved road

Unpaved road

Sampling sites

STEVENS BROOK WETLAND

LAKE CHAMPLAIN

FRANKLIN COUNTY, VERMONT

(after Bogucki and Gruendling (1978))

N

12a

J3

J4

J5

S3

SJ1

SJ2

SJ3

C1

C2

SJ4

C3

C4

B1

SJ1a

S2

S1

J2

J1

Jewett

Brook

Stevens

Brook

St. Albans Bay

Sewage treatment

plant outfall

Road

Brook

Ditch

Fence

Monitoring

 stations

X XXXX

XXX

XXX

Legend

ST. ALBANS BAY WATERSHED

FRANKLIN COUNTY, VERMONT

LAROSE FARM SAMPLING LOCATIONS
Part 614

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Chapter 1 Introduction

(450-VI-NWQH, September 2003) 1–11

Step 8 Sampling frequency The number of samples collected also varied with the level of monitoring

and duration (table 1–3). The project was designed for a 10-year time frame.

Table 1–3 St. Albans Bay monitoring frequency

Level Frequency

1 monthly (Oct – Apr)

biweekly (May – Jul)

weekly (Aug – Sep)

2 Two 48-hour and one 72-hour composite/week from 8-

hour samples

bacteria weekly

3 4 hr composites

4 every 20 days

biological every 5 years

periphyton 3 times per week

benthos 2 times per year

fish 2 times per year

Step 9 Station type The type of station used varied with the level of sampling. Level 1 sampling was conducted at reference points in the Bay. A Kemmerer sampler

was used to collect water samples. A Wisconsin sampling net was used

to obtain plankton samples.

The level 2 stations were permanent structures located adjacent to the

streams. Each station was heated, had 110 VAC power, but ran on batteries. Bubbler-type stage-height recorders and automatic samplers were

used. Stilling wells were added to most stations.

The level 3 stations were temporary installations in field ditches that

included a sharp-crested 120 degree v-notch weir, bubbler gage, and

automatic sampler. The stations were heated with propane gas.

The level 4 sampling stations were grab sites as were the biological

monitoring sites. Periphyton was collected on plastic slides. A Surber

sampler was used to collect benthos in riffles. Hester-Dendy samplers

were also used. Block nets and a back-pack electrofisher were used to

collect fish samples.

Example 1–1 Case study—St. Albans Bay RCWP—Continued
Part 614

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Chapter 1 Introduction

1–12 (450-VI-NWQH, September 2003)

Step 10 Sample collection Sample collection, preservation, and analysis followed EPA guidelines

and analysis (USEPA 1983). Automatic samples were collected in tubing with a

peristaltic pump and stored in acid-washed, distilled water rinsed bottles

in refrigerated samplers. Bacteria samples were collected in sterilized

bottles. Samples were preserved with acid and analyzed within EPA

recommended holding times (USEPA 1983). A quality assurance and

quality control plan was developed, and the success of quality control

was reported quarterly. Field test kits were generally not used; however,

in situ analysis was made of dissolved oxygen and conductivity. Daily

field sheets were used, and each technician used individual field books.

Step 11 Land use and An elaborate program of land use and management monitoring was used

management in this study. A daily field log developed for each farm was left with the

monitoring landowners. Twice each year the farm was visited, the logs were picked

up, and any missing data were reconstructed. Data were collected on a

field-by-field basis and included the date, amount, and type of applications of manure, fertilizer, and pesticide. In addition, baseline information was collected on soils, topography, stream courses, roads, and farm

and field boundaries. Livestock numbers were also tracked for each

farm. Annually, 35mm slides obtained from the Agricultural Stabilization

and Conservation Service (ASCS) were consulted for land use changes

in areas where land use data were missing. These flyovers include only

cropland as part of program compliance by ASCS.

The entire system was managed in a Geographic Information System

(GIS). Maps and tables were used to track land use and management

activities, such as where manure was applied and whether it was incorporated.

Step 12 Data management A computer-based data management system, Bayqual, was developed

specifically for the project. Water quality and precipitation data were

manually entered into the computer. Stage charts were digitized. All data

were stored on a VAX computer with backup on a mainframe computer.

Currently data are archived in both paper and computer disk format.

Statistical analysis was conducted first on mainframe and then on PC

computers. The PC revolution occurred in the middle of the project, and

a general transfer of many data management activities to PC’s occurred.

Data entry included a validation process that involved double-entry with

an error checking program. Tests of reason were also programmed, such

as the impossibility of orthophosphorus exceeding total phosphorus.

Summaries of the data were presented quarterly and annually at project

meetings. Written reports were also provided. This frequent reporting

was found to be highly useful.

Example 1–1 Case study—St. Albans Bay RCWP—Continued
Part 614

National Water Quality Handbook

Chapter 1 Introduction

(450-VI-NWQH, September 2003) 1–13

614.104 References

American Public Health Association, American Society

of Civil Engineers, American Water Works Association, and Water Pollution Control Federation.

1969. Glossary of water and wastewater control

engineering.

Canter, L.W. 1985. River water quality monitoring.

Lewis Publ., Inc., Chelsea, MI.

Cassell, E.A., J.C. Clausen, R.C. Furbush, M. Long, and

D.W. Meals, Jr. 1983. St Albans Bay Watershed

comprehensive monitoring and evaluation and

socioeconomic monitoring and evaluation. Report No. 1, Background information. Vermont

Water Resources Research Center, Burlington,

VT.

Office of Management and Budget. 1992. Coordination

of water data information. OMB Cir. M-92-01,

Washington, DC.

Ponce, S.L. 1980. Water quality monitoring programs.

USDA Forest Serv., Watershed Sys. Dev. Group

Tech. Pap WDG-TP-00002, Fort Collins, CO.

Potash, M., and E.B. Henson. 1978. Significance of

geographic positioning for water quality monitoring in Lake Champlain. Proc. Establishing water

quality monitoring programs. Amer. Water

Resourc. Assoc., pp. 58-73.

Rechard, P.A., and R. McQuisten. 1968. Glossary of

selected hydrologic terms. Water Resourc. Res.

Inst., Water Resourc. Serv. No. 1, Univ. WY,

Laramie.

Sanders, T.G., R.C. Ward, J.C. Loftis, T.D. Steele, D.D.

Adrian, and V. Yevjevich. 1983. Design of networks for monitoring water quality. Water

Resourc. Pub., Littleton, CO.

Smith R.A., and R.B. Alexander. 1983. Evidence for

acid-precipitation-induced trends n stream chemistry at hydrologic benchmark station. U.S. Geol.

Surv. Circ. No. 910, Alexandria, VA.

Solomon R.M., and P.E. Avers. 1987. A water quality

monitoring framework to satisfy legal requirements. Proc. Symp. on monitoring, modeling, and

mediating water quality, Amer. Water Resourc.

Assoc., Bethesda, MD, pp. 231-242.

Tinlin, R.M., and L.G. Everett. 1978. Establishment of

ground water quality monitoring programs. In

Establishment of water quality monitoring programs. Proc. Amer. Water Resourc. Assoc.,

Minneapolis, MN.

United States Department of Agriculture, Soil Conservation Service. 1993. National Planning

Procedures Handbook, part 600.2. Washington,

DC.

United States Environment Protection Agency. 1983.

Methods for chemical analysis of water and

wastes. EPA 600/4-79-020, Off. Res. and Dev.,

Cincinnati, OH.

Veatch, J.O., and C.R. Humphrys. 1966. Water and

water use terminology. Thomas Print & Publ. Co.,

Kau Kauna, Wi.

Ward, R.C., J.C. Loftis, and G.B. McBride. 1986. The

"data-rich but information poor" syndrome in

water quality monitoring. Environ. Manag.

10(3):291-297.

Ward, R.C., J.C. Loftis, and G.B. McBride. 1990. Design

of water quality monitoring systems. Van

Nostrand Reinhold, New York, NY.

Whitfield, P.H. 1988. Goals and data collection designs

for water quality monitoring. Water Resourc. Bul.

24(4):775-780.
Part 614

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Chapter 1 Introduction

1–14 (450-VI-NWQH, September 2003)
Part 614

National Water Quality Handbook

Chapter 1 Introduction

(450-VI-NWQH, September 2003) 1–15

Project Title

1. Water Quality Problem

2. Objectives

Project:

Monitoring:

3. Statistical Design

Plot _________________ Above and below ____________ Paired ______________________

Multiple _____________ Trend ___________________________________________________

4. Study Scale

Stream: Plot ____________________Field ______________ Watershed ______________________

Ground water: Plot ____________________Field ______________ Watershed ______________________

Lake: Limnocorral ____________Bay _______________ Lake-wide _________ Outlet ______

5. Variables

_________________________________________ ___________________________________________

_________________________________________ ___________________________________________

_________________________________________ ___________________________________________

6. Sample Type

Grab ______________________ Composite ______________________ Integrated __________________

Continuous ________________ Time ___________________________ Flow _______________________

Steps In Planning A Water Quality Monitoring System
Part 614

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Chapter 1 Introduction

1–16 (450-VI-NWQH, September 2003)

7. Sampling Location

Water body: _______________________________ Location: _____________________________________

Water body: _______________________________ Location: _____________________________________

Water body: _______________________________ Location: _____________________________________

8. Sampling Frequency and Duration

n = __________________ per ____________________ Duration ___________________________________

9. Station Type

Discharge _________________________________ Concentration _________________________________

Precipitation ______________________________ Other ________________________________________

10. Sample Collection and Analysis

Preservation ______________________________ Lab methods __________________________________

Field methods ____________________________________________________________________________

11. Land Use And Management

Monitoring method ________________________________________________________________________

________________________________________________________________________________________

Data management _________________________________________________________________________

________________________________________________________________________________________

Relating land treatment to water quality ______________________________________________________

________________________________________________________________________________________

12. Data Management

Storage system ___________________________________________________________________________

Validation ________________________________________________________________________________

________________________________________________________________________________________

Reporting frequency _______________________________________________________________________

By: ___________________________________________________________________ Date: _________________

Steps In Planning A Water Quality Monitoring System (continued)
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resource

Conservation

Service

Part 614

National Water Quality Handbook

Chapter 2 Water Quality Problem
(450–VI–NWQH, September 2003) 2–i

Chapter 2 Water Quality Problem

Contents: 614.0200 Introduction 2–1

614.0201 Characteristics 2–1

614.0202 Syntax 2–2

614.0203 References 2–3

Tables Table 2–1 Water quality symptoms and problems 2–1
(450–VI–NWQH, September 2003) 2—1

Chapter 2 Water Quality Problem

614.0200 Introduction

The first step in developing a water quality monitoring

study is to define the water quality problem. The

definition of the water quality problem is normally

conducted before the design of the monitoring project.

However, a redefinition or clarification of the water

quality problem may often result as a monitoring

design is developed or during actual monitoring.

In some cases a definite water quality problem may

not exist, but rather a trend toward an emerging water

quality problem is being monitored. For example, in

Nebraska, monitoring of ground water nitrate concentrations has been used to identify trends toward exceeding a standard (Ehrman, et al. 1990). Chapter 2

describes defining the water quality problem. The

Water Quality Indicators Guide by Terrell and

Perfetti (1989) may be useful in using biological and

habitat approaches to identify surface water quality

problems.

614.0201 Characteristics

In formulating a water quality problem statement, the

difference between a problem and a symptom needs to

be distinguished. A water quality problem is a water

quality issue requiring a solution, often stated in the

form of a question. A symptom is a characteristic or

condition of a water body indicating a problem or

cause of the problem. For example, a poor fishery

might be symptomatic of a sediment or dissolved

oxygen problem. Excessive algal blooms might be

symptomatic of excessive nutrient loadings. Every

water quality problem typically has several symptoms.

The problem statement should be written in terms

of a use impairment. Uses may include contact

recreation, aesthetics, irrigation, fishing, or drinking.

Ecological integrity is increasingly thought of as a use

by some.

An indication of the impaired water body also helps to

clarify the water quality problem statement. The type

of water body could be described generically (e.g.,

lake, estuary, stream, vadose zone, ground water) or

more specifically by name (e.g., Lucky Lake). Finally,

identification of the cause of the problem and the

source of that cause lend further definition to the

problem statement. Table 2–1 summarizes some typical symptoms and problems and lists typical use

impairments. Example water bodies are also summarized.

Table 2–1 Water quality symptoms and problems

Symptom Problem Use impairment Water body Cause Source

Color Algae, sediment, organic acids Drinking Lake Erosion Fields

Excess algae Nutrients Aesthetics Lake P, N Animal waste

Excess macrophytes Nutrients, abundant light Recreation Lake P Fertilizers

Hypoxia Nutrients Fishing Estuary N Wastewater

Low biotic diversity Toxics, nutrients Fishing Bay PCB, Contaminated

pesticides sediment

Taste Salinity, algae, metals Drinking Ground Salts Geologic

water formation

Turbidity Algae, sediment Irrigation Stream Erosion Return flows
Part 614

National Water Quality Handbook

Chapter 2 Water Quality Problem

2–2 (450–VI–NWQH, September 2003)

614.0202 Syntax

Based upon the characteristics of a water quality

problem, a syntax for developing a water quality

problem statement can be given. Thus, the water

quality problem statement should include information

about the problem, the use impairment, the specific

water body, the cause of the problem, and the source

of the causal agents. A suggested syntax for writing a

water quality problem statement is:

problem +

impaired use +

water body +

cause +

source

A good example of a definition of a water quality

problem is:

The lack of recreation in St. Albans Bay is

because of eutrophication caused by excessive

phosphorus loading from agricultural sources.

The problem has been stated with sufficient clarification to set monitoring and project objectives. The

water quality problem is identified as eutrophication.

A symptom of that problem, although not stated, might

be algal blooms. The water body is St. Albans Bay. The

cause identifies the driving factor for eutrophication,

which in this case is phosphorus. A more complete

discussion of causality is in part 615 of this handbook.

Finally, the source of the pollutant is identified as

agricultural in this case.

In many cases the actual source of the pollutant or the

actual cause of the problem may not be known when

designing the monitoring study. This is often the case

where water quality data are limited or do not exist. In

such cases the statement of the water quality problem

may need to include some uncertainty. For example:

The lack of recreation in St. Albans Bay is

because of excess nutrients (N or P) from

unknown sources.

Another limitation may be knowledge of causality for

the problem. The problem may be so new that a causal

relationship has not been developed yet. As described

in the preface, the actual purpose of monitoring may

be to determine the source of the problem.

On the other hand, an example of a poor definition of a

water quality problem is:

Bad fishing.

For this example, the real problem is unknown. Is

fishing poor because of toxics, dissolved oxygen,

sediment, food, or some other causal factor? Also,

what is the source of the problem contributing to the

causal factor? Therefore, to adequately define the

problem, some knowledge of the condition of the

resource must be available. Some data are needed. The

problem must also be of a scale that is addressable by

the project. For example, a study on a small plot in the

watershed of a large lake will not allow determining

whether the water quality problem of the lake has

been corrected, but may address a water quality problem in a tributary to the lake.

The absence of a proper statement of the water quality

problem is a common impediment to proper design

and execution of a water quality monitoring study.
Part 614

National Water Quality Handbook

Chapter 2 Water Quality Problem

(450–VI–NWQH, September 2003) 2–3

614.0203 References

Ehrman, R.L., M.L. Link, J.J. Gottala. 1990. Special

protection areas: A new nonpoint source management option in Nebraska. J. Soil and Water

Conserv. 45(2):263-264.

Terrell C.R., and P.B. Perfetti. 1989. Water quality

indicators guide: Surface waters. USDA Soil

Conserv. Serv., SCS-TP-161, Washington, DC.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

National Water Quality Handbook

Chapter 3 Objectives
(450–VI–NWQH, September 2003) 3–i

Chapter 3 Objectives

Contents: 614.0300 Introduction 3–1

614.0301 Forming objectives 3–1

(a) Monitoring objectives .................................................................................. 3–1

(b) Management objectives ............................................................................... 3–2

614.0302 Objectives tree 3–2

614.0303 Objective attributes 3–3

614.0304 References 3–4

Figure Figure 3–1 Water quality monitoring objective tree 3–3
(450-VI-NWQH, September 2003) 3—1

614.0301 Forming objectives

Much time has been devoted to debating the differences among objectives, goals, and purposes. Although

the distinction between goals and objectives has been

made, the differences are subtle to most but the academician (Dickerson and Robershaw 1975, Keeney 1988,

Keeney and Raiffa 1976). Therefore, for the purposes

of this handbook, all these terms are grouped under

the term objective.

(a) Monitoring objectives

In general, an objective describes the answer to the

following question: "What must be done?" It also states

what is desired to accomplish. By definition, an objective includes an object as part of the statement. A

useful syntax for writing an objective is:

 infinitive verb + object word or phrase + constraints

The first component is the infinitive verb. An infinitive

is a verb form that is usually preceded by the word to.

An infinitive typically is used as a noun in objective

statements. These infinitives allow determining

whether or not they are achieved and are not subjective. Some examples for monitoring objectives are:

To determine...

To evaluate...

To assess...

The second component of an objective statement is

the object. The object receives the action of the verb

and answers the question, "What?" An example of a

monitoring objective statement with an infinitive and a

noun is:

To determine the effects of implementing

conservation practices...

The third component of an objective statement is the

constraints to the objective. This component is not

necessary to make an objective statement. Constraints

limit the objective statement to specified areas. The

objective becomes constrained from the whole world

Chapter 3 Objectives

614.0300 Introduction

The second step in developing a water quality monitoring study, after defining the water quality problem, is

to define the monitoring objectives. The objectives of

a monitoring study must address the water quality

problem. A well thought out objective or set of objectives drives the rest of the monitoring study design and

is critical to a successful monitoring project. This

chapter presents methods for formulating objectives

and gives several examples of objectives. In addition, a

process for organizing a multitude of objectives is

provided.

Unfortunately, two types of objectives emerge when

planning a monitoring project: management objectives

and monitoring objectives. Management objectives

refer to the goals of the project that monitoring is

intended to assess. Monitoring objectives refer to

obtaining knowledge about the system. Often these

two types of objectives become confused; yet, both are

important to the success of the project. Therefore,

both types of objectives are presented in this chapter.

Setting objectives can be viewed as a series of three

steps:

• Identifying the objective

• Developing an objective hierarchy

• Specifying attributes to measure the level of

achievement of these objectives
Part 614

National Water Quality Handbook

Chapter 3 Objectives

3–2 (450-VI-NWQH, September 2003)

of opportunities or alternatives. Appropriate constraints can include the water quality variables to be

sampled or the location of the study. For example, the

completed monitoring objective could be:

To determine + the effect of implementing

conservation practices + on fecal coliform

levels in Long Lake.

Some constraints may be unnecessary and may overly

limit the study design. For example, to limit the water

quality variables to test for when the cause of pollution is unknown. The constraint would then interfere

with determining the cause of the problem.

Coffee and Smolen (1990) suggest that monitoring

objectives should specify the water quality variables,

location of monitoring, the degree of causality, and the

anticipated result of the management action.

(b) Management objectives

For management objectives, the infinitives show a

direction of preference; however, achievement of

these objectives may be more subjective, depending

upon how they are stated. The infinitives for management objectives include:

To reduce...

To increase...

To eliminate...

An example of a management objective statement with

an infinitive and a noun is:

To reduce bacterial loading...

The completed management objective somewhat

related to the monitoring objectives described above

is:

To reduce fecal coliform loading

to Long Lake.

This management objective is subjective. An example

of a nonsubjective management objective is:

To implement fecal coliform controls on

75 percent of the farms in the Long Lake

watershed.

614.0302 Objectives tree

Most projects have several objectives. These objectives may be complementary or even sometimes

competitive. To achieve some overall general objective, several subobjectives may be needed. Thus, the

subobjectives might be viewed as hierarchical.

The relationships among objectives can be better

understood by developing an objective tree. An objective tree displays all of the monitoring objectives in a

hierarchical manner so that priorities can be established on which objective to tackle first. Two objectives in the tree are connected if the achievement of

one objective contributes directly to the achievement

of the other objective. Higher-order objectives are

more general and stable than lower-order objectives.

The lower-order objectives help to define the higherlevel objectives more specifically and may change

from time to time with expanding knowledge.

One way to develop the objective tree is to write each

objective on a separate card and compare all possible

combinations of card pairs using the statement: "Does

the achievement of card A contribute directly to the

achievement of card B?" If the answer is yes, the two

objectives are connected in the direction indicated.

One of the advantages of developing the objective tree

is that it shows the order in which objectives must be

accomplished so that the overall objective can be

attained.

An example of a monitoring objective tree is shown in

figure 3–1. For this example, the system contains a

wetland that receives tributary loadings before runoff

outlets to the lake. The watershed has both point and

nonpoint sources of bacteria. Also, the lake is not wellmixed and exhibits water quality gradients that appear

to be influenced by wind-driven circulation patterns. In

this case, before we could determine the effect of

implementing BMPs in the watershed on the levels of

bacteria in the lake, the circulation in the lake and the

effect of the wetland would need to be assessed. Also,

point and nonpoint sources of bacteria would need to

be separated.
Part 614

National Water Quality Handbook

Chapter 3 Objectives

(450-VI-NWQH, September 2003) 3–3

Figure 3–1 Water quality monitoring objective tree

614.0303 Objective

attributes

The final step in developing objective statements is to

determine attributes for the objectives. Attributes

define the level of achievement for each objective.

Monitoring objectives are typically binary. They are

either achieved or not achieved. For example, an

assessment of the circulation patterns in Long Lake is

either achieved or not. Another monitoring objective

attribute could relate to time, such as:

To determine circulation patterns in Long

Lake in 1 year.

One of the problems associated with binary attributes

is that they have no intermediate steps upon which to

evaluate progress.

Management or programmatic objectives may use

other scaler quantities as attributes to measure their

achievement. For instance, for the Long Lake example,

an appropriate attribute for a management objective

could be:

...the percent of farms in the watershed

receiving fecal coliform controls

Another attribute could be:

...the percentage change in bacteria loading

to Long Lake.

The attribute should be so stated that it helps answer

the question, "...how do you know when you have

monitored enough?"

In conclusion, monitoring objectives are often redefined after going through these three steps as well as

after gaining experience in the monitoring project.

Such changes are appropriate, expected, and should

be encouraged.

To assess circulation

in Long Lake

To determine the effect 

of the wastewater 

treatment plant on

tributary bacteria

To assess the role of the

wetland in bacteria 

treatment

To determine the effect of

implementing BMPs on fecal 

coliform levels in Long Lake

To determine the effect of

manure management of

bacteria in field runoff

To determine the effect of 

the BMPs on tributary 

bacteria

Higher

order

Lower

order

Overall:

Objectives
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National Water Quality Handbook

Chapter 3 Objectives

3–4 (450-VI-NWQH, September 2003)

614.0304 References

Coffee, S.W., and M.D. Smolen. 1990. The nonpoint

source manager’s guide to water quality monitoring. NC State Univ. Water Quality Group, Raleigh,

NC.

Dickerson, S.L., and J.E. Robershaw. 1975. Planning

and design: the systems approach. Chapter 2:

Defining the problem. Lexington Books, Lexington, MA.

Keeney, R.L. 1988. Value-focused thinking and the

study of values. In Decision making: descriptive,

normative, and prescriptive interactions, chapter

21. D.E. Bell, J. Raiffa, and A. Tversky (Eds.)

Cambridge Univ. Press, Cambridge, NY, pp. 465-

494.

Keeney, R.L., and H. Raiffa. 1976. Decisions with

multiple objectives: preferences and value

tradeoffs. Chapter 2: The structuring of objectives. John Wiley & Sons, New York, NY.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

National Water Quality Handbook

Chapter 4 Statistical Designs
(450-VI-NWQH, September 2003) 4–i

Chapter 4 Statistical Designs

Contents: 614.0400 Introduction 4–1

614.0401 Reconnaissance 4–1

(a) Advantages .................................................................................................... 4–2

(b) Disadvantages ............................................................................................... 4–2

614.0402 Plot 4–3

(a) Advantages .................................................................................................... 4–3

(b) Disadvantages ............................................................................................... 4–3

(c) Statistical approach ...................................................................................... 4–3

614.0403 Single watershed 4–5

(a) Advantages .................................................................................................... 4–5

(b) Disadvantages ............................................................................................... 4–5

(c) Statistical approach ...................................................................................... 4–6

614.0404 Above-and-below watersheds 4–6

(a) Advantages .................................................................................................... 4–7

(b) Disadvantages ............................................................................................... 4–7

(c) Statistical approach ...................................................................................... 4–7

614.0405 Two watersheds 4–7

(a) Advantages .................................................................................................... 4–7

(b) Disadvantages ............................................................................................... 4–7

(c) Statistical approach ...................................................................................... 4–7

614.0406 Paired watersheds 4–8

(a) Advantages .................................................................................................... 4–9

(b) Disadvantages ............................................................................................... 4–9

(c) Statistical approach ...................................................................................... 4–9

614.0407 Multiple watersheds 4–10

(a) Advantages .................................................................................................. 4–10

(b) Disadvantages ............................................................................................. 4–10

(c) Statistical approach .................................................................................... 4–10
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614.0408 Trend stations 4–11

(a) Advantages .................................................................................................. 4–11

(b) Disadvantages ............................................................................................. 4–11

(c) Statistical approach .................................................................................... 4–11

614.0409 References 4–12

Tables Table 4–1 Causal factors for alternative monitoring designs 4–5

Figures Figure 4–1 Layout example of a plot study 4–4

Figure 4–2 Single watershed design 4–5

Figure 4–3 Above-and-below watershed design 4–6

Figure 4–4 Paired watershed design 4–8

Example Example 4–1 Sampling locations determined by reconnaissance 4–1

monitoring
(450–VI–NWQH, September 2003) 4–1

Chapter 4 Statistical Designs

614.0400 Introduction

Several experimental designs can be used to evaluate

the effect of a conservation practice or a number of

practices on water quality. The design selected depends primarily on the study objective. The study

design must be determined before the project begins

because the design of the project dictates most other

aspects of the project including the study scale, the

number of sampling locations, the sampling frequency,

and the station type.

The study designs considered in this chapter include

the reconnaissance, plot, single watershed, above-andbelow, two watersheds, paired watershed, multiple

watershed, and trend station. A more complete description of the statistical aspects of study designs is

given in part 615 of this handbook.

614.0401 Reconnaissance

Reconnaissance or synoptic designs have been used to

determine the magnitude and extent of the water

quality problem or as a preliminary survey where no

data exist. The term synoptic has been used to imply

either obtaining a general view of water quality or

obtaining samples at approximately the same time.

Reconnaissance surveys differ greatly among the type

of water body, whether stream, lake, or ground water.

A properly stated objective also is critical for a reconnaissance survey. This type of monitoring is used to

target critical areas as well.

Reconnaissance surveys are often grab sampling

programs. For stream systems, one approach for

determining sources of pollution was based on the

number of contributing tributaries (Sanders, et al.

1983). In a downstream fashion, the number assigned

to a stream segment is the sum of the numbers assigned to the upstream segments. The total number of

segments at the most downstream station is used to

select sampling locations. That number could be

divided by two, four, and so forth, to obtain a desired

number of sampling stations for the preliminary survey. The number obtained would describe which

segment to sample. Example 4–1 illustrates this.

1

1

1

8

1

1

1

1

1 2 2

4 2

6

Example 4–1 Sampling locations based on contributing

tributaries

Determine the sampling

locations for reconnaissance

monitoring for the numbered

stream segments. Assume two

stations will be used.

8

2 = 4

Sample segments 8 and 4
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Other approaches might include designs based upon a

percentage of the basin sampled, at known sources of

pollution, and at shifts in land use or geology. One

approach recommended by the World Health Organization (WHO) based the number of water quality

stations on a percentage of the stream gaging stations,

which in turn are based on a minimum density for

different climate zones (WHO 1978). They also recommended "basic stations" to classify water quality and

"auxiliary" stations to understand the assimilative

capacity of streams. Basic stations were generally

located at the mouth and major tributaries, at political

boundaries, at water intakes, below outfalls, and

below urban areas. In addition, when biological monitoring is being conducted, different stream habitats

(riffle, pool) should be considered when selecting

sampling stations.

Reconnaissance biological monitoring approaches,

such as the Rapid Bioassessment Protocol I, must

consider the major factors influencing aquatic organisms (Plafkin, et al. 1989). These factors include pollution sources, bottom types, stream habitats, flow

characteristics, and other physical characteristics,

such as shade (Klemm, et al. 1990). A biological reconnaissance is also important in determining ultimate

sample sizes and taxa of importance. Reference stations are also recommended for reconnaissance biological monitoring.

The goal for stream reconnaissance surveys is often to

locate the areas not meeting their intended uses and

those that are the most polluted. Other design considerations in stream reconnaissance surveys are the

frequency of sampling (chapter 9 and the number of

locations needed per unit area.

Lake synoptic surveys typically involve collecting a

large number of samples over a short time. Locations

could be determined on an areal basis by overlaying a

grid on the lake and sampling randomly located grid

intersections. Other approaches include sampling

bays or sampling longitudinally along lake gradients.

Design of ground water reconnaissance surveys depends on whether there is a local concern or more

regional concern in knowledge about ground water

quality. In local monitoring, monitoring wells are

located above and below the potential pollution

source. At a minimum the survey should have three

wells located in a triangular array about the area of

interest. This array allows the preliminary determination of flow direction. Additional wells could be added

to further determine the extent of the contaminant

plume. In regional reconnaissance surveys, wells could

be located based on a grid bases as for lakes, or existing wells could be surveyed.

(a) Advantages

Reconnaissance surveys are less expensive than fixedstation monitoring.

(b) Disadvantages

Because of the frequent lack of statistical designs,

reconnaissance surveys may miss important information. For example, stream grab sampling based on

equal time intervals (e.g., weekly) often results in

oversampling baseflow conditions and undersampling

stormflow periods. As a result a smaller variability will

be observed than actually exists. Also reconnaissance

surveys have the potential to include judgment bias in

the selection of sampling locations. Sampling just

below outfalls, at tributaries, and at easily accessible

locations, such as bridges, may give unrealistic representations of general water quality conditions.
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614.0402 Plot

Plots have been used for conducting agricultural

experiments in the United States since before 1900

(LeClerg, et al. 1962). They are generally small areas

(fractions of an acre) that are replicated on the landscape or in the water. Plot size is a difficult decision.

Generally, smaller plots that have many replicates are

preferred to larger plots with fewer replicates

(LeClerg, et al. 1962). For agronomy studies, three to

six replicate plots have been recommended. A 0.01

acre plot might be 6 feet wide by 72.6 feet long (USDA

1979). On land, runoff plots might be used for studies

of erosion, the surface transport of chemicals, or soil

water nutrient status. In water, limnocorrals have been

used in lakes to evaluate nutrient and acid additions.

Plots are generally too small for ground water studies.

The influence of the plot treatment on ground water

below the plot may be insignificant in relation to other

inputs to the ground water. However, field plots have

been used to study water in the vadose zone.

For a plot design, all plots are treated alike except for

the factor(s) under study. Plots are typically located

across the slope in homogeneous areas, although such

placement of plots can introduce a factor of bias

(LeClerg, et al. 1962). Differences of an area can be

accounted for by blocking. An example of blocking in

a plot study is shown in figure 4–1. This example

shows three replicates of four treatments. One treatment would be a control, the other three could be

different rates of sludge applications, for example.

Individual treatments would be randomly assigned to

the plots. Blocking could be used to determine if there

was an upslope-downslope effect.

(a) Advantages

The greatest advantage to a plot study is that the

treatments are replicated; most watershed studies

have no true replicates. Also, plots generally allow

control of several variables, such as soil type, including the treatment (Striffler 1965). Plots are generally

small enough that precipitation should be uniform

over the area. A major advantage of the plot design is

that it has a control. A control is a plot that is monitored like all others, but does not receive the treatment.

(b) Disadvantages

The results from plot studies are not transferable to

other watersheds, especially larger watersheds

(Striffler 1965). Plots also may be too small a unit to

adequately represent the hydro-ecosystem. Because of

their small size, plots do not receive "real world"

management. They must be separated from each other

by some method to prevent cross-contamination of the

treatment from one plot to another.

(c) Statistical approach

The primary statistical approach is the analysis of

variance of a randomized complete block design. The

area where the plots are to be located is divided into

blocks, with the number of blocks equal to the number

of replicates chosen. Each block serves as a replication. Blocks are assumed to be homogeneous areas.

For the example in figure 4–1, three blocks are shown

at difference elevations. Each block contains all treatments. The treatments are assigned to plots within the

blocks randomly. This design allows for the removal of

the effect of the block that might be caused by differences in the field. Other more complicated designs are

available including the Latin square and split plot

designs, or a factorial arrangement of treatments

(Snedecor & Cochran 1980). These designs are described in part 615 of this handbook.
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Figure 4–1 Layout example of a plot study with blocking

Elevation

800

798

796

794

Runoff plot

Runoff

collection

Block

1

Block

2

Block

3

Control T-2 T-1 T-3

T-1

T-3

Control

T-2

T-2

Control

T-1

T-3
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614.0403 Single watershed/

before-after

A single watershed has sometimes been used to evaluate the water quality effectiveness of a conservation

practice (fig. 4–2). Water quality monitoring is conducted both before and after the practice is applied.

The before period has sometimes been referred to as

baseline data. Generally, this technique is not recommended and should be avoided (see 614.0403(b)).

However, a second manner in which a single watershed could be used was described by Striffler (1965).

For this technique a water quality variable could be

related to a climate variable(s), such as precipitation.

The difference because of the conservation practice

could be evaluated as a change in the relationship

between the water quality characteristic and the

climate variable. The interpretation of results would

be somewhat constrained. For example, a result might

be: "For an equal amount of monthly precipitation, the

concentration declined." More specific results are

generally needed, such as the percent reduction in a

water quality variable resulting from the practice.

(a) Advantages

The primary advantage of the single watershed design,

with monitoring before and after a practice is implemented, is that it is the simplest of all designs. Only

one monitoring station needs to be monitored. This

design is applicable for most watersheds (Striffler

1965).

(b) Disadvantages

This design should not be used because the effect by

the practice cannot be separated from other confounding effects. As indicated in table 4–1 for the single

watershed design, the effect because of the treatment

(e.g., BMP) cannot be separated from year-to-year

climate differences. If a dry year occurred when the

practice was implemented, following a wet year when

the watershed was in the pre-practice stage, stream

concentration reduction would generally occur because of the climate differences. Also, an interaction

would most likely occur between climate and the

practice that could not be assessed by the study. For

example, during a drought a field terrace might be

expected to reduce sediment loading to a stream.

However, during a wet year the terrace could be

overtopped, resulting in increased suspended solids

loading.

Using the alternative relationship approach described

by Striffler (1965) on a single watershed is more complex, requires a longer calibration period, and is less

precise than a paired watershed design. The single

watershed design also has the disadvantage of not

being able to transfer results to other areas.

Table 4–1 Causal factors for alternative monitoring

designs

Design Cause

Single watershed/ before-after BMP or climate

Above-and-below watershed BMP or watershed

Two watersheds BMP or watershed

Paired watershed BMP

Figure 4–2 Single watershed design

Monitoring

station
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(c) Statistical approach

The difference in water quality caused by the practice

generally is expressed as the difference between the

means for the two periods. A t-test is most often used

for this type of comparison (Snedecor and Cochran

1980). An appropriate null hypothesis (Ho:) might be

that the mean concentrations are equal between the

two periods, for example:

Ho: mean tss (period 1) = mean tss (period 2)

As described further in part 615 of this handbook,

rejection of the null hypothesis is desirable. Errors can

be made in accepting the null hypothesis.

A paired t-test is not appropriate for this design because the samples collected are not paired in any

meaningful way. For example, the water quality associated with months across years cannot be paired

because of random components in water quality.

To perform a parametric t-test, the samples would

need to be random, independent, normally distributed,

and have equal variances. A nonparametric comparison of means could be used where data are not normally distributed.

The statistical approach for using the relationship

between water quality and a climate variable would be

similar to that described for the paired watershed

below. The differences between the slopes and intercepts of the two regression relationships (one prepractice, one post- practice) would be analyzed using

analysis of covariance. Multivariate regressions that

include flow or climate variables might improve these

relationships.

Examples of the statistical approach to apply to a

single watershed design are given in part 615 of this

handbook.

614.0404 Above-and-below

watersheds

The above-and-below design is applied after the treatment is in place. This approach is sometimes viewed

as a single watershed with monitoring above and

below a practice (fig. 4–3), or in the case of ground

water monitoring, upgradient and downgradient from

the activity of interest. In actuality, two watersheds

are being monitored, one nested within the other. In

some cases the above station is erroneously thought of

as "background water quality," and the below station is

the one believed to be influenced by the practice.

This design is probably the most commonly used

strategy in-ground water monitoring. Placement of the

wells is important because ground water sites are

three-dimensional. Gradients may occur in both vertical as well as horizontal directions.

If the above-and-below approach is applied both

before and after the practice is installed, this approach

can be analyzed as a paired watershed design as

described below.

Figure 4–3 Above-and-below watershed design

Above

station

Practice

Below

station
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Chapter 4 Statistical Designs

(450-VI-NWQH, September 2003) 4–7

(a) Advantages

The above-and-below approach is not as susceptible to

year-to-year climatic differences as is the single watershed approach using before and after sampling. Also, it

may be relatively easy to locate a watershed where a

practice could be implemented between the above and

below stations on a stream. This technique may be

useful for isolating critical areas. The above-and-below

design is well suited to biological as well as chemical/

physical monitoring.

(b) Disadvantages

Water quality measurements from nested watershed

may not be independent. The water quality downstream is most likely a function of the upstream water

quality. For example, a high concentration upstream

would most likely result in a large concentration

downstream.

A second major disadvantage of this design is that the

differences between the above and below stations

might be caused by inherent watershed differences

(e.g., geology) or to some interaction between the

practice and the watershed, and not only because of

the practice itself (table 4–1). These various causal

factors cannot be separated using this design; however, proper site selection may reduce this effect.

(c) Statistical approach

The above-and-below design is analyzed as a t-test of

the differences between paired observations at the

above and below stations (see part 615). An appropriate null hypothesis might be:

Ho: difference = 0

Parametric and nonparametric (distribution free) t-test

approaches are available. A nonparametric analysis

uses the rank of the data rather than the data itself

(part 615).

Another approach would be to compare regressions

between concentration and a climate variable, such as

flow, for the above and below stations (Ponce 1980).

614.0405 Two watersheds

Two watersheds, one with the practice and one without, have been incorrectly used to evaluate the effects

of a practice on water quality. This design should

always be avoided. The two watershed design is not

the same as the paired watershed design. There is no

calibration period for the two watershed design when

the two watersheds are in the identical treatment, but

there is for the paired watershed approach.

(a) Advantages

Two watersheds, each in a different land use, are

relatively easy to locate.

(b) Disadvantages

The differences in water quality between the two

watersheds may be caused by the practice, inherent

watersheds differences, or an interaction between

these two factors, and there is no way to distinguish

among these causal factors (table 4–1).

(c) Statistical approach

Although a statistical examination of the water quality

associated with two watersheds may not be appropriate, the water quality could be compared using the

same approach as that for the nested watersheds. That

is, a paired t-test or nonparametric t-test of treatment

means could be used. In some cases regressions between water quality and a climate variable could be

compared.
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614.0406 Paired watersheds

Paired watersheds have been used for over 40 years to

evaluate the effects of silvicultural practices on watershed quantity and quality (Wilm 1949). The basic

approach requires a minimum of two watersheds and

two periods of study. The two watersheds are called

control and treatment; the two periods of study are

referred to as calibration and treatment (fig. 4–4). The

control watershed serves as a check over year-to-year

or seasonal climate variations and receives no changes

in management practices during the study.

During the calibration period, the two watersheds are

treated identically and paired water quality data are

collected. Such paired data could be annual means or

totals, or for shortened studies, the observations could

be seasonal, monthly, weekly, or event-based.

During the treatment period, one randomly selected

watershed is treated with a practice while the control

watershed remains in the original management. The

reverse of this schedule is possible for certain practices. Both watersheds might already be treated with a

conservation practice during the calibration period.

During the treatment period, one of the watersheds

could be treated with a traditional practice.

For ground water monitoring, an above-and-below

approach to the paired watershed design is recommended. During the calibration period, monitoring

would take place upgradient and downgradient for

both the control and treatment portions of the ground

water formation being studied. During the treatment

period, one of the areas bounded by wells would

receive a practice, while the other control area would

remain as before.

Guidelines for paired watershed studies include:

• Steady-state—The control watershed should be

at or near a steady-state condition during the life

of the study (Reinhart 1967). Steady-state is used

here to mean that there are no gradual changes

that would result in a trend in water quality. For

example, a watershed that had a gradual shift in

crop types would not make a good control.

• Size—The watersheds should be small enough to

obtain a uniform treatment over the entire area

(Reinhart 1967). The size will vary depending on

climatic region. In humid areas the watersheds

generally would be less than 5 square miles in

area. In arid climates, they could be larger.

• Range—The calibration period should encompass the full range of observations expected

(Reinhart 1967, Wilm 1949). Normally, this refers

to wet and drought years. This allows reasonable

comparison of treatment data to calibration data.

• Calibration length—The calibration period

should be long enough to develop significant

regression relationships between the two watersheds so that data for the treatment watershed

can be predicted knowing data from the control

watershed within certain error limits (Striffler

1965). Methods for determining the length of

calibration are described in part 615.

Figure 4–4 Paired watershed design

Control Treatment

Calibration Treatment

Period of study

Station A Station B

Station A Station B
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• Response—The designed treatment should be

expected to have a large enough response to

exceed prediction errors. At least a 10 percent

change in the variable of interest is suggested

(Hewlett & Pienaar 1973).

• Watershed similarity—The watersheds should be

similar in size, slope, location, soils, and land

cover (Hewlett 1971, Striffler 1965). They

should also have been in the same land cover for

a number of years before the study (Hewlett

1971). Chemical characteristics of the soils

should be similar. However, no two watersheds

are identical, nor can they be considered representative.

• Monitoring suitability—Each watershed should

have a stable channel, a stable control section for

monitoring, and should not leak around the

gaging station at the watershed outlet (Reinhart

1967).

(a) Advantages

The greatest advantage of the paired watershed approach is that variation not associated with the treatment, such as climate differences over years, are

statistically controlled (Kovner & Evans 1954). Also,

the control watershed eliminates the need to measure

and understand all the mechanisms generating the

response (Hewlett & Pienaar 1973). The water quality

of runoff from the two watersheds need not be identical. Finally, the calibration phase can be done in

reverse with the treatment period preceding the calibration period (Reinhart 1967).

(b) Disadvantages

Several disadvantages to the paired watershed approach also apply to all the study designs.

• The variances in water quality data are not likely

to be equal between time periods because the

treatment on one of the watersheds is often quite

drastic. It is also difficult to satisfy the assumptions of normality and independence of observations. Shortened calibrations may increase the

likelihood of serially correlated data (Reinhart

1967).

• The treatment effect may be gradual and not

constant with time (Reinhart 1967; Hewlett &

Pienaar 1973). Thus overall comparisons may

mask interesting results.

• The paired watershed experiment is costly and

time consuming (Hewlett & Pienaar 1973).

• Long-term changes in the soils or vegetation may

occur in the control watershed. Other catastrophes, such as fires, dust storms, hurricanes, and

insect infestations, could occur, which could

destroy the meaning of results. This disadvantage

applies to all watershed designs.

(c) Statistical approach

The basis of the paired watershed approach is that

there is a quantifiable relationship between paired

water quality data for the two watersheds and that this

relationship will persist until a major change is made

in one of the watersheds (Hewlett 1971). This does not

require that the quality of runoff be the same for the

two watersheds; but rather that the relationship between the water quality of the two sites, except for the

influence of the treatment (practice), remains the

same over time. In fact, most often the water quality is

different between the two watersheds. This inherent

difference between all watersheds further substantiates the need to use the paired watershed approach.

The primary statistical approach is to develop significant regression relationships between the control and

treatment watersheds during both the calibration and

treatment periods (see part 615). These two regression

relationships are then compared for identical slopes

and intercepts using analysis of covariance (Reinhart

1967). During the calibration period the significance of

the regression is tested using analysis of variance for

regression (Snedecor & Cochran 1980). Procedures for

determining the length of the calibration period have

been described by Wilm (1949), Kovner and Evans

(1954), and Reinhart (1967) and are presented in part

615 of this handbook. An alternative analysis approach

has been presented by Green (1979), Bernstein and

Zalinski (1983), and Carpenter, et al. (1989).
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614.0407 Multiple watersheds

The multiple watershed approach involves more than

two watersheds (Clausen and Brooks 1983, Striffler

1965, Wicht 1967). Watersheds with the treatments

already in place are selected from across the region of

interest. The region could be as large as a state or as

small as an individual field. Sampling of the runoff is

conducted from these watersheds over a period of

time.

As an example, multiple watersheds could be used as a

method to assess the water quality effect of storing

manure during the winter and not daily spreading as a

conservation practice. About 15 watersheds in each

treatment could be selected. That is, 15 fields or watersheds where daily spreading was occurring during the

winter, and 15 fields where no spreading occurred.

During runoff periods, these fields could be sampled

for the concentrations of appropriate pollutants, such

as nitrogen and phosphorus.

Another example could be a test of irrigation water

management. Runoff from fields in flood irrigation

could be compared to runoff from sprinkler irrigated

fields.

(a) Advantages

The greatest advantage of the multiple watershed

approach is that the results are transferable to the

region included in the monitoring. A second major

advantage is that the true variability among watersheds is included in the variance for each treatment.

(b) Disadvantages

The multiple watershed approach is difficult to conduct using intermittent streams or field runoff because

sampling must be timed with stormflow periods. Also,

mass calculations would only be point estimates, and

annual mass calculations would be expensive to obtain

using a large number of watersheds. However, the

probability approach has been used to determine

annual mass estimates, which could reduce the number of samples that need to be collected (Richards

1989).

(c) Statistical approach

The basic statistical approach is the comparison of the

means of two populations using the t-test. The testing

would be for unpaired samples that may be of unequal

sizes.
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614.0408 Trend stations

Trend stations are single watersheds monitored over

time. A trend is a persistent change in the water quality variable(s) of interest over time. In many cases the

most appropriate design may be the use of long-term

trend stations. Trend stations are single, independent

watersheds where a group of conservation practices

might be implemented gradually over time or where

the response to a practice might take a long time.

It is important for trend analysis that there not be gaps

in the data set, that methods of water quality analysis

not change during the study, that hydrologic control at

the monitoring station is stable, and that a causal link

can be made between water quality and the watershed

treatments. This implies that collection of hydrologic

data and land use activities are crucial to trend analysis. In addition, for some trend analysis techniques,

water quality data must be collected or aggregated to

fixed time intervals (Valiela & Whitfield 1989; Montgomery & Reckhow 1984; Hirsch, et al. 1982).

The use of a control watershed for trend detection

cannot be emphasized enough. The control should

have a stable land use and no changes in practices

during the life of the trend investigation.

Although models are sometimes used to simulate longterm trends, the purpose of this handbook is to discuss

the applicability of monitoring and not modeling.

(a) Advantages

A long-term trend station is relatively easy to establish

for watersheds drained by permanent streams. For

complex watersheds, conservation practices are

typically installed at different times over several years.

This prevents use of short-term designs. For example,

it may take many years for water quality to respond to

practices because of the residual storage of nutrients.

(b) Disadvantages

A true commitment to long-term (>10 years) monitoring is difficult to achieve because of changing priorities and changing personnel within funding and monitoring agencies. A significant effort must be made for

land use data tracking. Over the long term, the potential is greater for unwanted disturbances, such as a

new road or urban development, to affect water

quality.

(c) Statistical approach

A large number of parametric and nonparametric

techniques are available for detecting trends in water

quality data. Several techniques should be used before

reaching a conclusion (WHO 1978). These techniques

are described below and discussed in detail with

examples in part 615 of this handbook.

Time plot—A graph of the water quality versus time

is useful in detecting obvious trends (WHO 1978).

Least square fit regression—A linear or nonlinear

regression could be fit through the data, which would

allow quantification of the slope or trend rate (WHO

1978).

Comparison of annual means—A t-test could be

used to compare averages for shorter, equal time

periods within the trend total period (WHO 1978). For

example, annual means could be compared. An analysis of variance, followed by a multiple comparison

test, would be a more appropriate method because the

overall variance would be pooled (Snedecor and

Cochran 1980).

Cumulative distribution curves—Two cumulative

distribution curves (which portray the percent cumulative distribution as a function of concentration) for

two different time periods could be compared for

shifts to determine trends (WHO 1978).

Q-Q plot—A Q-Q plot is a comparison of the quartiles

of one data set plotted against those of another data

set for the variable of concern. By comparing the data

from different time periods, a shift in the data as

compared to a y=x line can be determined (WHO

1978).
Part 614

National Water Quality Handbook

Chapter 4 Statistical Designs

4–12 (450-VI-NWQH, September 2003)

Double mass analysis—Typically used for precipitation records, double mass analysis is a comparison of

the accumulated data from one station plotted against

the accumulated averages of data from several stations. A break in the slope would indicate a change in

that one station as compared to the others, which

could be interpreted as a trend (Dunne & Leopold

1978).

Paired regressions—A "before" period can be compared to an “after” period by the comparison of the

regression equations between data from a control

trend station and a treatment trend station. This analysis is identical to the paired watershed analysis described above.

Time series analysis—Because water quality data

collected at the same station may be autocorrelated,

time series analysis could be used to detect trends

(McLeod, et al. 1983). However, the forecasting features of time series analysis are not likely to be relevant (Vandaele 1983).

Seasonal Kendall test—This nonparametric approach is especially useful where seasonality exists in

the data set. A seasonal Kendall slope estimator is

used to determine the magnitude of the trend (Hirsch,

et al. 1982).

Generally, when applying several approaches to trend

detection, the results rarely vary in direction, although

the statistical significance of these techniques will

vary. All of the methods, except paired regressions,

only provide information on whether a trend exists

and not why it exists. Only the paired regression

approach allows linking the trend to causes other than

hydrologic because a control is used. An alternative

approach would be to adjust the trend data set for

hydrologic influences. This is described in part 615 of

this handbook.

614.0409 References

Bernstein, B.B., and J. Zalinski. 1983. An optimum

sampling design and power tests for environmental biologists. J. Environ. Mgmt. 16(1):35-43.

Carpenter, S.R., T.M. Frost, D. Heisey, and T.K. Kratz.

1989. Randomized intervention analysis and the

interpretation of whole-ecosystem experiments.

Ecology 70(4):1142-1152.

Clausen, J.C., and K.N. Brooks. 1983. Quality of runoff

from Minnesota peatlands: II. A method for

assessing mining impacts. Water Resour. Bull.

19(5):769-772.

Dunne, T., and L.B. Leopold. 1978. Water in environmental planning. W.H. Freeman and Co., San

Francisco, CA.

Green, R.H. 1979. Sampling design and statistical

methods for environmental biologists. John

Wiley and Sons, New York, NY.

Hewlett, J.D. 1971. Comments of the catchment experiment to determine vegetal effects on water

yield. Water Resour. Bull. 7(2):376-381.

Hewlett, J.D., and L. Pienaar. 1973. Design and analysis

of the catchment experiment. In Proc. Symp.,

Use of small watersheds, E.H. White (ed.), Univ.

KY.

Hirsch, R.M., J.R. Slack, and R.A. Smith. 1982. Techniques of trend analysis for monthly water

quality data. Water Resour. Res. 18(1):107-121.

Klemm, D.J., P.A. Lewis, F. Faulk, and J. Lazorcnak.

1990. Macroinvertebrate field and laboratory

methods for evaluating the biological integrity of

surface waters. U.S. Environmental Protection

Agency. Office of Research and Development,

Washington, DC. EPA/600/4-90/030.

Kovner, J.L., and T.C. Evans. 1954. A method for determining the minimum duration of watershed

experiments. Trans. Amer. Geophys. Union.

35(4):608-612.
Part 614

National Water Quality Handbook

Chapter 4 Statistical Designs

(450-VI-NWQH, September 2003) 4–13

LeClerg, E.L., W.H. Leonard, and A.G. Clark. 1962.

Field plot technique. 2nd ed., Burgess Publ. Co.,

Minneapolis, MN.

McLeod, A.I., K.W. Hipel, and F. Comancho. 1983.

Trend assessment of water quality time series.

Water Resour. Bull. 19(4):537-547.

Montgomery, R.H., and K.H. Reckhow. 1984. Techniques for detecting trends in lake water quality.

Water Resour. Bull. 20(1):43052.

Plafkin, J.L., M.T. Barbour, K.D. Porter, S.K. Gross, and

R.M. Hughes. 1989. Rapid bioassessment protocols for use in streams and rivers: benthic

macroinvertebrates and fish. U.S. Environmental

Protection Agency, Office of Water, Washington,

DC. EPA/444/4-89-001.

Ponce, S.L. 1980. Water quality monitoring programs.

USDA Forest Serv., Watershed Sys. Dev. Group.

WSDG Tech. Pap. WSDG-TP-00002, Fort Collins,

CO.

Reinhart, K.G. 1967. Watershed calibration methods.

In Proc. Intern. Symp. on forest hydrology. W.E.

Sopper and H.W. Lull (eds.), Pergamon Press,

Oxford, pp. 715-723.

Richards, R.P. 1989. Determination of sampling frequency for pollutant load estimation using flow

information only. In Proc. Symp., Design of

water quality information systems. R.C. Ward,

J.C. Loftis, and G.B. McBride (Eds.) CO Water

Resour. Res. Inst. Inf. Ser. No. 61, Fort Collins,

CO.

Sanders, T.G., R.C. Ward, J.C. Loftis, T.D. Steele, D.D.

Adrian, and V. Yevjevich. 1983. Design of networks for monitoring water quality. Water

Resour. Pub., Littleton, CO.

Snedecor, G.W., and W.G. Cochran. 1980. Statistical

methods. 7th Ed. IA State Univ. Press, Ames, IA.

Striffler, W.D. 1965. The selection of experimental

watersheds and methods in disturbed forest

areas. Publ. No. 66. I.A.S.H. Symp. of Budapest.

pp. 464-473.

United States Department of Agriculture. 1979. Field

manual for research in agricultural hydrology.

Agric. Handb. 224, Washington, DC.

Valiela, D., and P.H. Whitfield. 1989. Monitoring strategies to determine compliance with water quality

objectives. Water Resour. Bull. 20(1):127-136.

Vandaele, W. 1983. Applied time series and BoxJenkins models. Academic Press, Inc., New York,

NY

Wicht, C.L. 1967. The validity of conclusions from

South African multiple watershed experiments.

In Proc. Int. symp. on forest hydrol. W.E. Sopper

and H.W. Lull (eds.), pp. 749-760.

Wilm, H.G. 1949. How long should experimental watersheds be calibrated? Amer. Geophys. Union

Trans., part II. pp.618-622.

World Health Organization. 1978. Water quality surveys—A guide for the collection and

interpretation of water quality data. IHD-WHO

Working Group on Quality of Water. UNESCO/

WHO, Geneva, Switzerland.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

National Water Quality Handbook

Chapter 5 Scale of Study
(450–VI–NWQH, September 2003) 5–i

Chapter 5 Scale of Study

Contents: 614.0500 Introduction 5–1

614.0501 Point scale 5–1

614.0502 Plot scale 5–2

614.0503 Field scale 5–4

614.0504 Watershed scale 5–5

614.0505 References 5–6

Tables Table 5–1 Objective by study scale matrix 5–1

Table 5–2 Type of water resource by study scale matrix 5–2

Table 5–3 Relative cost and time requirements of various study 5–2

scales

Table 5–4 Number of plots required based on the number 5–3

of treatments

Table 5–5 Practice by study scale matrix 5–3

Examples Example 5–1 Plot scale 5–3

Example 5–2 Field scale 5–4

Example 5–3 Watershed scale 5–6
(450-VI-NWQH, September 2003) 5–1

Chapter 5 Scale of Study

614.0500 Introduction

The fourth step in developing a water quality monitoring study is to determine the size or scale of the area

to monitor. The study scale depends in part on: 1)

study objectives, 2) available resources, 3) study

duration, 4) type of water resource, and 5) the complexity of the project to monitor. These individual

factors are described later in this chapter.

Although considered as a separate step, study scale is

actually coupled with the statistical design. However,

scale is provided as a separate subpart to force consideration of this decision in the overall design of a water

quality monitoring study.

This chapter recognizes four scale categories—point,

plot, field, and watershed—although it is acknowledged that the latter three scale types are in reality all

watersheds.

For lake systems, the terminology is different. Plots

are limnocorrals, fields are bays or regions, and watersheds are lakes. In ecology, scales are referred to as

either microcosm (e.g., point), mesocosm (e.g., plot,

limnocorral), and macrocosm (e.g., field, watershed,

lake) (Odum 1984).

One potential barrier to selecting the appropriate scale

of the project is where the monitoring objectives are

not clearly stated. Contemplating the scale of the

project often results in a clarification of the objectives

in a feedback sense.

614.0501 Point scale

Points are the smallest scale considered for water

quality monitoring and are characterized by obtaining

single observations. The term "point scale" means a

point in space, but not a point in time. Examples of

point-scale monitoring include precipitation gages,

snow samples, soil samples, most vadose zone lysimeters, and many lake samples. Ground water wells and

stream samples are considered watershed-scale

samples and not point-scale samples even though they

may be taken at one location.

Point sampling is appropriate for trend monitoring, for

problem definition or compliance monitoring, for

research and fate and transport monitoring, or for

evaluating certain types of models (table 5–1). Point

samples are used in both vadose zone and lake studies

(table 5–2). Point sampling is considered cheaper than

larger scales, but the frequency of visits and the duration of sampling will vary greatly depending on the

study objectives.

Table 5–1 Objective by study scale matrix

Objective Point Plot Field Watershed

1. Baseline X X

2. Trends X X

3. Fate and transport X X X X

4. Problem definition X X X

5. Critical areas X X

6. Compliance X X X

7. BMP effectiveness X X

8. Program effectiveness X

9. Wasteload allocations X X

10. Model evaluation X X X X

11. Research X X X
Part 614

National Water Quality Handbook

Chapter 5 Scale of Study

5–2 (450-VI-NWQH, September 2003)

614.0502 Plot scale

Plots are mesocosm sampling units (LeClerg, et al.

1962). They are appropriate monitoring units if the

objective is to replicate several treatments as part of a

fate and transport study or if the effectiveness of a

conservation practice or a model is evaluated (table

5–1). When considering the type of water body being

studied, a plot scale is appropriate when investigating

soil solution water or overland flow, but not for

ground water, streamflow or lake studies. This is

because these systems are larger than plot boundaries

(table 5–2). An exception to the use of plots for lakes

and streams would be the use of limnocorrals or

seepage meters and artificial stream channels, which

are actually plots of a mesocosm scale. Limnocorrals

are floating water column enclosures that do not allow

mixing with lake water (Odum 1984). Seepage meters

are barrels placed on the land bottom that allow

sampling of the flux through lake sediment (Lee 1977).

Artificial streams divert some stream water into a

controllable, constructed channel.

Plot studies work well for short duration (<5 years)

studies, but may require a greater investment of personnel time and funds than other study scales. This, of

course, depends upon the complexity of the study

(table 5–3). The number of plots needed for an experimental study is a function of the number of treatments

applied. A single treatment requires twice the number

of plots as the number of replications because an equal

(recommended) number of control plots is needed.

For example, if the number of replicates determined

based on the variability in runoff data were 5 (see

chapter 9), the total number of plots needed would be

10. For two treatments, an additional five plots would

be needed (table 5–4). The plot design is appropriate

for evaluating a large number of individual practices

(table 5–5).

From a water quality perspective, a critical requirement for the design of plots is that the treatment on

each plot is isolated from all the other plots, or

through monitoring, the effects of one plot are

Table 5–2 Type of water resource by study scale matrix

Waterbody Point Plot Field Watershed

Overland flow X X

Vadose zone X X X

Ground water X X

Streamflow X X

Lakes X X X X

Table 5–3 Relative cost and time requirements of

various study scales

Point Plot Field Watershed

Cost Low High Low Moderate

to high

Frequency varies events events- weekly +

 of visits weekly

Duration varies <5 years <5 years >5 years

separated from the other plots by subtraction. For

example, plots should be separated far enough apart

so that a spray treatment on one plot could not drift

onto other plots. Plots also may need to be isolated

from overland flow from upslope areas. If the plot is

designed for soil solution monitoring (e.g., via lysimeters), the plots may need to be configured to allow

measurements of the soil solution of subsurface water

entering the plot from above as well as at the bottom

of the plot.

Several studies have used single replication plots; for

example, one plot in treatment A, one plot in treatment

B, and one control, for a total of three plots. This

design is insufficient to determine the effects of the

treatment. One can determine that the plots are different, but cannot distinguish between the difference as a

result of the treatment or the individual plot.
Part 614

National Water Quality Handbook

Chapter 5 Scale of Study

(450-VI-NWQH, September 2003) 5–3

The University of Rhode Island established 18

plots to monitor the water quality associated

with turfgrass management (Morton, et al. 1988).

Plots were 7 by 50 feet, were sloped at 2 to 3

percent, and had a 5-foot sod alley between

them. Soil solution water was collected from 18

plots using ceramic lysimeter plates. The plots

received six treatments consisting of three rates

of nitrogen application and two irrigation rates

per each nitrogen treatment. Each treatment was

replicated three times. Overland flow collection

occurred on 12 plots using an orifice flow splitter

(10% of flow) to collection barrels.

This plot study determined that overwatering

concurrently with fertilization can result in

significantly higher nitrogen losses than controls.

However, with scheduled irrigation, nitrogen

losses were not different from controls. The

study took 2 years to complete.

Table 5–5 Practice by study scale matrix

Practice Plot Field Watershed

Vegetative/tillage practices

Conservation cropping X X

Conservation tillage X X

Contour farming X

Cover crop X X

Crop residue X X

Crop rotation X

Filter strip X X

Mulching X X

Hayland planting X X

Riparian buffer X X

Stripcropping, contour X X

Structural practices

Grassed waterway X

Streambank protection X

Terrace X

Management practices

Animal waste mgmt X X

Irrigation mgmt X X

Pasture/hayland mgmt X X

Pesticide management X X

Plant nutrient mgmt X X

Woodland mgmt X X

Table 5–4 Number of plots required based on the Example 5–1 Plot scale

number of treatments (assuming

replicates=5)

Treatments Plots

1 10

2 15

3 20
Part 614

National Water Quality Handbook

Chapter 5 Scale of Study

5–4 (450-VI-NWQH, September 2003)

614.0503 Field scale

Monitoring on a field scale implies a larger area than

an individual plot, although the entire plot design

taken together could cover an area larger than a single

field. The area of a field is difficult to state because it

varies greatly in different parts of the United States. A

field in humid (precipitation > evapotranspiration)

areas is an area smaller than that required to produce

a first order stream. In subhumid and arid areas (precipitation < evapotranspiration), a field typically

would be larger, and many fields may occupy the area

required to produce a first order stream.

Identical to the plot scale, a field scale monitoring

project is appropriate if the objective was to investigate the fate and transport of a substance or the effectiveness of an individual conservation practice or a

model (table 5–1). Field scale studies also are appropriate for ground water, vadose zone, and overland

flow studies (table 5–2). The cost of monitoring a field

scale project generally is not as great as either plot

studies or watershed scale projects. Field scale

projects are usually of short duration (<5 years), but

could be longer.

Field scale projects are most suitable for evaluating

individual practices on a field. For example, the practices may include field nutrient management, erosion

control, or conservation cropping (table 5–5). If a field

scale project is selected, it is important that the appropriate design (chapter 4) be matched to this scale.

Monitoring a single field before and after a practice is

installed is not an acceptable design unless the effects

of climate over time are accounted for.

The scale of filter strips and many other constructed

conservation practices, such as wetlands, lies somewhere between plot and field scales. Monitoring is

usually conducted above and below the practice and

typically has not been replicated.

For lake systems, different regions of a lake are synonymous with different fields on the land. Lake regions may be represented by bays, areas near sources,

such as beaches, or gradient zones.

Example 5–2 Field scale

Two fields were used in Vermont to determine

the effect of conversion from conventional

tillage to conservation tillage on pesticides in

runoff (Clausen, et al. 1990). The two fields were

compared using the paired watershed technique

(subpart 614.02). During the calibration period,

the two fields were moldboard plowed. During

the treatment period, one field was conventionally tilled, while the other field was disk harrowed and planted with a conservation tillage

planter. The two fields were 1.6 and 2.1 acres in

area and had slopes ranging from 3 to 7 percent.

Field runoff was continuously monitored with

heated,1.5-foot H-flumes and water level recorders. Flow proportional samples (0.1% of total

flow) were obtained by tubing connected to the

throat of the flume and to a storage carboy.

Using the paired watershed technique, conservation tillage was found to reduce runoff from the

field. Therefore sediment loss and the mass

export of the pesticides atrazine and cyanazine

also were decreased.
Part 614

National Water Quality Handbook

Chapter 5 Scale of Study

(450-VI-NWQH, September 2003) 5–5

614.0504 Watershed scale

A project scale larger than either plots or fields is

needed if the monitoring objectives are to determine

long-term trends, identify critical areas, examine

standard compliance, make wasteload allocations, or

verify watershed scale models (table 5–1). In addition,

where a number of BMP systems are being installed in

a watershed with the intent of improving downstream

water quality, watershed scale monitoring is a necessity.

Watershed scale monitoring also is desired if the water

resource system of concern is either ground water, a

stream, or a lake/estuary (table 5–2). Watershed scale

monitoring costs range from moderate to high depending on the size of the system being monitored. Large

streams or lakes are more costly to monitor than

smaller water bodies. Watersheds are studied for

longer durations than are either plots or fields. For

most individual BMPs, watersheds are not an appropriate scale of study. However, exceptions might include

riparian buffers and streambank protection, which

could be evaluated on a watershed basis (table 5–5).

The watershed scale would be more appropriate for

biological and habitat monitoring than smaller scales.

The most difficult decision regarding watershed scale

projects is the selection of watershed size. Several

factors influence the selection of watershed size

including: drainage pattern, stream order, stream

permanence, climate region, the number of manageable landowners, the homogeneity of land uses, and

watershed geology and geomorphology.

No real relationship exists between a watershed area

and most stream characteristics, including stream

order, stream length, and drainage density (stream

length /watershed area) (Harlin 1984). For example,

the relationship L=1.4A0.6 (where L=stream length and

A=watershed area) has been found to be regional. The

primary reasons for the lack of relationships are the

differences in climate regions and geology across the

U.S. It is not surprising that watershed area and watershed discharge would vary from humid climate regions

to arid or subhumid regions. The ratio of potential

evapotranspiration to precipitation has been used to

distinguish between climate regions, with a ratio of

one separating humid from subhumid areas (Holdridge

1962). If precipitation equals or is less than evapotranspiration, very little runoff would be expected and

a larger basin would be needed to generate a permanent stream. On the other hand, if precipitation exceeds evapotranspiration, runoff would most likely

occur, and a smaller basin would be needed to generate streamflow.

Streams draining small watersheds in humid regions

(precipitation > evapotranspiration) are usually first or

second order, intermittent, and < 500 acres in area.

Moderately sized watersheds are from 500 to 5,000

acres in area, are permanent, and have third or fourth

order streams. Stream order, according to Strahler's

method (Ruhe 1975), is determined by numbering the

smallest streams highest in the watershed as first

order streams. The joining of two first order streams

results in a second order stream, and so on.

Humid watersheds larger than 5,000 acres and less

than 50,000 acres are considered large. Watersheds

larger than 50,000 acres are considered very large and

may be inappropriate for monitoring because of their

likely heterogeneity in land uses.

The size of the watershed selected influences the

response to implementation of conservation practices.

For example, the export of phosphorus from agricultural watersheds generally decrease per unit area as

the watershed size increases (T.-Prairie & Kalff 1986).

This effect was not observed for forested watersheds.

Comparing different agricultural land uses, this decreasing phosphorus export with increasing watershed

area occurred for row crop and pasture watersheds,

but not for mixed agricultural or non-row crop basins.

The authors attributed this difference to a combination

of decreasing sediment delivery ratios, a reduction of

drainage density, and decreasing slope with increasing

watershed area. Because an average of 84 percent of

the total phosphorus exported from agricultural watersheds was found in the particulate rather than dissolved form, the decreasing sediment delivery would

result in decreasing phosphorus delivery. For forested

watersheds, less than 50 percent was in the dissolved

form (T.-Prairie & Kalff 1986). Phosphorus yield from

watersheds less than 5,000 acres was particularly

sensitive to watershed size.
Part 614

National Water Quality Handbook

Chapter 5 Scale of Study

5–6 (450-VI-NWQH, September 2003)

The importance of these findings is twofold. First,

using markedly different watershed sizes for control

and treatment areas could introduce a bias in response. If the practice installed influenced sediment

delivery, a smaller watershed will react differently

from a larger one. Second, because sediment delivery

per unit area is greater in smaller watersheds, there

may be differences in flushing of sediment stored in

channels of different sized watersheds.

A final consideration may be whether the stream is

intermittent or permanent. Intermittent streams appear to exhibit a first flush phenomenon after extended dry periods where concentrations of nutrients

are higher than anticipated based on discharge measurements. Also, the biotic community in an intermittent stream is controlled, in large part, by the periodic

lack of flow. Some biotic community changes may be

influenced more by flow than water quality changes.

This is not to say that intermittent watersheds are

inappropriate for study. Intermittent watersheds are

smaller, and therefore greater control over watershed

land activities can be exercised.

Example 5–3 Watershed scale

614.0505 References

Clausen, J.C., F.I. Potter, III, W.S. Douglas, W.E.

Jokela, and J.W. Williams. 1990. Conservation

tillage use of pesticides for corn: surface water

contamination. Vermont Water Resour. Res.

Cent., Burlington, VT.

Harlin, J.M. 1984. Watershed morphometry and time to

hydrograph peak. J. of Hydrol. 67:141-154.

Holdridge, L.R. 1962. The determination of atmospheric water movements. Ecology. 43(1):1-9.

LeClerg, E.L., W.H. Leonard, and A.G. Clark. 1962.

Field plot techniques. 2nd. Ed. Burgess Pub. Co.

Minneapolis, MN.

Lee, D.R. 1977. A device for measuring seepage flux in

lakes and estuaries. Limnol. Oceanog. 22(1):140-

147.

Morton, T.G., A.J. Gold, and W.M. Sullivan. 1988.

Influence of overwatering and fertilization on

nitrogen losses from home lawns. J. Environ.

Qual. 17(1):124-130.

Odum, E.P. 1984. The mesocosm. BioScience.

34(9):558-562.

Ruhe, R.V. 1975. Geomorphology: geomorphic processes and surficial geology. Houghton Mifflin

Co., Boston, MA.

T.-Prairie, Y., and J. Kalff. 1986. Effect of catchment

size on phosphorus export. Water Resour. Bull.

22(3):465-470.

One of the objectives of the St. Albans Bay watershed RCWP was to determine the effect of implementing BMPs on the water quality of the bay

and its tributaries. Water quality monitoring, both

chemical and biological, was conducted in the

bay and four tributaries. At each stream monitoring location, flow was continuously recorded and

samples were taken at 8-hour intervals and

composited. Bacteria grab samples were taken

weekly.

The watersheds were 3,400, 6,000, 3,800, and

14,400 acres in area. Trend analysis applied to

the bacteria data revealed that bacteria abundance declined significantly in all tributary

streams by 60 to 70 percent. The decline was

attributed to bacterial dieoff during manure

storage and greater incorporation of manure

applied to fields, both of which were BMPs.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

National Water Quality Handbook

Chapter 6 Variable Selection
(450–VI–NWQH, September 2003) 6–i

614.0600 Introduction 6–1

614.0601 Factors affecting variables 6–1

(a) Objectives ...................................................................................................... 6–1

(b) System type ................................................................................................... 6–2

(c) Designated use .............................................................................................. 6–3

(d) Pollutant source ............................................................................................ 6–3

(e) Analysis difficulty ......................................................................................... 6–8

(f) Water quality problem .................................................................................. 6–8

614.0602 Prioritizing variables 6–10

(a) Ranking ........................................................................................................ 6–10

(b) Activity matrices ......................................................................................... 6–10

(c) Correlations ................................................................................................. 6–10

(d) Probability of exceeding standard ............................................................ 6–12

614.0603 References 6–13

Tables Table 6–1 Water quality variable groups by water resource 6–2

system type matrix

Table 6–2 Water quality variable groups by intended water 6–3

resource use

Table 6–3 Water quality variable groups by nonpoint source activity 6–4

Table 6–4 Water quality variable groups by construction, landfill, 6–5

 and mining activities

Table 6–5 Water quality variable groups by silvicultural activity 6–6

Table 6–6 Water quality variable groups by urban activity 6–7

Table 6–7 Relative cost of analysis for water quality variables 6–8

Table 6–8 Water quality variable groups by water quality problem 6–9

Chapter 6 Variable Selection

Contents:
Part 614

National Water Quality Handbook

Chapter 6 Variable Selection

6–ii (450-VI-NWQH, September 2003)

Figure Figure 6–1 Water quality variable selection 6–1

Examples Example 6–1 Variable correlations 6–11

Example 6–2 Probability of exceeding a standard 6–12
(450-VI-NWQH, September 2003) 6–1

Chapter 6 Variable Selection

614.0600 Introduction

The term variable is used in this handbook to denote

water quality characteristics that exhibit variability

(e.g., algae counts, dissolved oxygen, nutrient concentrations). Although the term parameter is often used

interchangeably with the term variable, in this handbook parameter is meant to be quantities that characterize statistical samples (mean, variance).

The selection of water quality variables to include in a

project requires consideration of several factors. The

tendency is to sample for more variables than are

generally needed. The major reason for not sampling

"full suite" is that there are trade-offs in the study

design. Water quality monitoring is expensive, and

resources committed to unnecessary water quality

characteristics may be at the expense of a successful

experimental design. Where funding is limited, fewer

stations, and the number of samples at each station,

can be monitored when more water quality variables

are added to a project. As a final test in considering

which water quality variables to include in a project, a

written justification statement is recommended for

each variable. If the justification is weak, the variable

may be of low priority and might not be essential.

This chapter discusses the various factors that affect

the selection of water quality variables. Also several

methods for prioritizing variables are presented including: variable matrices, variable cross-correlations, and

the probability of exceeding standards.

Water quality variables receive various names and are

classified differently in different references. For this

chapter, the naming conventions that appear in American Public Health Association’s standard methods

(APHA 1989) were used. Two excellent references

describe the meaning of various water quality variables. They are Hem (1970) and McKee and Wolf

(1963). Additional descriptions are in IHD-WHO

(1978), McNeely et al. (1979), and Stednick (1991). The

importance of biological characteristics is described in

Cairns et al. (1982), Plafkin et al. (1989), Terrell and

Perfetti (1989), and Weber (1973).

614.0601 Factors affecting

variables

Considerations that influence the variables to sample

include the study objectives, the type of water resource, the use or classification of the water body, the

type of nonpoint source activity, the difficulty or cost

in analysis of the variable, and the water quality problem. An overall schematic of these considerations is

given in figure 6–1.

(a) Objectives

A properly stated objective assists in defining the

water quality variables to monitor. In fact, selecting

the water quality variables may result in a redefinition

or clarification of the objectives in a feedback manner.

The constraint part of the objective may specifically

mention the water quality variables (chapter 3). For

example, the following objective statement from

chapter 3 clearly indicates that the variable to measure

is fecal coliform levels:

To determine the effect of implementing conservation practices on fecal coliform levels in Long

Lake.

Figure 6–1 Water quality variable selection

Objective

System Type

Lake, Stream, Wetland, Soil & Ground Water

Use

Fish, Recreation, Irrigation, Drinking

Nonpoint Source

Agriculture, Construction, Landfill,

Mining, Silviculture, Urban

Cost/difficulty

Analysis, Handling

Water Quality Problem

Eutrophication, Pathogens, Toxics,

Salinity, Fishery, Standards,

Turbidity, Aesthetics
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Chapter 6 Variable Selection

6–2 (450-VI-NWQH, September 2003)

(b) System type

The type of water resource being studied also influences the variables selected. Table 6–1 indicates that

the appropriate variables of interest differ primarily

between subsurface systems, such as soil water and

ground water, and surface water systems, including

lakes, streams, and wetlands. For example, chemical

nutrients may be important to all systems, but particulate forms of nutrients are meaningful only for lake,

stream, and wetland systems and not for soil water or

ground water systems.

In addition, different variable selections may be made

for intermittent or permanent stream systems (USDA

1976). Generally, more variables can be justified for a

perennial water body than for an intermittent one. The

biota in intermittent streams is limited by the flow

regime, and therefore may not be good water quality

indicators in that situation.

Tables 6–1 through 6–8 provide a list of potential

water quality variables to consider when designing a

monitoring program.

Table 6–1 Water quality variable groups by water resource system type matrix (general guidelines; in some circumstances

variables that are not marked should be considered)

Variable - - - - - - - - - - - - - - - - - - - - - - - - - - - System type - - - - - - - - - - - - - - - - - - - - - - - - - - -

Lake Stream Wetland Soil water Ground water

Physical

Dissolved oxygen X X X

Discharge X X X X X

Embeddedness X

Habitat assessment X

Riffle/pool ratio X

Salinity X X X X X

Secchi disk transparency X

Specific conductance X X X X X

Substrate characteristics X X

Suspended solids X X X

Temperature X X X

Total dissolved solids X X X X X

Turbidity X X X

Chemical

BOD5 XXX

Inorganic nonmetals: Cl, F X X X X

Nutrients - N, P dissolved X X X X X

total or particulate X X X

Metals: As, Ca, Cd, Cr, Co, Cu, Fe, X X X X X

 Hg, K, Pb, Mg, Mn, Na, Ni, Zn

pH X X X X X

Biological

Bacteria X X X X X

Chlorophyll 'a' X X

Indices (SCI, BI, IBI)* X X

Invertebrates X X X

Fish X X

Macrophyton X X X

Periphyton X X

Plankton (algae) X X

Protozoa X X

* SCI = Sequential Comparison Index

BI = Beck's Biotic Index

IBI = Index of Biotic Integrity
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Chapter 6 Variable Selection

(450-VI-NWQH, September 2003) 6–3

(c) Designated use

Variable selection may be modified by the intended or

designated use of a water body (US EPA, 1981b). A

water body being used for recreation, including aesthetic uses, might emphasize variables associated with

sediment, nutrients, toxic and biological characteristics because all these are visual or affect visual characteristics of water bodies. However, water having an

irrigation use might not include biological variables

(table 6–2). Water intended to be used for drinking,

recreation, or fisheries might include analysis of

biological and toxic substances.

(d) Pollutant source

The nonpoint source of the water quality problem also

influences variable selection, as will certain activities

for those sources. The major nonpoint source categories include:

• agriculture

• construction

• landfill

• mining

• silviculture

• urban

Table 6–2 Water quality variable groups by intended water resource use (general guidelines; in some circumstances

variables that are not marked should be considered)

Variable - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Intended use - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Fish Recreation contact Aesthetics Irrigation Drinking

Physical

Dissolved oxygen X X X

Discharge

Salinity X X X

Secchi disk transparency X X X

Specific conductance X X

Suspended solids X X X XX

Temperature X

Total dissolved solids X X X

Turbidity X X X XX

Chemical

BOD5 X X

Inorganic nonmetals: Cl, F X X X

Nutrients - N, P dissolved X X X

 total or particulate X X

Metals: As, Ca, Cd, Cr, Co, X X X X

 Cu, Fe, Hg, K, Pb, Mg, Mn,

Na, Ni, Zn

pH X X X

Biological

Bacteria X X

Chlorophyll 'a' X X X

Indices (SCI, BI, IBI) X X

Invertebrates X

Fish X

Macrophyton X X

Periphyton

Plankton (algae) X X X

Protozoa X
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National Water Quality Handbook

Chapter 6 Variable Selection

6–4 (450-VI-NWQH, September 2003)

Within each of these categories are specific activities

that influence certain water quality variables. Agricultural activities are shown in table 6–3. Almost all

agricultural activities justify monitoring dissolved

oxygen or BOD, flow, suspended solids, nutrients in all

forms, and invertebrates. Most agricultural activities

might also influence turbidity and bacteria. Pesticide

monitoring requires fewer variables to analyze, although the metabolites should also be monitored. In

addition, metals can be added with certain pesticides,

such as copper sulfate or a zinc fungicide.

Pesticides in field runoff are carried in both dissolved

and particulate forms. Generally, the concentration of

the pesticide is greater in the particulate form; however, the annual mass export may be greater in the

dissolved form.

Three forms of nutrients (total, dissolved, and particulate) are appropriate for most agricultural activities.

However, all three forms may not need to be analyzed

since they are highly related. Including the other forms

in the monitoring study would require justification.

Table 6–3 Water quality variable groups by nonpoint source activity (general guidelines; in some circumstances variables

that are not marked should be considered)

Variable - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Activity - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Field runoff* Pesticide Fertilizer Barnyard/feedlot Stream access Pasture Animal waste

Physical

Dissolved oxygen X X X X X X

Discharge X X X X X X X

Salinity X X

Secchi disk transparency X X X X X X

Specific conductance

Suspended solids X X X X X

Temperature

Total dissolved solids X X X X X

Turbidity X X X X X

Chemical

BOD5 X XXX X

Inorganic nonmetals: Cl, F

Nutrients - N, P dissolved X X X X X X

 total or particulate X X X X X

Metals: As, Ca, Cd, Cr, Co,

 Cu, Fe, Hg, K, Pb, Mg, Mn,

Na, Ni, Zn

pH

Biological

Bacteria X X X X X

Chlorophyll 'a' X X X X X X X

Indices (SCI, BI, IBI) X X X X X X X

Invertebrates X X X X X X X

Fish X

Macrophyton X X X X X X X

Periphyton X X X X X X X

Plankton (algae) X X X X X X X

Protozoa X

* Includes runoff from hayland, rangeland, and cropland.
Part 614

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Chapter 6 Variable Selection

(450-VI-NWQH, September 2003) 6–5

An activity by variable matrix for additional nonpoint

source categories is given in table 6–4. Most of the

activities have the potential to directly influence

discharge, sediment and nutrients. Therefore, additional indirect effects may occur to oxygen, transparency, and several biological characteristics. Landfill

leachate may contain a wide range of water quality

constituents; therefore, a large number of physical,

chemical, and biological variables are usually monitored.

The water quality variables selected for mining operations would change with the type of mining. Acid mine

drainage, associated with coal mining, might involve

monitoring several physical variables, as well as

metals and biological characteristics. Mining of taconite, sylvite, rock phosphate, and sand and gravel

might imply other, more specific variables.

Table 6–4 Water quality variable groups by construction, landfill, and mining activities (general guidelines; in some

circumstances variables that are not marked should be considered)

Variable - - - - - - - - - - - - - - - - - - - - - - Activity - - - - - - - - - - - - - - - - - - - -

Construction Landfill Mining

Physical

Dissolved oxygen X X

Discharge X X X

Salinity X

Secchi disk transparency X X

Specific conductance X X

Suspended solids X X X

Temperature X X

Total dissolved solids X X X

Turbidity X X

Chemical

BOD5 X

Inorganic nonmetals: Cl, F X X

Nutrients - N, P dissolved X X

 total or particulate X X

Metals: As, Ca, Cd, Cr, Co, X X

 Cu, Fe, Hg, K, Pb, Mg, Mn,

Na, Ni, Zn

pH X X

Biological

Bacteria X

Chlorophyll 'a' X X X

Indices (SCI, BI, IBI) X X X

Invertebrates X X X

Fish X X X

Macrophyton X X

Periphyton X X

Plankton (algae) X X

Protozoa X
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Chapter 6 Variable Selection

6–6 (450-VI-NWQH, September 2003)

Several activities are associated with silvicultural

operations (table 6–5). Of these activities, road construction, grazing, and site preparation have the greatest potential to influence the most water quality characteristics. Timber harvesting alone only influences

the water quality variables affected by riparian vegetation removal. Transporting the timber out of the

forest causes most of the potential water quality

effects. However, water yield changes associated with

timber harvesting can have additional water quality

impacts.

Urban activities may influence several physical, chemical, and biological variables, as indicated in table 6–6.

Impervious areas and combined sewer overflows

(CSOs) influence the same variables directly and

indirectly because their primary sources of pollutants

are runoff from impervious surfaces.

Table 6–5 Water quality variable groups by silvicultural activity (general guidelines; in some circumstances variables that

are not marked should be considered)

Variable - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Activity - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Harvesting Roads Site preparation Grazing Pesticide

Physical

Dissolved oxygen XXXX

Discharge X X X

Salinity

Secchi disk transparency X X

Specific conductance

Suspended solids X X X

Temperature X

Total dissolved solids X X X

Turbidity X X X

Chemical

BOD5

Inorganic nonmetals: Cl, F

Nutrients - N, P dissolved X X X

 total and particulate X X X

Metals: As, Ca, Cd, Cr, Co,

 Cu, Fe, Hg, K, Pb, Mg, Mn,

Na, Ni, Zn

pH

Biological

Bacteria X

Chlorophyll 'a' XXXX

Indices (SCI, BI, IBI) XXXX

Invertebrates XXXXX

Fish XXXXX

Macrophyton XXXXX

Periphyton XXXXX

Plankton (algae) XXXXX

Protozoa X
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National Water Quality Handbook

Chapter 6 Variable Selection

(450-VI-NWQH, September 2003) 6–7

Table 6–6 Water quality variable groups by urban activity (general guidelines; in some circumstances variables that are not

marked should be considered)

Variable Impervious areas Lawns Combined sewer overflows Pets

Physical

Dissolved oxygen XXXX

Discharge X X X

Salinity

Secchi disk transparency XXXX

Specific conductance X

Suspended solids X X

Temperature

Total dissolved solids

Turbidity X X

Chemical

BOD5 X X

Inorganic nonmetals: Cl, F X X

Nutrients - N, P dissolved XXXX

 total or particulate X X X

Metals: As, Ca, Cd, Cr, Co, X X

 Cu, Fe, Hg, K, Pb, Mg, Mn,

Na, Ni, Zn

pH

Biological

Bacteria X X X

Chlorophyll 'a' XXXX

Indices (SCI, BI, IBI) XXXX

Invertebrates X X X

Fish X X X

Macrophyton X X X

Periphyton XXXX

Plankton (algae) XXXX

Protozoa X X X
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National Water Quality Handbook

Chapter 6 Variable Selection

6–8 (450-VI-NWQH, September 2003)

(e) Analysis difficulty

The difficulty or cost of analysis should be considered

when selecting water quality variables. Table 6–7

presents some relative costs of analysis for specific

water quality variables. These costs are relative to the

cost of analyzing the sample for either pH or conductance. When water quality characteristics are highly

related, but the analysis cost of one is much cheaper

than the other, the less expensive variable could be

selected. For example, analysis of turbidity is less

costly than suspended solids, both of which are less

expensive than total solids. Also, nitrate nitrogen is

cheaper than ammonia nitrogen or total Kjeldahl

nitrogen because digestion of the sample is not required.

The range and level of accuracy are also important.

For example, Inductively Coupled Plasma (ICP) emission spectroscopy will determine elements cheaper,

but not as accurately, as atomic absorption. Sample

holding times also influence parameter selections. For

example, nitrate and ortho-phosphate are recommended by the Environmental Protection Agency

(USEPA 1983) to be analyzed within 48 hours of collection, whereas nitrate+nitrite and total phosphorus

can be held for 28 days before analysis if preserved

(see table 11–1 in chapter 11).

(f) Water quality problem

Finally, the water quality problem itself influences the

variables to sample. The major water quality problems

are summarized in table 6–8 along with the appropriate water quality variables. Eutrophication problems

require monitoring of several physical, chemical, and

biologic characteristics. Excess algae might suggest

sampling of dissolved oxygen and temperature, flow

for mass balance purposes, turbidity or secchi disk

transparency, nutrients, plankton abundance/type, and

chlorophyll 'a' concentrations. Because many of these

variables are related, not all would be needed to detect

changes. Also, an index, such as Carlson's Trophic

State Index (TSI) could be used (Carlson 1977). It

combines some of these variables.

A problem associated with either a standard violation

or a toxic substance might focus on monitoring that

particular standard or toxicant.

Table 6–7 Relative cost of analysis for water quality

variables (based on Beetem et al. 1980)

Variable - - - - - - - - - Cost ($/analysis) - - - - - - - -

dissolved total particulate

Ions

Ca, Mg 4.70 12.00

Na, K, SiO2 3.40 10.00

Cl 5.35

F 5.25

SO4 5.80

Trace metals

As, Hg 5.20 22.70

Cd, Co, Cu, Pb, Ni 6.20 10.00

Cr 10.50 2.90

Fe, Mn 3.40 10.00

Zn 4.20 10.00

Physical

Alkalinity 3.55

pH 1.00

Specific conductance 1.00

Total solids 8.95

Turbidity 1.80

Nutrients

NH3, NO3, NO2 3.40

TKN 8.90

Total P 9.55

PO4 3.40
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National Water Quality Handbook

Chapter 6 Variable Selection

(450-VI-NWQH, September 2003) 6–9

Table 6–8 Water quality variable groups by water quality problem (general guidelines; in some circumstances variables

that are not marked should be considered)

Variable - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Problem - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Aesthetics Bacteria Algae Macrophytes Salinity Sediment Toxics

Physical

Dissolved oxygen X X

Discharge X

Salinity X

Secchi disk transparency X X X

Specific conductance X

Suspended solids X X

Temperature

Total dissolved solids X

Turbidity X X

Chemical

BOD5

Inorganic nonmetals: Cl, F X

Nutrients - N, P dissolved X X X

total or particulate X X X

Metals: As, Ca, Cd, Cr, Co,

Cu, Fe, Hg, K, Pb, Mg, Mn,

Na, Ni, Zn

pH

Biological

Bacteria X

Chlorophyll 'a' X X X

Indices (SCI, BI, IBI) XXXX

Invertebrates X X

Fish X X

Macrophyton X X X

Periphyton X X X

Plankton (algae) X X X

Protozoa X
Part 614

National Water Quality Handbook

Chapter 6 Variable Selection

6–10 (450-VI-NWQH, September 2003)

614.0602 Prioritizing 

variables

Because virtually hundreds of water quality variables

exist and are therefore candidates for monitoring, a

method for prioritizing their selection is important.

The four basic approaches for prioritizing water quality variables are ranking, activity matrices, correlations, and probability of exceeding a standard.

(a) Ranking

Sanders et al. (1983) suggest a hierarchical approach

of:

• Primary—water quantity variables that serve as

a carrier of water quality, e.g., discharge, volume,

head

• Secondary—water quality variables that are the

result of aggregated effects, e.g., temperature,

pH, conduction, dissolved oxygen, turbidity,

anions, cations

• Tertiary—water quality variables that produce

aggregated effects, e.g., radioactivity, suspended

matter

Variables higher in the hierarchy would be selected

over lower-ranked variables. Greater priority should

be placed on primary variables than on secondary

variables when the number of variables to monitor

need to be limited.

Another example of prioritizing suggests two levels of

analysis (USEPA 1981 a, b). Level I is the minimum list

of variables needed to evaluate program effectiveness

associated with a particular water quality problem and

use of the water resource. For example, chlorophyll ‘a’

would be the level I variable for a stream experiencing

excessive algal growth and being used for drinking

water. Level II includes more detailed, multiparameter

variables. For the example above, nitrogen and phosphorus species would be added to the chlorophyll 'a'

sampling.

(b) Activity matrices

The water quality variable matrices given in tables

6–1 through 6–6 serve as a second method in selecting

water quality variables. Ponce (1980) assigned values

of 1, 2, or 3 to primary, secondary, and tertiary sampling priority codes in a forest management activity

matrix with water quality variables. This method

combines the ranking and activity matrices approaches. The activity matrix variable provides an

initial list of variables to consider when planning the

monitoring study.

(c) Correlations

Correlations between variables can be used to reduce

the variable list. A number of water quality variables

are often correlated. Total phosphorus often is highly

related to ortho-phosphorus. In lake systems, total

phosphorus has been reported to be highly related to

secchi disk transparency and chlorophyll 'a' (Reckhow

& Chapra 1983). Other variables that might be expected to exhibit correlations are conductivity and

dissolved solids and suspended solids and turbidity.

Since these variables may be highly related, one variable could be dropped from the monitoring program or

monitored less frequently.

Correlation coefficients are readily computed in most

statistical packages. This topic is further discussed in

part 615 of this handbook. The correlation coefficient

(r) can be determined from:

r

X XY Y

X X YY

i i

i i

= ( ) − ( ) −

( ) − ( ) −

∑

∑ ∑

2 2 [6–1]

where:

 and = the means of the variables X and Y,

respectively

Xi and Yi = individual values of variables X and Y,

respectively

To use correlation coefficients, some monitoring data

would have to be available either from a previous

study or from preliminary monitoring in the watershed

of interest.

X Y
Part 614

National Water Quality Handbook

Chapter 6 Variable Selection

(450-VI-NWQH, September 2003) 6–11

Another consideration for correlated variables is the

proximity of the range in values to the detection limit

for that variable. Values below detection limits, termed

censored values, require adjustments when calculating

means and variances. Variables that do not include

censored values are preferred.

Example 6–1 illustrates variable correlations.

Example 6–1 Variable correlations

Muddy Bay is experiencing impairment caused

by excessive sedimentation and eutrophication.

Both nitrogen and phosphorus are believed to

contribute to the problem. Appropriate variables

include:

• Turbidity

• Total Suspended Solids (TSS)

• Volatile Suspended Solids (VSS)

• Total Phosphorus (TP)

• Ortho-Phosphate (OP)

• Total Kjeldahl Nitrogen (TKN)

• Ammonia Nitrogen (NH3)

• Nitrate Nitrogen (NO3)

Based on cost data, these analyses would cost a

total of $40.45 per site visit (1980 dollars). You

have $25 budgeted to monitor water quality per

sampling period. Which parameters would you

monitor?

Note that based on sampling in Muddy Bay

during 1 year, the following correlation matrix

was developed.

Correlation matrix (r)

Turbidity TSS TKN NO3 TP 

TSS 0.577 1.000 --- --- --- 

VSS 0.764 0.855 --- --- --- 

NH3 --- --- 0.836 0.281 --- 

NO3 --- --- -0.057 1.000 --- 

OP --- --- --- --- 0.915

The correlations between TP and OP, TKN and

NH3, and TSS and VSS are significant and very

high. Adequate monitoring could be achieved by

choosing TSS, total P, and TKN for less than $25

to meet sedimentation and eutrophication objectives. In nitrogen-limited systems, measurement

of NO3 should be included.
Part 614

National Water Quality Handbook

Chapter 6 Variable Selection

6–12 (450-VI-NWQH, September 2003)

Using the St. Albans Bay data, the mean fecal

coliform bacteria count for Jewett Brook in 1989

was 149 organisms/100 mL. The standard deviation was 493 organisms/100 mL. Using a water

quality standard of 200 organisms/100 mL, what

is the probability of exceeding the fecal coliform

standard?

Z = − = 200 149

493

0 10 .

From a standard Z-table (appendix A), the probability would be 0.4602 or 46 percent. This probability may be higher than that for other water

quality variables, and therefore would be given

higher priority.

(d) Probability of exceeding

standard

An alternative method for determining the priority of

variables to monitor would be to select those with the

highest probability of exceeding a particular standard

(Moser & Huibregtse, 1976). To determine this probability requires knowledge of the mean ( X ), standard

deviation (S), and numerical standard value (Xstd) not

to be exceeded. The probability is determined from the

Z-statistic as:

Z X X

S

std = − [6–2]

Using a standard Z-table (appendix A), the probability

would be obtained. Not all variables have adopted

numerical values for standards. For example, nitrogen

and phosphorus generally are not included in lists of

numeric standards. In such cases a eutrophication

value, such as 0.05 mg/L for total phosphorus could be

used. Another alternative would be to set a concentration goal to achieve and substitute that for a standard

value.

Example 6–2 illustrates this approach.

Example 6–2 Probability of exceeding a standard
Part 614

National Water Quality Handbook

Chapter 6 Variable Selection

(450-VI-NWQH, September 2003) 6–13

614.0603 References

American Public Health Association. 1989. Standard

methods for the examination of water and wastewater. 17th Ed. American Public Health Assoc.

Washington, DC.

Beetem, W.A., L.C. Friedman, G.R. Perryman, and C.A.

Wottersan (eds). 1980. 1981 Water quality laboratory services catalog. U.S. Geol. Surv. Open-file

Rep. 80-1279.

Cairns, J., Jr., A.L. Buikema, Jr., D.S. Cherry, E.E.

Herricks, R.A. Matthews, B.R. Niederlehner, J.H.

Rodgers, Jr., and W.H. van der Schalie. 1982.

Biological monitoring in water pollution. Pergamon Press, Elmsford, NY.

Carlson, R.E. 1977. A trophic state index for lakes.

Limnol. Ocean. 22:361- 369.

Hem, J.D. 1970. Study and interpretation of the chemical characteristics of natural water. U.S.. Geol.

Surv. Water-Supply Pap. 1473. US GPO, Washington, DC.

IHD-WHO Working Group on the Quality of Water.

1978. Water quality surveys—a guide for the

collection and interpretation of water quality

data. Stud. and Rep. in Hydrol. No. 23. United

Nations Educational, Scientific, and Cultural

Organization. Paris, France, and World Health

Organization, Geneva, Switzerland.

McKee, J.E., and H.W. Wolf. 1963. Water quality criteria. 2nd Ed. California State Water Quality

Control Board. Publ. No. 3-A. Sacramento, CA.

McNeely, R.N., V.P. Neimanic, and L. Dwyer. 1979.

Water quality sourcebook—a guide to water

quality parameters. Inland Water Directorate,

Water Quality Branch. Ottawa, Canada. Cat. No.

EN 37- 541.

Moser, J.H., and K.R. Huibregtse. 1976. Handbook for

sampling and sample preservation of water and

wastewater. USEPA 600/4-76-049.

Plafkin, J.L., M.T. Barbour, K.D. Portor, S.K. Gross, and

R.M. Hughes. 1989. Rapid bioassessment protocols for use in streams and rivers: benthic

macroinvertebrates and fish. USEPA 444/4-89-

001. Office of Water. Washington, DC.

Ponce, S.L. 1980. Water quality monitoring programs.

WSDG Tech Pap. No. WSDG-TP-00002. Watershed Systems Development Group, USDA Forest

Service. Ft. Collins, CO.

Reckhow, K.N. and S.C. Chapra. 1983. Engineering

approaches for lake management. Vol. 1: Data

analysis and emphirical modeling. Butterworth

Publ. Woburn, MA.

Sanders, T.G., R.C. Ward, J.C. Loftis, T.D. Steele, D.D.

Adrian, and V. Yevjevich. 1983. Design of networks for monitoring water quality. Water

Resourc. Pub. Littleton, CO.

Stednick, J.D. 1991. Wildland water quality sampling and

analysis. Academic Press, Inc., San Diego, CA.

Terrell, C.R., and P.B. Perfetti. 1989. Water quality

indicators guide: surface waters. USDA, Soil

Conserv. Serv., SCS-TP-161. Washington, DC.

United States Department of Agriculture, Soil Conservation Service. 1976. A general guideline for the

assessment of water quality. Tech. Rel. No. 58.

Eng. Div., Washington, DC.

United States Environmental Protection Agency.

1981a. Conceptual framework for assessing

agricultural nonpoint source projects. NC State

Univ., Raleigh, NC.

United States Environmental Protection Agency.

1981b. Guidelines for evaluation of agricultural

nonpoint source water quality projects. NC State

Univ., Raleigh, NC.

United States Environmental Protection Agency. 1983.

Methods for chemical analysis of water and

wastes. US EPA 600/4-79-020. Environ. Monit.

and Support Lab., Cincinnati, OH.

Weber, C.I. (Ed.) 1973. Biological field and laboratory

methods for measuring the quality of surface

waters and effluents. US EPA 670/4-73-001. Off.

Res. and Dev., Cincinnati, OH .
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

National Water Quality Handbook

Chapter 7 Sample Type
(450–VI–NWQH, September 2003) 7–i

Chapter 7 Sample Type

Contents: 614.0700 Introduction 7–1

614.0701 Grab samples 7–2

614.0702 Composite samples 7–2

(a) Time-weighted composite............................................................................ 7–2

(b) Flow-weighted composite............................................................................ 7–2

614.0703 Integrated samples 7–3

614.0704 Continuous samples 7–4

614.0705 References 7–4

Tables Table 7–1 Sample type as a function of monitoring study objective 7–1

Table 7–2 The suitability of various water quality variables 7–4

for continuous monitoring

Figure Figure 7–1 Factors contributing to variability in water quality data 7–1
(450–VI–NWQH, September 2003) 7–1

Chapter 7 Sample Type

614.0700 Introduction

If water quality did not vary in space or in time, there

would be little reason to collect more than one sample

to describe the quality of a particular water body.

However, water quality does vary spatially and temporally. Both random and deterministic components (fig.

7–1) are found in most water quality data. Variations in

water quality data are caused by seasonal differences,

trends, and the randomness associated with rainstorms. For example, suspended solids concentrations

increase during stormflow, especially during the early

part of the storm (Shelly & Kirkpatric 1975). Therefore, because of these temporal and spatial variations,

samples must be taken from the entire population of

water quality data possible.

The four types of water quality samples that can be

collected are grab, composite, integrated, or continuous. The sample type selected is governed by the study

objectives, the variable to sample, and whether concentration or mass is the desired outcome. Composite

samples are appropriate for most monitoring study

objectives, whereas grab sampling is recommended

for a few objectives directed toward reconnaissance

sampling (table 7–1). Continuous samples are appropriate only for research and fate and transport studies.

The variable to sample influences the sample type as

well. For example, bacteria samples must be taken as

grab samples with sterilized bottles and cannot be

stored in the field as a composite sample. The concentrations of other variables change dramatically during

storage and therefore are inappropriate for compositing. These include all dissolved gases, chlorine, pH,

temperature, and sulfide (APHA 1989). Water quality

variables that correlate highly with stream velocity,

especially those related to suspended sediment concentrations, may need to be sampled with depth integrated samplers. Grab samples may be insufficient to

determine mass loading values unless the concentrations are correlated to discharge (Baun 1982).

Figure 7–1 Factors contributing to variability in water quality data

Table 7–1 Sample type as a function of monitoring

study objective

Objective Grab Integrated Continuous

or composite

1. Baseline X X

2. Trend X X

3. Fate & transport X X

4. Problem definition X X

5. Critical areas X X

6. Compliance X X

7. Conservation practice

effectiveness X

8. Program effectiveness X

9. Wasteload allocations X

10. Model evaluation X

11. Research X X

Constant

mean, variation

Changing

mean, variation Trends Seasonality

Random Non-random

Laboratory

errors

Sampling

errors

Water quality

data
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Chapter 7 Sample Type

7–2 (450–VI–NWQH, September 2003)

614.0701 Grab samples

A grab sample is a discrete sample that is taken at a

specific point and time (APHA 1989; Ponce 1980).

Grab samples may not be representative of the water

quality of the body of water being sampled. For example, the water quality may vary with depth or distance from the streambank. Samples at a single location in a lake or a single well are really grab samples.

For lakes and ground water, variable concentrations

may vary with location and depth. For example, nitrate

concentrations have been found to be stratified in

some water table aquifers in the Midwest. Also, since

water quality often varies with time, grab samples may

not represent temporal variations.

Grab samples can be collected manually by hand or

automatically with a sampler.

614.0702 Composite

samples

A series of grab samples, usually collected at different

times and lumped together, are considered composite

samples. However, composite samples typically are

taken only at one point. These samples can be either

time-weighted or flow-weighted. The collection of

composite samples generally is done with the aid of an

automatic sampler, as described in chapter 9, although

manual techniques could be used as well. A distinct

advantage of the composite sample is that a savings in

laboratory and field costs can be realized. Also,

compositing will reduce sample-to-sample variability.

(a) Time-weighted composite

Time-weighting is the most common type of water

quality compositing. For this type of sample, a fixed

volume of sample is collected at prescribed time

intervals in either a large composite bottle or separate

bottles for compositing later. With automatic samplers, the time interval can range from 1 minute to 100

hours, and the volume collected can range from 10 mL

to 990 mL, although larger volumes are possible.

Equation 9–1 in chapter 9 can be used to determine the

number of samples (n) to take to make up a composite, where n is a function of the variability in the data

and the desired precision. For water quality variables

where the length of the composite time is greater than

the prescribed holding times (USEPA 1983), the collection bottles may be pre-acidified for preservation.

(b) Flow-weighted composite

Time-weighted compositing has been criticized as

being inappropriate for mass loading calculations and

inaccurate where the discharge and concentrations

vary (Baun 1982; Shelly & Kirkpatric 1975). Also, the

time interval may miss peak concentrations during

peak discharges. Therefore, flow-weighted

compositing is an alternative to time-compositing.

Where flow-weighted compositing is used, a sample is

taken after a specified volume (l3) of flow has passed

the monitoring station. This type of sampling requires

automatic equipment that monitors stream stage and
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Chapter 7 Sample Type

(450–VI–NWQH, September 2003) 7–3

calculates discharge. A number of automatic samplers

offer this function, or a data logger can be used.

To sample in this manner, the stage-discharge relationship must be known for the monitoring location. Stagedischarge relationships require a great deal of effort to

develop unless a calibrated flow devise, such as a weir

or a flume, is used.

Flow-weighted compositing also can be achieved using

certain types of passive samplers. A passive sampler is

one that collects a water quality sample by action of

the flow of water itself. A number of these types of

devices are described further in chapter 9.

614.0703 Integrated

samples

A specific type of grab sample is a depth-integrated

sample (USGS 1977). Such a sample may account for

velocity or stratification induced changes with depth,

but temporal variations would not be integrated.

Multipoint sampling at a station may be necessary

because of the horizontal and vertical variations in

water quality. The U.S. Geological Survey recommends

that streams should be sampled using a depth integrated sampler whenever practical (USGS 1977) except when the stream is too shallow to obtain that type

of sample.

For variations across the stream, samples can be

collected using either the Equal Width Increment

(EWI) method or the Equal Discharge Increment (EDI)

method. With the EWI method, depth integrated

samples are collected at equally spaced intervals at the

cross section. All subsamples are then composited.

The EDI method requires knowledge of streamflow

discharge by subsection in the cross section. The

section is divided into equal discharge subsections,

which are then sampled.

Depth-integrated samples may also be appropriate for

both lake and ground water systems. In lakes, depth

integration can be achieved by sampling each lake

strata, by obtaining a sample of the entire water column with a hose, or by automatic devices or pulleys

that collect at different depths over time.

Different ground water strata can be sampled with

certain types of bailers or with multilevel wells and

samplers.
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7–4 (450–VI–NWQH, September 2003)

614.0704 Continuous

samples

Continuous sampling is rare in nonpoint source pollution studies and is typically used for research purposes

(table 7–1). Continuous monitoring can be used for

any water quality variable that is measured using

electrometric methods (table 7–2). This would exclude

analysis of metals and organics.

Several problems are encountered when using continuous sampling. Most electrodes are temperature

dependent and have temperature limits beyond which

they cease to function. Electrodes normally cannot be

placed in areas of rapid water velocity, which influences readings by the probe. However, in-stream

stilling wells can be used to reduce this effect.

Several manufacturers produce submersible, multiple

recording probes for such variables as pH, dissolved

oxygen, conductance, and depth. These probes have

been widely used in lake systems.

614.0705 References

American Public Health Administration. 1989. Standard methods for the examination of water and

wastewater. 17th Ed. Amer. Pub. Health Assoc.,

Washington, DC.

Baun, K. 1982. Alternative methods of estimating

pollutant loads in flowing water. Tech. Bull. No.

133. WI Dep. Nat. Res. Madison, WI.

Ponce, S.L. 1980. Water quality monitoring programs.

WSDG Tech. Pap. WSDG-TP-0002. Watershed

Systems Development Group, U.S. Dep. Agric.,

Forest Serv., Fort Collins, CO.

Shelley, P., and G. Kirkpatric. 1975. An assessment of

automatic sewer flow samplers. U.S. Environ.

Prot. Agency 600/2-75-065, pp. 327-330.

United States Environmental Protection Agency. 1983.

Methods for chemical analysis of water and

wastes. USEPA 600/4-79-020, Environmental

Monitoring and Support Lab, Cincinnati, OH.

United States Geological Survey. 1977. National handbook of recommended methods for water-data

acquisition. Chapter 5: Chemical and physical

quality of water and sediment. Off. Water Data

Coord., USGS, Reston, VA.

Table 7–2 The suitability of various water quality

variables for continuous monitoring

(based on APHA 1989)

Suitable Not suitable

Ammonia Metals

Chloride Organic compounds

Conductivity Pesticides

Cyanide

Dissolved oxygen

Fluoride

Inorganic nonmetals

Nitrate

pH

Salinity

Temperature
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

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Chapter 8 Sampling Location
(450–VI–NWQH, September 2003) 8–i

Chapter 8 Sampling Location

Contents: 614.0800 Introduction 8–1

614.0801 Factors affecting locations 8–1

614.0802 Site selection criteria 8–2

614.0803 Within system locations 8–3

(a) Streams .......................................................................................................... 8–3

(b) Lakes .............................................................................................................. 8–5

(c) Ground water ................................................................................................ 8–6

614.0804 Optimizing locations 8–8

614.0805 References 8–10

Figures Figure 8–1 Within stream sampling locations for physical/ 8–3

chemical monitoring

Figure 8–2 Within stream sampling locations for biological 8–4

monitoring

Figure 8–3 Lake sampling locations 8–5

Figure 8–4 Ground water sampling locations 8–7

Examples Example 8–1 Mixing distances 8–4

Example 8–2 Specific conductance of gradient 8–6

Example 8–3 Optimizing sites and visits 8–9
(450–VI–NWQH, September 2003) 8–1

Chapter 8 Sampling Location

614.0800 Introduction

The question of where to sample is critical to a successful monitoring program. The factors that influence

the location of sampling stations are:

• The study objectives and experimental design

• The type of water body (e.g., lake, stream,

ground water)

Sampling locations may be viewed from two perspectives: macroscopic and microscopic. First, the overall

watershed spatial locations must be determined.

Second, the sampling locations within the system must

be found. Because there are trade-offs between the

number of sampling stations and the number of

samples taken, some optimal sampling location strategies are based on travel distances and other such

factors. Finally, when actually siting a station on the

ground, some site selection criteria should be considered.

614.0801 Factors affecting

locations

Definition of the study's objectives and the study

design should aid in defining the general spatial sampling locations. As described in chapter 3, the monitoring study design indicates the basic sample locations.

It is fairly obvious that needs differ in siting locations

for plot studies versus a paired watershed design.

Above-and-below or nested stations are particularly

difficult to site. If these stations are too far apart, there

may be no relationship between them. If they are

located too close together, there may not be a detectable difference because of the treatment, especially in

larger watersheds. Nested watersheds located too high

in the watershed may exhibit poor relationships because the upper location may be intermittent. Aboveand-below stations located lower in the watershed

might be dominated by watershed processes not

associated with the watershed treatment.

The most crucial element of sampling locations is

siting the control station location. The control site

must be stable and free from outside disturbances. For

example, road ditch changes or repair must not be

allowed to divert runoff into a control watershed. In

biological monitoring this is termed the reference

station.

The overall monitoring purpose, as described in the

preface, influences sampling locations. For example,

determining critical areas may require several watershed locations to isolate the major contributing sites.

In contrast, long-term trend analysis or program evaluation may involve only one or two locations. Compliance monitoring would be located very close to the

source. In contrast, fate and transport studies and

wasteload allocations require downstream locations.

The type of waterbody also influences the sampling

locations. To characterize a watershed outlet only

requires one sampling station. To characterize ground

water or the water quality of a lake would require

several more sampling locations. Biological monitoring

in any of these systems would require subsampling of

different habitats or niches in the system.
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Some specific recommendations have been made for

locating sampling stations for biological monitoring

(Klemm, et al. 1990)

• Select sampling locations with similar substrates,

depth, physical characteristics, and velocity. If it

is not possible to locate stations with similar

habitats, artificial substrate samplers may be

necessary.

• Include at least one reference station away from

all possible discharge points.

• Include a station directly below the source of

pollution. If the discharge is not mixed, include

left-bank, midchannel, and right-bank

substrations.

• Establish stations at various distances downstream from the source.

• Sampling locations for macroinvertebrates

should be close to sites used for chemical and

physical monitoring.

• Locations used for sampling should not be atypical, such as at bridges or dams. However, in

urban areas such structures may be typical.

• Sampling nonpoint sources of pollution may

require a number of stations along the water

body impacted.

614.0802 Site selection

criteria

The criteria used to determine sampling locations will

be specific to the individual project, and will obviously

change with the type of system (lake, ground water,

stream) and the scale of system (plot, field, watershed) being monitored. However, the following generalized criteria can serve as a beginning point.

All sites

• Accessible all weather

• Power available

• Cooperative landowner

• Equipment protected from vandals

• Close to problem area

Streams

• Appropriate habitat

• Impermeable streambed

• Stable streambed

• Sufficient stream gradient

• Straight, uniform cross-section and approach

• Not at obstructions

• Not at meander

• Control at all stages

• Confined channel

• No road drainage influence

• Obtain stage-discharge at all stages

• Appropriate land use

Ground water

• Water table divide definable

• Barrier locations (stream, strata) known

• Direction of flow appropriate

• Water levels high or low as needed

• Stratified or mixed concentrations as needed

• Depth to confining layer known

• Away from large volume well drawdown

Lakes

• Stratification depths known

• Longitudinal gradient defined

• Bays and beaches considered

• Water circulation patterns known

Field/Plot

• Homogeneous land use

• Definable watershed

• Homogeneous soil
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Chapter 8 Sampling Location

(450–VI–NWQH, September 2003) 8–3

614.0803 Within system

locations

Once the overall sampling location is determined, a

more specific location is needed to collect a representative sample (Canter 1985; Ponce 1980; Sanders, et al.

1983). These locations vary with system type.

(a) Streams

At a single stream cross section, water quality may

vary vertically and horizontally for several reasons.

Velocity profiles result in varying concentrations at a

cross-section, especially for sediment and sedimentbound concentrations (fig. 8–1a). The stream velocity

generally is greater in the center of the stream and just

below the water surface. The mean velocity is considered to be at 0.6 times the depth from the water surface for water less than 1 foot deep and at the average

of 0.2 and 0.8 times the depth for water more than 1

foot deep.

Lateral mixing below tributary junctions may be incomplete, resulting in a plume following one

streambank (fig. 8–1b). Meanders result in increased

velocity near the outside bank and reduced velocity

inside the meander near the point bar. Thus at a meander, lateral homogeneity would be small. The location

of meanders also changes with flow stage.

Sampling locations must account for these vertical,

horizontal, and longitudinal differences in water quality. Vertical and horizontal concentration differences

are minimized where the stream is completely mixed;

therefore, chemical sampling should be conducted at

locations expected to be well mixed. Mixing is better

in high velocity, turbulent stream sections and well

below tributary inputs.

Mixing distances can be determined using equation

8–1 (Sanders, et al. 1983):

L

d y

y = × 2 17

2

. *

σ μ

μ

[8–1]

where:

Ly = distance for complete lateral mixing

σy = distance from farthest bank of stream to point

of discharge

d = depth of flow

μ = mean stream velocity

μ* = shear velocity = (gRSe)0.5

where:

g = acceleration because of gravity

R = hydraulic radius = A/P

A = cross-section area

P = wetted perimeter

Se = slope of the energy gradient =

approximately the streambed slope

The sampling station should be located downstream of

a tributary, or other discharge to the stream, by a

distance equal to or greater than the mixing distance.

If differences in lateral concentrations still exist,

compositing samples taken at locations across the

stream can integrate these differences. Lateral locations can be width or flow integrated.

Differences in vertical gradients in streams also can be

accounted for by the sampling technique. As described

in chapter 10, a depth-integrating sampler, such as a

0.2d

Horizontal Vertical

Mixing distance

a Velocity profiles

b Mixing zone

0.6d

0.8d

μ

y

O

L y

Figure 8–1 Within stream sampling locations for

physical/chemical monitoring
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Chapter 8 Sampling Location

8–4 (450–VI–NWQH, September 2003)

DH-48, can be used to obtain a grab sample. For automatic samplers, a floating sampling tube can be used.

Biological sampling within streams must consider the

different stream habitats that occur as well as the

mixing phenomena described. Stream systems contain

pools, riffles, overhanging banks, logs, and debris that

will all influence the biotic community (fig. 8–2).

Within each of these habitats, stream velocity will

further stratify biological communities. Shaded and

sunny habitats will also differ. A good sampling program considers all of these habitats. For qualitative

sampling, the biologist would make sure that each

habitat was investigated. For quantitative sampling, a

representative sample per unit area must be obtained

from each habitat.

Example 8–1 Mixing distances

A tributary to Mill River contains a large amount

of sediment as compared to Mill River, which

results in a sediment plume following one of the

streambanks. How far downstream should a

sampling station be located on Mill River to

ensure complete mixing?

Mill River has a mean velocity (μ) of 1.5 feet per

second. The average depth (d) of the stream is 3

feet, and the average width (σy) is 20 feet. The

streambed slope (Se) is 0.005 foot per foot, based

on information from a topographic map.

20 ft

3 ft

R A

P = = ×+ + =

= ( )( )

3 20

3 3 20

2 31

32 2 2 31 0 00 2

ft ft

ft ft ft

ft

ft/s ft

.

. .. * s 5

0 61

2 17 20

3

1 5

0 61

711

2

( )

=

= ( )( )

=

μ* .

. .

.

 ft/s

ft

ft

ft/s

ft/s

ft

L

L

y

y = 0 13 . mi

The monitoring station should be located at least

0.13 mile downstream from the tributary. This

analysis assumes that the flow of the tributary is

small in relation to the flow in Mill River.

Figure 8–2 Within stream sampling locations for

biological monitoring

Pool

Riffle

Shade

Log

Grid

Sun

Overhanging

bank
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Chapter 8 Sampling Location

(450–VI–NWQH, September 2003) 8–5

(b) Lakes

The water quality of lake systems also is heterogeneous because of vertical stratification, longitudinal

gradients, and currents caused by winds and density

differences. Furthermore, many lake basins are actually a combination of sub-basins or bays that have

varying water quality. Near-shore water quality might

be expected to be different from open water concentrations. Also, biotic populations in lakes are impacted

by sediment types and some species are colonial.

Spatial variation within a lake is often greater when

the lake has many bays or coves. In such cases

samples may need to be located within each bay or

section of the lake (fig. 8–3a). The objective of the

study becomes very important in selecting lake sampling locations. Is it necessary to sample within the

lake or is the outlet sufficient to fulfill the objectives?

Because of temperature, and therefore density differences, lakes may stratify into three layers: epilimnion,

metalimnion, and hypolimnion (fig. 8–3b). Samples are

needed from each stratified layer in the system to

describe lake water quality at a particular point. Ideally, stratified random sampling should be used to

determine the number of samples to collect in each

layer (see ch. 9).

If information regarding individual layers is not

needed, individual samples could be composited. An

alternative approach is to collect a depth integrated

sample using a hose or other similar device.

Longitudinal gradients may exist in some lakes, particularly riverine lakes or lakes that are long and

narrow. If the objective includes defining the water

quality gradient, the station location can be determined based on the variability at a station (Potash and

Henson 1978). The procedure is to develop a linear

regression with the variable being a function of the

distance longitudinally through the lake (fig. 8–3c).

Using the mean value and the 95 percent confidence

limits, the distance either side of the station location is

calculated from:

 ±

( ) ± −  

 Distance=

X St a

b

x

[8–2]

where:

a and b= the regression intercept and slope,

respectively

= the mean

Sx = the standard deviation

t = student's 't' at p = 0.05

Graphically, this represents the intercept of the upper

and lower confidence limits with the regression line

(fig. 8–3c). These intercepts could then be projected to

the x-axis to determine the distances represented by

the station. Stations with overlapping distances could

be eliminated. Obviously, more stations will be needed

in regions of greater concentration changes than in

areas that have little gradient.

Biological monitoring in lakes must consider the

spatial variability of biotic community of interest.

Plankton will stratify within lakes. Blue-green algae

may be more prevalent in surface water than in deeper

water. Some zooplankton migrate diurnally from

Figure 8–3 Lake sampling locations

Inlet

Outlet

Beach Objective

Characterize lake

Assume mixed

Assess beach

X

X

a

b

c

Epilimnion

Metalimnion

Hypolimnion

Conductivity

Distance

- Conf. limit

Mean

+ Conf. limit

X
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shallow to deeper water. Fish seek layers of certain

temperatures and dissolved oxygen concentrations.

Horizontally, shallow, near-shore water contains

different habitats than those of deeper water. Benthic

organisms vary with lake sediment type. Certain

species are colonial, growing in lake bottom villages.

Choice of biotic sampling locations must consider

these variations. For plankton sampling, individual

samples can be taken at different depths, or less

accurately, a net can be towed vertically from a depth

of no light to the surface. For quantitative benthic

sampling, some estimate of spatial variability should

be used to determine the number of samples needed.

The same is true for macrophyte sampling.

(c) Ground water

The location of sampling stations within ground water

systems depends upon the objectives as well as the

type of aquifer system being monitored. The objectives

determine whether just the ground water concentrations or both concentration and flow for mass calculations are needed. For flow analysis, the well locations

need to be expanded to determine the flow into and

out of the area and the hydrogeologic properties of the

aquifer. Several textbooks cover this subject (Davis &

DeWiest 1970; Driscoll 1986; Domenico & Schwartz

1990; Freeze & Cherry 1979).

For concentration monitoring alone, the monitoring

system is simplified as compared to flow monitoring.

In siting ground water monitoring wells, the soils and

geology, the direction of ground water flow, and the

type of ground water system must be considered.

The two major types of aquifers are confined and

unconfined (Davis & DeWiest 1970). Unconfined

aquifers, also termed water table aquifers, are in direct

contact with the atmosphere through the soil. Confined aquifers, also termed artesian aquifers, are

separated from the atmosphere by an impermeable

layer (fig. 8–4a).

Ground water monitoring also must consider vertical,

horizontal, and longitudinal water quality differences.

More commonly, ground water monitoring requires a

two-staged approach. The first stage should be a

hydrogeologic survey that determines the ground

water surface elevations and flow directions. In some

ground water investigations it may be important to

locate the top of the ground watershed divide.

To investigate lateral ground water quality, sampling

wells should be located upgradient and downgradient

from the area of interest (fig. 8–4b). More than one

well should be located above, within, and below the

treatment area so that replications can be obtained.

The actual number of wells needed to characterize the

water quality of the aquifer can be determined from

the formula in chapter 9. Before monitoring wells are

sited, there must be knowledge of the general ground

water flow direction. Preliminary estimates of flow

direction can be obtained by triangulation using three

driven well points.

Example 8–2 Specific conductance of gradient

Conductivity data from Station #7 at Crown Point

in Lake Champlain was used to determine the

distance along Lake Champlain that the station

represents (Potash & Henson 1978). The mean

distance at the station was 112 miles. The value

of Sxt was 6.55.

The regression:

Conductivity = 110.3 – 0.13 (distance)

where distance is given in miles.

The confidence limits:

+ ( ) + −

−

+

Distance=

Distance=63.5 mi

112 6 55 110 3

0 13

. .

.

− ( ) − −

−

−

Distance=

Distance=37.3 mi

112 6 55 110 3

0 13

. .

.

Station #7 would adequately describe the conductivity concentration gradient 63.5 miles in one

direction and 37.3 miles in the other direction.

Adjacent stations could be evaluated to determine if there is overlap with station #7. If there

was, a station could be dropped while the gradient would still be adequately monitored.
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Chapter 8 Sampling Location

(450–VI–NWQH, September 2003) 8–7

The depth of the monitoring well also is important. If

sampling nitrate in unconfined aquifers, it may be

necessary to utilize multilevel wells because nitrate

concentrations are often stratified with higher levels at

the top of the aquifer (Eccles and Nicklen 1978). Such

wells can be constructed in the same bore hole (fig.

8–4c) or in separate borings. Poor sealing between

screens in the same borehold may make "nested" wells

undesirable. For monitoring water table wells, the

length of perforated screen should cover the full range

of water levels anticipated.

It is important when locating the depth of all wells that

the monitoring well be placed into the ground water of

interest and not into a localized perched condition

(fig. 8–4d).

Using existing wells for monitoring presents several

problems. Usually knowledge is lacking regarding well

construction, screen length, and other such information. Also, the well could be contaminated. New monitoring wells, developed for the purpose of monitoring,

are encouraged over existing wells.

Several geophysical techniques are available to characterize ground water conditions. Both surface and

borehole techniques can be used. Surface techniques

include (Driscoll 1986):

• seismic refraction/reflection

• gravimetric surveys

• electromagnetic surveys

• electrical resistivity

Figure 8–4 Ground water sampling locations

Well

Seal

Screen

Sand

pack

a Ground water aquifers

b Monitoring source areas

c Multilevel wells

d Vertical locations

Land surface

Stream

Impermeable layer

Confined aquifer

Bedrock

Equipotential

lines

Flow

lines

Well

Stream

130

120

110

100

Well

Surface

Source

Perched

water table

Clay

Water table

Bedrock

Source area

Water table

Unconfined aquifer
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All of these methods provide information on the geologic stratigraphy and presence of ground water.

Seismic methods can be used to determine the depth

to different geologic formations using a hammer and

geophones. Gravity meters can be used to measure

density differences in subsurface materials and are

especially useful in locating bedrock.

Ground-penetrating radar is useful for shallow (<50

feet) investigations of subsurface materials. The

device can be towed to obtain profiles of depths and

distances. Resistivity is used to identify the depth to or

thickness of subsurface strata. The depth to the water

table can also be determined. Additional methods can

be used in boreholes.

614.0804 Optimizing locations

Large monitoring programs generally include many

sampling locations and many visits per location. The

optimal number of stations and the number of visits

per stations can be determined so that the variability

about the mean is minimized. This has been described

as a combination of a cost function and a statement of

variability in the data (Hayne 1977; Mar, et al. 1986;

Reckhow & Chapra 1983). A cost function could be:

 C C SC SpvC =+ + os v [8–3]

where:

C = total cost of sampling

= total budget

Co = initial fixed cost

Cs = cost of establishing site

Cv = cost of visiting site

S = number of sites

pv = number of visits per site

= number of periods (p) times number of visits

(v) per period

The number of visits (v) per site is a function of the

variance caused by the number of sites, the number of

visits, an interaction between site and visit, and an

error term, such that:

v

CK C

pC pK K

v s

v s SV

= +

( ) +















 ⋅

1

2

[8–4]

where:

Ks

s

e

= σ

σ

2

2 [8–5]

 Kv

v

e

= σ

σ

2

2 [8–6]

KS V

S V

e

⋅

⋅ = σ

σ

2

2 [8–7]

where σ refers to the variance caused by the differences among sites (s), visits (v), a site by period interaction (s·v), and random error (e).
Part 614

National Water Quality Handbook

Chapter 8 Sampling Location

(450–VI–NWQH, September 2003) 8–9

The number of sites can be determined based upon the

optimum number of visits from:

 S C

C pvC s v

= + [8–8]

Example 8–3 Optimizing sites and visits

A study was conducted by Hayne (1977) to

determine the total number of small drainage

basins that would describe the water quality in a

river basin. Sampling sites were chosen randomly, and grab samples were collected and

analyzed for total phosphorus.

A preliminary 1-year study using 13 4-week

periods, 15 sites, and 2 randomly selected visits

per period resulted in the following information:

Total cost = $14,211.25

Per site cost = $153.18

Per visit cost = $79.47

Site variance = 0.01265

Visit variance = 0.06830

s·v variance = 0.04109

Error variance = 0.1153

Determine the optimum number of visits per site

and the number of sites needed given the available budget. If the budget were doubled what

would be the allocation between sites and visits?

K

K

K

s

v

S V

= =

= =

⋅ =

0 01265

0 1153

0 1097

0 06830

0 1153

0 5924

0 04109

.

. .

.

. .

.

0 1153

0 3564

14 211 25 0 5924 153 18

13 79 47 13 0 1097

. .

,. . .

. .

=

= ( ) +

( )( v  ) +  



















= =

= + ( )

0 3564

2 16 3

14 211 25

153 18 13 3 79 4

1

2

.

.

, .

. .

v

S

7

44 5 ( ) = = .

For the budget of $14,211.25, the optimal number

of sites would be 5 and the number of visits per

period would be 3 rather than the 2 used in the

preliminary study.

If the budget were doubled, the number of sites

could be increased to 9 and the number of visits

per period would remain 3.
Part 614

National Water Quality Handbook

Chapter 8 Sampling Location

8–10 (450–VI–NWQH, September 2003)

614.0805 References

Canter, L.W. 1985. River water quality monitoring.

Lewis Publ., Inc., Chelsea, MI.

Davis, S.N., and R.J.M. DeWiest. 1970. Hydrogeology.

John Wiley and Sons, Inc., NY.

Domenico, P.A., and F.W. Schwartz. 1990. Physical and

chemical hydrogeology. John Wiley and Sons,

Inc., NY.

Driscoll, F.G. 1986. Ground water and wells. 2nd Ed.

Johnson Div., St. Paul, MN.

Eccles, L.A., and R.R. Nicklen, 1978. Factors influencing the design of a ground water quality

monitoring network. Proc. Establishing water

quality monitoring programs. Amer. Water

Resour. Assoc.

Freeze, R.A., and J.A. Cherry. 1979. Ground water.

Prentice-Hall, Inc., Englewood Cliffs, NJ.

Hayne, D.W. 1977. Probability sampling of small

streams: problems and results. In Watershed

research in Eastern North America, A workshop

to compare results, Vol. II, Rep. NSF/RA 770255.

Smithsonian Inst., pp. 809-830.

Klemm, D.J., P.A. Lewis, F. Fulk, and J.M. Lazorchak.

1990. Macroinvertabrate field and laboratory

methods for evaluating the biological integrity of

surface waters. Office of Research and Development, Washington, DC, EPA/600/4-90/030.

Mar, B.W., R.R. Horner, J.S. Richey, R.N. Palmer, and

D.P. Lettenmaier. 1986. Data acquisition.

Environ. Sci. Technol. 20(6):545-551.

Ponce, S.L. 1980. Water quality monitoring programs.

WSDG Tech. Pap. No. WSDG-TP-00002. Watershed Sys. Dev. Group, USDA, Forest Serv., Ft.

Collins, CO.

Potash M., and E.B. Henson. 1978. Significance of

geographic positioning for water quality monitoring in Lake Champlain. Proc. Establishing water

quality monitoring programs. Amer. Water

Resour. Assoc., pp. 58-73.

Reckhow, K.N., and S.C. Chapra. 1983. Engineering

approaches for lake management. Vol. 1: Data

analysis and empirical modeling. Butterworth

Publ., Woburn, MA.

Sanders, T.G., R.C. Ward, J.C. Loftis, T.D. Steele, D.D.

Adrian, and V. Yevjevich. 1983. Design of networks for monitoring water quality. Water

Resour. Pub., Littleton, CO.

United States Department of Agriculture, Soil Conservation Service. 1985. National Engineering

Handbook, Section 4, Hydrology., chapter 14.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

National Water Quality Handbook

Chapter 9 Sampling Frequency and

Duration
(450–VI–NWQH, September 2003) 9–i

Chapter 9 Sampling Frequency

and Duration

Contents: 614.0900 Introduction 9–1

614.0901 Simple random sampling 9–2

(a) Estimate of the mean ................................................................................... 9–2

(b) Linear trend detection .................................................................................. 9–4

(c) Step trend ...................................................................................................... 9–5

614.0902 Stratified random sampling 9–5

614.0903 References 9–6

Tables Table 9–1 Relative sampling frequency and objectives 9–1

Table 9–2 Coefficients of variation 9–4

Figure Figure 9–1 Sampling interval as a function of system type 9–1

Examples Example 9–1 Sample size using simple random sampling based 9–3

on estimate of the mean

Example 9–2 Sample size for trend detection 9–4

Example 9–3 Sample size for step trend 9–5

Example 9–4 Stratified random sampling 9–6
(450–VI–NWQH, September 2003) 9–1

Chapter 9 Sampling Frequency and Duration

614.0900 Introduction

The most frequently asked questions when developing

a water quality monitoring study are "How many

samples and for how long?" Unfortunately, the correct

response is: "It depends." Several factors affect the

frequency of sampling. They include the objectives of

the study, the type of waterbody being studied, the

data variability, and the available resources. Table

9–1 summarizes general frequencies for various objectives for conducting a water quality study. Frequencies

are given in relative terms to each other because a

fixed time interval is inappropriate.

Long-term trend monitoring and programs evaluating

program effectiveness on a watershed basis can use

longer intervals between samples than other monitoring objectives. Frequent sampling or even a continuous recorder may be desirable for a study aimed at

understanding a mechanism controlling certain water

quality changes. The frequency of compliance monitoring should be approximately equal to the probability of

exceeding a standard.

Sampling frequency is also affected by the aquatic

system being studied. In general, the variance is

greater; therefore, more samples are needed for studying streams than for lakes. Intermittent streams are

often more variable than permanent streams. Ground

water also is considered less variable than streams,

but soil water samples can be highly variable (fig.

9–1).

Financial resources typically limit the sampling frequency, although time, people, and laboratory capability can also limit sampling frequency. However, financial resources should not be allowed to dictate a

sampling frequency. In cases where funds are limiting,

a consideration should be given to eliminating extra

parameters or stations. Compositing samples and

passive sampling (chapter 10) can save substantial

resources.

This chapter presents methods for calculating the

sampling frequency. The primary sampling techniques

described are simple random sampling and stratified

random sampling.

Table 9–1 Relative sampling frequency and objectives

Objective Relative interval between

samples

1. Baseline Long

2. Trends Long

3. Fate and transport Short

4. Problem definition Short

5. Critical areas Short

6. Compliance Probability of exceeding

 standard

7. BMP effectiveness Short

8. Program effectiveness Long

9. Wasteload allocations Short

10. Model evaluation Short to long

11. Research Continuous to short

Figure 9–1 Sampling interval as a function of system

type

Permanent stream

Intermittent

stream

Soil water

Lakes

Ground water

System Variability

Low High

Long Short

Sampling interval
Part 614

National Water Quality Handbook

Chapter 9 Sampling Frequency and Duration

9–2 (450–VI–NWQH, September 2003)

614.0901 Simple random

sampling

Sampling of water quality is needed to provide useful

information about the entire population of water

quality data that exists without measuring the entire

population. Sampling saves time and money. Simple

random sampling for water quality monitoring means

that every water quality sample has an equal chance of

being collected.

The calculation of sample size varies with the statistical objective of the monitoring study. Such objectives

include an estimate of the mean, linear trend detection, and a step trend. The methods used to calculate

sample sizes for each case are presented.

(a) Estimate of the mean

One goal may be to be able to estimate the mean for a

water quality variable with a certain amount of confidence in the estimate. The equation for calculating the

sample size has been widely reported and is based on

the variability and precision desired (Snedecor &

Cochran 1980; Freese 1962; Moser & Huibregtse 1976;

Ponce 1980; Rustagi 1983; Reckhow & Chapra 1983;

Sanders, et al. 1983). The sample size can be calculated from the relationship:

 n

t S

d =

2 2

2 [9–1]

where:

n = the calculated sample size

t = Student’s 't' (appendix B) at n-1 degrees of

freedom and confidence level (p)

S = the estimate of the population standard deviation

d = the allowable difference from the mean

The standard deviation (S) is calculated as the square

root of the variance (S2) which is determined from

(Snedecor & Cochran 1980):

 S

X

X

n

n

i

i

2

2

2

1 =

− ( )

−

Σ

Σ

[9–2]

where:

n = the sample size

Xi = the value of the ith observation

If the coefficient of variation rather than the standard

deviation is known, the following relationship may be

used (Koch, et al. 1982; Moser & Huibregtse 1976):

 n

t CV

X

=

2 2

2

% [9–3]

where:

CV = the coefficient of variation = 

S

X

% X = the percent deviation allowed from the true

mean

Ranges in coefficients of variation for select system

type are given in table 9–2 for certain water quality

variables. This formula should be used with a double

iterative procedure as shown in the following examples.

If the variance (S2) is not known, an approximation

can be made based on the range in the data using

equation 9–4 (Ponce 1980; Sanders, et al. 1983):

 S2

2

2 4 = ( ) Range [9–4]

where:

Range = the range from the smallest to the largest

values expected to be encountered during

the sampling period
Part 614

National Water Quality Handbook

Chapter 9 Sampling Frequency and Duration

(450–VI–NWQH, September 2003) 9–3

Based on historical monitoring in a stream, how

many samples are needed to be within 10 and 20

percent of the true annual mean total phosphorus

concentration? The following information was

obtained from the existing monitoring program

for 1 year:

mean = 0.886 mg/L

standard deviation = 0.773 mg/L

variance = 0.597 mg/L

maximum = 4.1 mg/L

minimum = 0.074 mg/L

n = 165

The difference (d) for 10 percent and 20 percent

would be:

d = 0.1 x 0.886 mg/L = 0.09 mg/L

d = 0.2 x 0.886 mg/L = 0.18 mg/L

The t-value would be 1.96 for >120 degrees of

freedom and p=0.05 (appendix B). A two-tailed

t-value can be obtained from most statistics

books, such as table A–4 in Snedecor and

Cochran (1980).

1st iteration—10%

n = ( )( )

( ) = 1 96 0 773

0 09

283

2 2

2

. .

.

Because the t-value would not change for n=283

degrees of freedom, no additional iterations are

necessary.

1st iteration—20%

n = ( )( )

( ) = 1 96 0 773

0 18

71

2 2

2

. .

.

This result is a fourth of the 10% result. However,

the t-value must be adjusted for the degrees of

freedom.

2nd iteration—20%

n = ( )( )

( ) = 1 993 0 773

0 18

73

2 2

2

. .

.

Therefore 73 samples should be taken to estimate the mean annual total phosphorus concentration within 20% of the true mean.

The variance could have been estimated based

on the range as follows:

S mg L 2

2 2

16

4 1 0 074

16 = = 1 013 ( ) − = Range . . . /

This estimate of the variance is greater than the

measured variance listed above, and would result

in a larger sample size being taken.

Example 9–1 Sample size using simple random sampling based on estimate of the mean
Part 614

National Water Quality Handbook

Chapter 9 Sampling Frequency and Duration

9–4 (450–VI–NWQH, September 2003)

(b) Linear trend detection

Another goal may be to determine the number of

samples needed to detect a linear trend in the water

quality data (Ward, et al. 1990). The sample size may

be calculated from:

 n

t S

d = 12 2 2

2 [9–5]

where:

S = the standard deviation of the water quality data

collected over time with any trend removed from

the data

d = the minimum magnitude of the trend

Example 9–2 Sample size for trend detection

Using example 9–1, determine the number of

samples needed to detect a trend of at least 0.5

mg/L per year.

1st iteration

n = ( )( )

( ) = 12 1 96 0 773

0 5

110

2 2

2

. .

.

2nd iteration

n = ( )( )

( ) = 12 1 981 0 773

0 5

113

2 2

2

. .

.

Therefore, 113 samples per year would be

needed to detect a linear trend of 0.5 mg/L per

year. The greater the trend, the fewer samples

that would be needed.

Table 9–2 Coefficients of variation1 (dashes indicate data not available)

Parameter Agricultural Lakes Ground Treatment Edge-of-field

streams water plant

Temperature 0.7-1.2 0.4-0.7 0.4-0.7

Dissolved oxygen 0.2-0.6 0.2-0.4 0.2-0.7

pH 0.03-0.1 0.05-0.1 0.03-0.1

Conductivity 0.2-0.7 0.1-0.5 0.2-1.3

Secchi disk --- 0.1-0.7 ---

Fecal coliform 0.9-27.1 1.6-9.5 0.6-39.2

Fecal streptococci 1.2-94.0 1.5-32.0 0.9-11.2

Turbidity 0.7-5.5 0.6-2.5 0.4-3.8

Total suspended solids 1.0-9.0 0.1-3.7 0.3-3.4

Volatile suspended solids 0.7-4.4 0.5-2.8 0.3-2.2

Total phosphorus 0.6-2.2 0.3-2.4 0.3-0.9

Ortho phosphorus 0.5-2.1 0.4-3.3 0.5-1.4

Total Kjeldahl nitrogen 0.4-1.8 0.1-1.4 0.3-1.1

Ammonia nitrogen 0.8-4.0 0.3-3.9 0.4-2.2

Nitrate nitrogen 0.1-4.8 0.7-2.0 0.4-4.4

Chlorophyll 'a' --- 0.2-4.0 ---

1 St. Albans Bay RCWP
Part 614

National Water Quality Handbook

Chapter 9 Sampling Frequency and Duration

(450–VI–NWQH, September 2003) 9–5

(c) Step trend

The goal may be to determine if there has been a

change in the mean water quality between two time

periods. This would be equivalent to a step trend

(Sanders, et al. 1983). The number of samples needed

to detect a stated change is determined from:

 n

t S

d = 2 2 2

2 [9–6]

where:

n = the size of each sampling period, which is

assumed to be equal

S = the pooled standard deviation for both periods

d = the allowable difference (precision) from the

mean

The total number of samples needed to detect the

difference would be 2n.

Example 9–3 Sample size for step trend

For example 9–2, determine the number of

samples needed to detect a change in the mean

total phosphorus concentrations between a preimplementation period and a post-implementation period with 20 percent precision. No

changes in the original sampling data were

assumed.

d mg L mg L

n

n

=× =

= ( )( )

( ) =

=

0 2 0 886 0 18

2 1 96 0 773

0 18

141

2 28

2 2

2

.. / . /

. .

.

2

Therefore, 282 samples would need to be taken

over the two time periods to detect a difference

in the means between the two periods. Note that

the level of precision would only be 20 percent;

therefore, the difference would need to be

greater than 20 percent to be detectable.

614.0902 Stratified

random sampling

Instead of each water quality sample having the equal

chance of being collected, there may be advantages to

dividing the population of water quality samples into

subgroups that are each more homogeneous than the

whole data set. Samples could then be taken from

each subgroup or strata. This type of sampling is

termed stratified random sampling (Snedecor &

Cochran 1980). More samples are allocated to subgroups that have greater variability. Two examples of

appropriate applications of this technique would be:

• grouping by a flow period (snowmelt, summer

low flow) or

• grouping by strata in a lake (epilimnion,

hypolimnion).

The sample size for stratified random sampling can be

calculated from the relationship (Reckhow & Chapra

1983):

 n

t wS

d

i i = ( ) ∑2 2

2 [9–7]

where:

n = the total number of samples

t = Student's 't' at n–1 degrees of freedom

wi = the proportional size of stratum i

Si = the standard deviation of the water quality data

for stratum i

d = the difference from the mean

The number of samples for each individual stratum is

determined from:

 n

nw S

w S i

i i

i i

=

∑( ) [9–8]

where:

ni = the number of samples of stratum i
Part 614

National Water Quality Handbook

Chapter 9 Sampling Frequency and Duration

9–6 (450–VI–NWQH, September 2003)

Example 9–4 Stratified random sampling

Mudd Lake stratifies in the summer; therefore, it

is desirable to subsample each layer to determine lake-wide phosphorus concentrations.

Preliminary sampling resulted in the following

information:

- - - Thickness - - - Standard deviation

(ft) (%) (mg/L)

epilimnion 14 (35) 0.012

metalimnion 6 (15) 0.005

hypolimnion 20 (50) 0.010

Determine the total number of samples and the

number of samples within each stratum to be

within 10 percent of the true mean at the 95

percent confidence level. The overall mean was

0.04 mg/L total phosphorus.

1st iteration

2nd iteration

 

n

n

= ( )( )

( )

= =

2 069 0 00995

0 004

26 5 27

2 2

2

. .

.

.

Allocate the 27 samples among the 3 strata by:

n

n

epi

meta

= ( )( ) =

= ( )( )

27 0 35 0 012

0 00995

11 4

27 0 15 0 005

0 009

. .

. .

. .

. 95

2 0

27 0 50 0 010

0 00995

13 6

=

= ( )( ) =

.

. .

. n . hypo

Therefore 11, 2, and 14 samples should be taken

from the epilimnion, metalimnion, and hypolimnion, respectively.

614.0903 References

Freese, F. 1962. Elementary forest sampling. USDA

Forest Serv., Agric. Handb. No. 232, Washington,

DC.

Koch, R.W., T.G. Sanders, and H.J. Morel-Seytoux.

1982. Regional detection of change in water

quality variables. Water Resour. Bull. 18(5):815-

821.

Moser, J.H., and K.R. Huibregtse. 1976. Handbook for

sampling and sample preservation of water and

wastewater. U.S. Environ. Prot. Agency 600/4-76-

049.

Ponce, S.L. 1980. Water quality monitoring programs.

WSDG-TP-00002, Watershed Sys. Dev. Group,

USDA Forest Serv., Ft. Collins, CO.

Reckhow, K.H., and S.C. Chapra. 1983. Engineering

approaches for lake management. Volume 1:

Data analysis and empirical modeling.

Butterworth Publ., Woburn, MA.

Rustagi, K.P. 1983. Determination of sample size in

simple random sampling. Forest Science.

29(1):190-192.

Sanders, T.G., R.C. Ward, J.C. Loftis, T.D. Steele, D.D.

Adrian, and V. Yevjevich. 1983. Design of networks for monitoring water quality. Water

Resour. Pub., Littleton, CO.

Snedecor, G.W., and W.G. Cochran. 1980. Statistical

methods. 7th ed. IA State Univ. Press, Ames, IA.

Ward, R.C., J.C. Loftis, and G.B. McBride. 1990. Design

of Water Quality Monitoring Systems. Van

Nostrand Reinhold, NY, pp. 1-13.

n = ( ) ( )( )  + ( )( ) + ( )( )  

 1 96 0 35 0 012 0 15 0 005 0 50 0 010

0 1

2 2

. .. .. ..

. 0 0 04

23 8 24

2

( )( )  



= =

.

n .
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

National Water Quality Handbook

Chapter 10 Station Type
(450–V–NWQH, September 2003) 10–i

Chapter 10 Station Type

Contents: 614.1000 Introduction 10–1

614.1001 Discharge stations 10–1

(a) Plot discharge ............................................................................................. 10–1

(b) Edge-of-field discharge .............................................................................. 10–2

(c) Stream discharge ........................................................................................ 10–3

(d) Staff gages ................................................................................................... 10–5

(e) Stage recording ........................................................................................... 10–5

(f) Stage-discharge relationship ..................................................................... 10–9

(g) Heating in cold climates........................................................................... 10–12

614.1002 Concentration sampling 10–13

(a) Grab samples ............................................................................................ 10–13

(b) Passive samplers ....................................................................................... 10–14

(c) Automated samplers ................................................................................ 10–16

(d) Actuated sampling .................................................................................... 10–17

614.1003 Precipitation monitoring 10–17

614.1004 Soil water sampling 10–20

614.1005 Biotic sampling 10–20

(a) Plankton .................................................................................................... 10–20

(b) Periphyton ................................................................................................. 10–21

(c) Macrophyton ............................................................................................. 10–21

(d) Macroinvertebrates .................................................................................. 10–21

(e) Fish ............................................................................................................. 10–22

614.1006 Sediment sampling 10–24

614.1007 References 10–25
Part 614

National Water Quality Handbook

Chapter 10 Station Type

10–ii (450–VI–NWQH, September 2003)

Figures Figure 10–1 Runoff plots 10–2

Figure 10–2 Field runoff H-flumes 10–3

Figure 10–3 Weirs 10–4

Figure 10–4 Natural channel gaging station 10–4

Figure 10–5 Porcelain staff gage 10–5

Figure 10–6 Stage recorders 10–6

Figure 10–7 Pygmy current meter 10–8

Figure 10–8 Stage-discharge rating curve 10–9

Figure 10–9 Stream hydrograph 10–11

Figure 10–10 Heating devices 10–12

Figure 10–11 Grab samplers 10–13

Figure 10–12 DH-48 sampler 10–13

Figure 10–13 Tipping bucket with passive sampler 10–15

Figure 10–14 Coshocton wheel 10–15

Figure 10–15 Stage sampler 10–15

Figure 10–16 ISCO automatic sampler 10–16

Figure 10–17 Depth-integrating intake 10–16

Figure 10–18 ISCO liquid level actuator 10–17

Figure 10–19 Standard rain gage 10–18

Figure 10–20 Standard rain gage with tipping bucket and funnel 10–18

gages

Figure 10–21 Standard rain gage altar shield 10–18

Figure 10–22 Gages for precipitation chemistry 10–19

Figure 10–23 Soil water samplers 10–20
Part 614

National Water Quality Handbook

Chapter 10 Station Type

(450–VI–NWQH, September 2003) 10–iii

Figure 10–24 Biotic samplers 10–22

Figure 10–25 Biotic and sediment samplers 10–23

Figure 10–26 Hand-held sediment corer 10–24

Example Example 10–1 Developing a rating equation 10–10
(450–VI–NWQH, September 2003) 10–1

Chapter 10 Station Type

614.1000 Introduction

The purpose of this section is to provide guidance on

the design, operation, and maintenance of hydrologic

and water quality monitoring stations. This chapter is

divided into the types of monitoring to be conducted:

• discharge

• concentration

• precipitation

• soil water

• biota

• bottom sediment

Generally, several optional methods for conducting the

monitoring are available for each type of monitoring

station needed. Also, the costs of installation and

operation of these stations differ.

When designing monitoring stations, three principles

are recommended: redundancy, simplicity, and quality.

Important hydrologic variables, such as stage, should

be measured in more than one way. Power failures and

the unexpected seem to influence any monitoring

record. Whenever possible, the most simple alternative

is often the best. Complicated monitoring station

designs invite problems. Finally, whatever is done

should be installed with high quality. A neat and sturdy

monitoring setup will be a safe and reliable one.

Agricultural Handbook No. 224 (USDA 1979) is an

important reference for designing monitoring stations.

The U.S. Geological Survey has published a series of

Techniques of Water Resource Investigations (TWI)

reports that addresses many of the issues related to

designing monitoring stations. A listing of TWI 1

through TWI 8 is given following the references. Other

references are also listed at the end of this chapter.

The type of station desired will, of course, depend on

the objectivities as well as other components of the

study design. Not all study designs require a fixed

station, especially biological monitoring. This chapter

is intended to give guidance on possible approaches

and the equipment currently available to achieve

certain monitoring goals.

614.1001 Discharge

stations

The type of discharge station to construct is a function

of the scale of the project (plot, field, or watershed),

the project duration, and the project budget.

(a) Plot discharge

Two types of devices for measuring the amount of plot

runoff are shown in figure 10–1. A simple, small plot

design is shown in figure 10–la. Sheet metal (18 gauge)

cutoff walls are driven into the soil. Overland flow

from just within the plot flows into a rain gutter installed flush with the soil surface, and then into a

collection jug. The lip on the rain gutter can be inserted into the soil to prevent underflow. The plot can

be sized based on expected overland flow so that the

volume of the jug will not be exceeded. For example, a

3 by 6 foot plot has been used in the northeast United

States. This type of plot can be installed in about 20

minutes and removed during field cultivation. A tipping bucket device (Chow 1976; Johnson 1942) can be

used at the bottom of the plot instead of a collection

jug. In some cases a large barrel could be installed to

capture all the flow. This sampler determines flow

based on the volume of sample collected.

Runoff volumes from such small runoff plots are

highly variable plot to plot; therefore, a large number

of plots may be necessary to obtain a good estimate of

runoff (see chapter 9).

An example of a runoff plot used for research purposes is shown in figure 10–lb. This type of plot used a

multislot divisor. The total runoff volume is computed

from the sample volume collected by the divisor

(USDA 1979). Dressing, et al. (1987) describe an expensive sampler that determined flow based on the

volume of sample collected.
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(b) Edge-of-field discharge

Some of the devices described previously for plots can

be enlarged for edge-of-field situations, especially that

described by Dressing, et al. (1987). Because ponding

of water on a field and high sediment and plant remains loads are undesirable, a flume, rather than a

weir, is most often used for field discharge. The H-type

flume is the most commonly used (fig. 10–2). This

flume is so named because it was the eighth developed

in a series starting with the A flume (Gwinn and Parsons 1976). The others include HS (small) and HL

(large) flumes.

A complete description of the H-flume is given in

Agricultural Handbook 224 (USDA 1979). The flume is

often constructed of sheet metal; however, stainless

steel flumes have been used for pesticide sampling

(Smith, et al. 1985), and prefabricated fiberglass

flumes are available as well. Rating tables and

Figure 10–1 Runoff plots

Rain

gutter

Carboy

Garbage

can

Sheetmetal

cutoff walls

Plot

Boundary

Conveyance channel

Sludge tank

Divisor

1st Aliquot tank

2nd Aliquot tank

Collector Collector

Approach

channel

Flume

Conveyance

channel

Alternate scheme using

H-flume for runoff

measurement.

a Small-scale runoff plot

b Larger-scale runoff plot
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equations are readily available (Gwinn and Parsons

1976; USDA 1979; Grant 1979). An approach channel to

the flume is needed to reduce velocity and turbulence

in the flow (fig. 10–2). A false side sloping floor (1:8)

can be used when sedimentation in the flume is significant. The H-flume needs a method of recording stage,

generally in a stilling well attached to the flume. Stage

recording is described later in this chapter.

Other types of flumes have been used to measure

edge-of-field runoff including Parshall and longthroated flumes (USDA 1979; Replogle & Clemmens

1981).

(c) Stream discharge

Many options are available for determining discharge

in streams. The selection of the type of station varies

with individual site conditions, such as slope, sediment

load, and stream size. The major options include

flumes, wiers, and a natural channel. The use of existing structures, such as culverts, will also be discussed.

The practical limit to H-flumes is about a peak discharge of 100 cubic feet per second (5 ft head); however, larger flumes can be built onsite. Specialized

flumes have been developed for use in the Western

States where streams may be flashy and ephemeral

(USDA 1979). Sufficient slope in the streambed is

needed to prevent backwater into the flume and allow

the freefall of water at the outlet opening.

Wiers are another common device used in streams for

discharge measurement. Figure 10–3b shows several

configurations for weir types. They include v-notched,

rectangular, and Cipolletti wiers. Wiers can be constructed of wood, sheet metal, or concrete.

The practical size for a prefabricated weir made of

plywood with a metal or plastic sharp crest is 5 cubic

feet per second (1.3 ft head). Larger plywood weirs

may fail. The weir must not leak. The weir plate

should extend well into the streambed and be connected to a channel sill that extends upstream of the

weir.

A natural channel is often necessary when flow is too

large for an artificial structure. The basic features of

recording discharge for a natural channel are shown in

figure 10–4a. The cross-section is located at a control

section; that is, a stable streambed and streambank

location where the channel is straight. Also, stream

gaging must be possible at or near the cross-section.

A basic setup for a natural channel includes a stilling

well for stage measurement with intake pipes connected to the stream. The stilling well should not be

placed in the stream because of velocity effects and

icing problems, but rather should be installed in the

streambank. The well diameter could range from a

12-inch PVC pipe to a 48-inch corrugated metal pipe

(CMP). A gage house is either placed on top of the

stilling well or, for large diameter culverts, is part of

the well itself. The total cross-section area of the

Figure 10–2 Field runoff H-flumes

H

flume Approach channel

Recorder

Recorder

Stilling

well

h

H

flume
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for discharge measurements (USDA 1979). The author

believes that culverts generally should be avoided for

discharge measurements. At high flows, culverts can

be submerged, a hydraulic jump may form at the

culvert entrance, or the water level may drop because

an entrance is constricted (fig. 10–4b). These conditions yield false stage values. Culverts also present

problems by collecting debris and icing in winter.

intake pipes should be about 1 percent of the area of

the stilling well. Venting the gage house helps to

prevent moisture buildup.

For some study designs, using an open channel with

point measurement of discharge may be sufficient to

achieve the study objectives. However, such discharge

monitoring does not give any information about the

discharge between sampling dates. Existing structures, including culverts, dams, and spillways, are used

Figure 10–3 Weirs Figure 10–4 Natural channel gaging station

V notch

Cipolletti

Rectangular

Rectangular

suppressed

Staff gage

Nappe

3

2

1

0

h

a Components of typical weir 

b Weir types

Air

4-5h

Sill

Culvert

Staff

gage

Water surface

Intakes

Stilling

well

Recorder

a Station cross-section

b Flow at culvert
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(d) Staff gages Figure 10–5 Porcelain staff gage

All discharge stations should include a staff gage. A

staff gage is typically a vertical calibrated gage made

of porcelain enameled steel (fig. 10–5). It should be so

constructed or so placed as to not catch debris and to

shift easily upward or downward. A point gage should

be used in an instrument shelter, either with a separate

float or using a graduated float tape. The outside staff

gage reading is the true stage to which all recording

gages should be set. The elevation of the staff gage

should be checked periodically for shifts.

(e) Stage recording

Stage is most often recorded in a stilling well, although

bubbler gages have made this requirement unnecessary. The primary methods for recording stage are

through the use of floats, bubblers, pressure transducers, and ultrasonic sensors (fig. 10–6). Several floatlevel recorders are highly reliable and remain the

preferred method of stage recording for many hydrologists. Advantages of bubbler gages are that no stilling

well is required and they can be easily combined with

automatic water samplers. Almost all stage recorders

available today allow for data logging. Those with

programmable data loggers can control automatic

water sampling. Pressure transducers and ultrasonic

sensors are not widely used at this time; however, they

are very useful for data logging.
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Figure 10–6 Stage recorders (photos c, d, e, f courtesy Instrumentation Specialties Company)

a Float-level b Punch tape

c Bubbler
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Figure 10–6 Stage recorders—Continued

d Ultrasonic e Pressure transducer

f Bubbler
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(f) Stage-discharge relationship

Because stage is only a measure of the height of the

water, not the discharge in the stream, a stage-discharge relationship for the open channel station must

be developed. Simultaneous measurement of stage and

discharge is needed to develop the rating equation for

an open channel stage recorder. Once the relationship

is developed, stage measurements can be used to

compute discharge. Discharge in open channels typically is determined using current meter measurements

(fig. 10–7).

The primary method for determining discharge is the

velocity-area method, although other techniques, such

as the salt dilution method, exist as well (USDI, BOR

1977). The velocity-area method uses the equation:

 Q AV = [10–1]

where:

Q = discharge

A = cross-sectional area of stream

V = stream velocity

Figure 10–7 Pygmy current meter

When conducting a discharge measurement using a

velocity meter, the stream cross-section is divided into

subsections and velocity measurements are taken at

each subsection. For sections deeper than 2.5 feet, two

velocity measurements are taken at 0.2 and 0.8 times

the depth; otherwise a single velocity measurement is

taken at 0.6 times the depth.

A good description of guidelines for making discharge

measurements is given in Buchanan and Somers

(1969) and the National Handbook for Recommended

Methods for Water-Data Acquisition (USGS 1977).

Example 10–1 shows the recommended steps for

developing a rating equation.

The general form of the rating equation is:

 Q CHb = [10–2]

where:

Q = the discharge (ft3/s)

C = the regression intercept, which is the discharge

where H = 1.0

H = the stage (ft)

b = the slope of the regression
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Example 10–1 Developing a rating equation

Use the following steps to develop the rating

equation:

1. Log transform paired values of Q and H

2. Perform a linear regression of Q vs. H with Q

as the dependent variable.

3. Obtain intercept (C) and slope (b)

4. Add coefficients to the equation:

logQ=logC+blogH

5. Transform equation to the form:

Q CHb =

by taking the antilog of equation in step 4, so

that:

Q Hc b = 10

For example, if the intercept (C) was 0.05

and the slope (b) was 2.54, the equation

would be:

Q H = 100 05 2 54 . .

or

Q H = 1 12 2 54 . .

Figure 10–8 Stage-discharge rating curve

10

1

0.1

0.1 1 10

Deposition

Scour

Width decreases

Original rating

Width increases

Discharge (ft /s)

Stage (ft)

3

This equation should plot as a straight line on log-log

paper. Figure 10–8 shows an example rating curve.

Note: By convention, the discharge (Q) is plotted as

the abscissa even though it is the dependent variable.

A minimum of 15 pairs of stage and discharge measurements should be used to develop the rating equation shown as points on figure 10–8. At times, two

rating equations are developed; one for low flow and

one for high flow. The ratings should be checked

periodically because shifts in the equation may occur.

Changes in the rating curve may be caused by scouring

or filling the streambed, the growth of aquatic vegetation, or by icing. Figure 10-8 displays two of these

cases. If scour occurs, the rating would be expected to

move to the right and concave downward. That is, for

an equal stage, the discharge would be greater after

scouring. With filling, the rating would move left and

concave upward (USGS 1977).
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If the width of the downstream control section increased, the intercept would be expected to increase.

That is, for an equal discharge, the stage would be

lower if the width decreased. The opposite would

happen if the width of the control decreased.

Several methods are available for extending the relationship for higher observed stages (Schulz 1976;

USGS 1977). Also, additional adjustments can be made

to the rating. For example, there is a histeresis effect

of rising limb discharge exceeding falling limb discharge at the same stage (fig. 10–9). Assistance of

agencies, such as the U.S. Geological Survey, may be

necessary where large streams are involved.

(g) Heating in cold climates

Year around monitoring is necessary in many cases. In

cold climates, heating may be needed to guarantee

sample collection. Heating design varies with the type

of gaging station. Generally, heating requirements can

be reduced by insulating. For many gaging stations,

insulating means having the stilling well buried into

the soil as far as possible. Weir plates can be kept

open by covering with a wooden box during the winter. The box also can be heated for further protection.

Where electric power is present, heating is relatively

easy. Heat lamps, light bulbs, space heaters, or stock

tank heaters have all proven to prevent freeze-up.

Figure 10–9 Stream hydrograph

Time, hr

0 2 4 6 8 10

10

8

6

4

2

0

Discharge, ft3/s

Rising

limb

Peak

discharge

Falling

limb

Figure 10–10 Heating devices

b Catalytic propane

heater

a Pilot light

propane heater

Sample lines to automatic samplers can be prevented

from freezing by wrapping with electrical heat tape.

When electric power is not present, propane can

provide heat. A regulator with a "fail safe" must be

used with the pilot light to prevent gas leakage and

possible explosions in the stilling well. A pilot light

propane heater is shown in figure 10–10a. This type of

system could heat a stilling well and instrument shelter on little gas. Catalytic propane heaters can be used

to provide a more directed heat source, such as

needed at the mouth of an H-type flume (fig. 10–10b).

However, these heaters require much more gas than

the smaller pilot light heater.
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614.1002 Concentration

sampling

A variety of devices have been developed for taking

samples for water quality analysis. Sampling may be

either attended or unattended, and unattended sampling may be either passive or automated. The type of

sampling device varies with the scale of the project,

the objectives, and the project budget.

(a) Grab samples

A grab sample is a discrete sample that is taken at a

specific place and time. A series of grab samples

lumped together are considered composite samples.

Grab samples may not be representative of the water

quality of the body of water being sampled for several

reasons. Water quality may vary with depth or distance

from the streambank.

A grab sample typically is taken by hand with a sampling bottle. The bottle should be held just below the

surface of the water to avoid contaminants in the

surface film. The sample bottle can be connected to a

holder on the end of a rod with plastic tubing to obtain

a sample at some distance away (fig. 10–11a).

Sampling lake systems requires more specialized

equipment. Frequently used samplers include Kemmerer, VanDoren, or Beta bottles. These samplers can

obtain a sample from any depth in the water column.

An inexpensive sampler consisting of a bottle with a

pullable stopper (fig. 10–11b) has been described by

Schwoerbel (1970) and WHO (1978). The same effect

could be achieved by lowering a weighted, open bottle

upside down, and inverting it with a second rope,

allowing the air to escape and the bottle to fill with

water.

Depth integrating samplers have been used especially

for sediment sampling. For example, the DH-48 sampler (fig. 10–12) is designed to continuously obtain a

sample as it is lowered to the streambed and then

raised to the surface. In lakes, hoses have been used to

obtain a sample of the total column of water. The hose

is lowered into the water and allowed to fill. A rope

attached to the bottom end is used to raise the lower

end of the hose to the surface thereby collecting the

entire sample of water in the hose. Pumps also have

been used to sample lake water.

Figure 10–11 Grab samplers

Figure 10–12 DH-48 sampler

a Rod sampler

b Lake sampler
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(b) Passive samplers

A passive sampler collects a water quality sample by

action of the flow of water itself. A tipping bucket

discharge station is well suited to passive sampling

(fig. 10–13). Slots or funnels under the tipping bucket

have been used to collect water samples (Chow 1976;

Johnston 1942; Russell 1945). H-flumes also have been

widely used for passive sample collection. The

Coshocton wheel (fig. 10–14) has been used to sample

1 percent of discharge for sediment sampling (USDA

1979). A splitter below a Coshocton wheel has been

used to reduce the size of the sample to 0.1 percent of

discharge (Coote & Zwerman 1972). Holes drilled in

the mouth of an H-flume also have been used to collect

stage-integrated samples through tubing.

Passive devices have been used for plot runoff. Most

involve some sort of divisor and collection tank (Coote

& Zwerman 1972; Dressing, et al. 1987; Geib 1933;

Kohnke & Hickok 1943; USDA 1978) unless the plot is

sized to collect the entire sample in a collection jug, as

shown in figure 10–1.

The primary advantages of a passive sampler are that

it can be unattended, requires little maintenance, and

no power.

Stage samplers are another type of unattended passive

sampler. Originally devised for suspended sediment

sampling, a stage sampler consists of a series of

bottles attached to a board arranged vertically at

different stages (fig. 10–15). Each bottle has two tubes

at different heights, which creates a siphon when

filling. The disadvantages of this type sampler include

collection of debris, some bias in size of sediment

collected, sample taken near the water surface during

the rising stage, and a filled bottle may have some

mixture with later water (USDA 1979).

A single stage sampler was used by Schwer and

Clausen (1989) to sample the outflow from dairy

milkhouse waste pipes. Tubing was connected to the

milkhouse drainage pipe with an extension collar.

When the pipe flowed, part of the wastewater flowed

through the tubing into a collection bottle. The bottle

had a second tube as an air outlet.
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Figure 10–13 Tipping bucket with passive sampler

Figure 10–14 Coshocton wheel

Figure 10–15 Stage sampler
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(c) Automated samplers

Automated samplers are needed for larger streams and

unattended sampling. These samplers typically allow

programming of sample volume, time or flow interval

between samples, and whether composite or discrete

samples are taken. A summary of some of the older

models available is in the National Park Service’s

publication "Automatic Water Samplers for Field Use"

(NPS 1983). One of the common samplers in use is

shown in figure 10–16. The ISCO sampler also can be

connected to an ISCO flow meter to assist flow proportional sampling.

An inexpensive sampler developed in Canada is a

submerged pipe section that has an opening operated

by a solenoid. At timed intervals, a solenoid opens a

port and allows a sample to enter the pipe. The volume

of sample taken is proportional to the stage of the

stream. The sample is removed by vacuum pump

during a field visit.

The advantage of automated samplers is that they

operate at all times, especially during runoff events,

without attendance. However, these samplers are

expensive and require maintenance.

One of the criticisms of pumping samplers is that a

sample is taken from one point in the stream profile.

Depth integrated intakes have been described by Eads

and Thomas (1983) and McGuire, et al. (1980). These

devices use a float to raise the intake with the stage

and can collect a depth-integrated sample if the intake

is perforated along its entire length (fig. 10–17).

Figure 10–16 ISCO automatic sampler (courtesy Instrumentation Specialties Company)

Float

Sampler

line

Perforated intake

Anchor Streambed

Figure 10–17 Depth-integrating intake
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614.1003 Precipitation

monitoring

The extent of precipitation monitoring varies with the

objectives of the study, but some precipitation monitoring is necessary in most monitoring projects. Precipitation data are useful for event sampling, for computing runoff coefficients for quality assurance programs, and for documenting rainfall conditions relative

to a normal year. For most installations, both

nonrecording and recording rain gages should be used.

The nonrecording gage gives the total amount of

precipitation; whereas the recording rain gage gives

the time of precipitation. The total precipitation obtained by the recording rain gage should be adjusted to

that measured in the nonrecording rain gage. A good

background in precipitation monitoring is described in

Agricultural Handbook 224 (USDA 1979), and guidance

on maintenance is given in Weather Bureau Observing

Handbook No. 2 (USWB 1970).

A variety of nonrecording and recording rain gages

are commercially available. For the nonrecording

gage, the National Weather Service standard 8-inch

(20 cm) gage is most often used (fig. 10–19). For

summer operation, a small amount of oil reduces

evaporation. For winter operation, antifreeze can be

added to the gage. The most common types of recording rain gages are either weighing bucket or tipping

bucket (fig. 10–20). A weighing bucket gage can

collect both rain and snow. For a tipping bucket gage

to operate in the winter, it must be heated. However,

the tipping bucket gage is easily adapted to data

logging.

The location of the gage is important to precipitation

monitoring. Recording and nonrecording gages should

be placed at the same height and be leveled. The gages

must be located in an opening where there is no obstruction within 45° of the lip of the gage. In areas of

snowfall, the use of a windshield (fig. 10–21), such as

an Alter shield, should be considered (USDA 1979). A

windshield would be especially important in an open

installation.

For some water quality studies, more than one gage

may be necessary. The objective of precipitation

monitoring must be considered when designing the

(d) Actuated sampling

Actuated sampling is effective for sampling intermittent streams or for just sampling during storm events.

Several options are available for initiating sampling

during storms. Liquid level actuation has been used to

initiate an ISCO sampling sequence (fig. 10–18). Precipitation sensors can also be used to initiate sampling. Programmable data loggers that also are monitoring stage could be used to initiate sampling. Various

homemade float devices have been used to trip a

switch and initiate samplers.

Figure 10–18 ISCO liquid level actuator (courtesy

Instrumentation Specialties Company)
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Figure 10–19 Standard rain gage

Figure 10–20 Standard rain gage with tipping bucket and funnel gages

Figure 10–21 Standard rain gage altar shield
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precipitation network. Other factors influencing the

number and location of rain gages include topography,

storm type, and the size of the area being studied.

Monitoring in mountainous areas should definitely

consider multiple gages.

Knowledge of the quality of precipitation may be

desired for some water quality studies. For example,

studies examining the mass budget of nitrogen might

consider N inputs in precipitation. Two common

methods for sampling precipitation quality are wetonly collection and bulk precipitation.

Bulk precipitation can be easily sampled using a funnel gage (fig. 10–20) as described by Eaton et al

(1973). A loop in the tubing leading from the funnel to

the collection jug prevents evaporation (fig. 10–22a). A

screen is recommended in the funnel opening to prevent large insects from entering the sample. Although

this type of sampler is inexpensive and easy to construct, it collects any dry deposition that occurs on the

funnel surface as well as rainfall. In addition, the

funnel will not collect snow without bridging unless it

is heated.

A wet-only sample can be obtained from a wet-dry

deposition sampler as used by the NADP (Bigelow

1982). This sampler covers the precipitation bucket

during dry periods thus preventing dry deposition from

contaminating the sample (fig. 10–22b). A precipitation

sensor opens the wet bucket during rainfall. The time

of opening and closing the lid can be recorded on a

rain gage that has a second pen attachment.

Figure 10–22 Gages for precipitation chemistry

Funnel

Loop

Screen

Collection

bottle

a Funnel collector b Wet-dry deposition sampler
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614.1004 Soil water sampling

Sampling the soil water may be useful for determining

nutrient concentrations and possibly mass fluxes in

the vadose zone of soils. A number of sampling techniques have been used to sample soil water. These

samplers generally can be classified as tension and

zero-tension. Tension lysimeters extract a sample of

soil water at some suction and include porous ceramic

cups, plate lysimeters (fig. 10–23a), and capillary-wick

samplers. The zero-tension lysimeters collect gravitational water and have included funnels, pans, and

troughs (fig. 10–23b).

Volumes of water collected in lysimeters are highly

variable; therefore, a large number of lysimeters may

be needed to adequately represent soil solution fluxes

in an area. Water quality concentrations collected by

tension and zero-tension lysimeters are different

(Haines, et al. 1982).

614.1005 Biotic sampling

Biologic sampling includes collection and analysis of

plankton, periphyton, macrophyton, macroinvertebrates, and fish. In addition, several techniques are

available for determining primary production. Although not discussed in this guide, biotic sampling

also may include bioassay.

(a) Plankton

Plankton are organisms that move with the currents.

Two major types of plankton are phytoplankton

(plants) and zooplankton (animals). Knowledge of the

phytoplankton is particularly useful in water quality

monitoring studies because they are good indicators of

nutrient enrichment.

Plankton are influenced by currents, temperature,

light, turbidity, and various chemical variables, such as

salinity, nutrients, and toxics (USEPA 1973). Most of

these factors vary with depth, except in well-mixed

systems.

Figure 10–23 Soil water samplers

a Porous cup and plate lysimeters b Outlet to funnel lysimeters
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Plankton samples can be obtained by net, water bottle,

or with a pump (Schwoerbel 1970). Various plankton

nets are available for sampling, the most common of

which is the Wisconsin plankton net (fig. 10–24a).

Plankton nets collect what is termed net plankton

because some plankton may pass through the net.

These nets are generally used for qualitative analysis.

Plankton also can be collected with a water bottle,

such as a Kemmerer (fig. 10–24b), VanDorn, or Beta

bottle. A quantitative sample of plankton can be obtained because the volume of water collected is

known. Water bottles obtain a sample of plankton

from a particular location and layer; therefore, the

number of samples needed is subject to the variability

in sampling (ch. 9).

Plankton samples collected with a pump can be obtained from any depth and of any volume. However,

the pump tubing should be cleaned between samples,

and the pump may break apart some plankton.

Once collected, plankton should be preserved and

enumerated using standard techniques (USEPA 1973).

In some cases chlorophyll analysis should be performed on the plankton as an indicator of the biomass.

(b) Periphyton

The periphyton are organisms that mostly are attached

to underwater substrates, such as rocks or macrophytes. These organisms may be predominant in

shallow and running bodies of water. They also indicate water quality conditions.

Artificial substrates are used to quantitatively collect

periphyton samples. They include glass microscope

slides or the Hester-Dendy sampler (fig. 10–24c).

Samplers are left in the field for about 2 weeks and

then removed. Zooplankton and macroinvertebrates

may graze on the periphyton, which will result in an

underestimate of periphyton growth. The resulting

samples should be preserved and enumerated. Biomass analysis is often used to express the amount of

periphyton present.

(c) Macrophyton

Large aquatic plants are termed macrophyton. In many

cases these plants are what many perceive to be the

water quality problem. Macrophytes are influenced by

light (turbidity), nutrients, and sediment. Qualitatively,

macrophytes may be identified to species and classified as to the relative cover. Quantitative sampling

might involve small plots with analysis of the number

of stems or the biomass. Air photography often is

used to delineate boundaries of plant communities.

(d) Macroinvertebrates

Aquatic macroinvertebrates are animals that are large

enough to be seen with the unaided eye and include

insects, mollusks, worms, and crustaceans. Their

presence is seasonally-dependant and influenced by

type of substrate, light, oxygen content, water velocity,

and various chemical constituents. They also are

susceptible to various stressors. Because their locations vary, proper sampling is important. Quantitative

sampling involves determining the numbers or biomass of macroinvertebrates per unit area. This type of

information is often used to calculate an index, such

as Beck’s Biotic Index (Terrell & Perfetti 1989).

Samples are collected using such devices as the Surber

sampler (fig. 10–24d). These samplers are difficult to

use in some habitats, such as rocky substrates.

Qualitative samples of macroinvertebrates also are

taken. Such sampling allows determining what is

present and the diversity of the community. Samples

are collected using a wide variety of devices, including

sediment samplers in deep water, such as the Ekman

or Peterson dredge (fig. 10–25a & b). These types of

samplers have several disadvantages (USEPA 1973).

Artificial substrates using baskets of rocks also have

been used to collect macroinvertebrates. Drift nets are

most commonly used to qualitatively assess the

macroinvertebrate community. These nets come in

various shapes (fig. 10–25c). Collected samples should

be preserved before identification (Klemm et al. 1990).

The EPA's Rapid Bioassessment Protocols (RBP) are

methods for assessing the biotic condition of streams

in comparison to reference stations (Plafkin et al.

1989). Several indices are recommended using RBP

level III.
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10–20 (450–VI–NWQH, September 2003)

Figure 10–24 Biotic samplers (courtesy Wildlife Supply Company)

a Wisconsin plankton net b Kemmerer water bottle

d Surber sampler

(e) Fish

Water quality influences fish species, abundance, and

health. Certain species of fish are sensitive to pollutants and serve as indicators of water quality. The

species, abundance by species, size, growth rate,

condition, reproductive success, and disease are of

interest where fish are used in biomonitoring (USEPA

1973). Sampling of fish has been classified as either

active or passive. Active sampling includes electrofishing and seines. Passive collection includes gill nets

and trap nets. The various methods used to collect fish

samples usually result in somewhat different species

being collected. Fish are not located randomly

throughout the water body; therefore, sampling must

be adjusted.

The Rapid Bioassessment Protocol level V for fish

describes methods for electrofishing and calculation

of the Index of Biotic Integrity (IBI) and other metrics

(Plafkin, et al. 1989).

c Hester-Dendy sampler
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National Water Quality Handbook

Chapter 10 Station Type

(450–VI–NWQH, September 2003) 10–21

Figure 10–25 Biotic and sediment samplers (courtesy Wildlife Supply Company)

a Ekman dredge c D-type drift net

b Peterson dredge
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Chapter 10 Station Type

10–22 (450–VI–NWQH, September 2003)

614.1006 Sediment sampling

The sampling of sediment varies between running

water and standing water. In running water, sediment

has been divided into suspended sediment and

bedload. Suspended sediment is carried by the water

above the bed of the stream (USGS 1977). Bedload

sediment is heavier than suspended sediment and

moves along the bed of the stream.

Sampling of suspended sediment was previously

described in this chapter. Suspended sedimentbedload sediment rating curves can be developed to

estimate bedload transport. Bedload sampling is

conducted by using bedload traps in the streambed or

net samplers of a certain height, or it can be conducted by measuring changing cross sections in the

stream.

In edge-of-field runoff, sediment is best sampled in

some type of proportional sampler, such as the

Coshocton wheel. Other bedload samplers have been

developed for use with flumes. They consist of a slot

across the flume that traps the bedload.

Sampling of sediment in standing water, such as lakes

and ponds, generally is conducted with a type of

coring device. The type of corer used varies with the

depth of the water and the thickness and type of

substrate. An example of a hand-held corer is shown in

figure 10–26. Other types of corers include piston or

drive samplers for deeper water.

In some cases lake sediment samples are obtained by

diving, so that the sample remains undisturbed. The

force of a sampler hitting the sediment may disturb the

upper organic deposits, thereby biasing the sample.

Sediment samples collected from standing water

bodies are often analyzed for particle sizes, organic

matter content, chemical content, dry weight, and

volume.

Figure 10–26 Hand-held sediment corer (courtesy Wildlife

Supply Company)
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Chapter 10 Station Type

(450–VI–NWQH, September 2003) 10–23

614.1007 References

Bigelow, D.S. 1982. NADP instruction manual. Site

operation. Natl. Atmos. Deposition Program, Nat.

Resour. Ecol. Lab., CO State Univ., Ft. Collins.

Bodhaine, G.L. 1968. Measurement of peak discharge

at culverts by indirect methods. United States

Geological Survey, TWI 3-A3, 60 pp.

Buchanan, T.J., and W.P. Somers. 1969. Discharge

measurement at gaging stations. Book 3, chap.

A8 in Techniques of water-resources investigations of the United States Geological Survey.

Buchanan, T.J., et al. 1968, Stage measurements at

gaging stations. United States Geological Survey,

TWI 3-A7, 28 pp.

Carter, R.W., et al. 1968. General procedure for gaging

streams. United States Geological Survey, TWI 3-

A6, 13 pp.

Chow, T.L. 1976. A low-cost tipping bucket flowmeter

for overland flow and subsurface stormflow

studies. Can. J. Soil Sci. 56: 197-202.

Coote, D.R., and P.J. Zwerman. 1972. A conveniently

constructed divisor for splitting low water flows.

Soil Sci. Soc. Amer. Proc. 36:970-971.

Dressing, S.A., J. Spooner, J.M. Kreglow, E.O. Beasley,

and P.W. Westerman. 1987. Water and sediment

sampler for plot and field studies. J. Environ.

Qual. 16(1):59.

Eads, R.E., and R.B. Thomas. 1983. Evaluation of a

depth proportional intake device for automatic

pumping samplers. Water Resour. Bull. 19(2):289-

292.

Eaton, J.S., G.E. Likens, and F.H. Bormann. 1973.

Throughfall and stemflow chemistry in a northern hardwood forest. J. Ecol. 61:495-498.

Geib, H.V. 1933. A new type of installation for measuring soil and water losses from control plots. J.

Amer. Soc. Agron. 25(7):429-440

Grant, D.M. 1979. ISCO open channel flow measurement handbook. Instrumentation Spec. Co.,

Lincoln, NE.

Guy, H.P. 1969. Laboratory theory and methods for

sediment analysis. United States Geological

Survey, TWI 5-C1, 58 pp.

Guy, H.P., et al. 1970. Field methods of measurement

of fluvial sediment. United States Geological

Survey, TWI 3-C2, 59 pp.

Gwinn, W.R., and D.A. Parsons. 1976. Discharge equations for the HS, H, and HL flumes. J. Hydraul

Div., Amer. Soc. Agric. Eng. 102:73-88.

Haines, B.L., J.B. Waide, and R.L. Todd. 1982. Soil

solution nutrient concentrations sampled with

tension and zero-tension lysimeters: Report of

discrepancies. Soil Sci. Soc. Amer. J. 46:658-661.

Johnston, C .N. 1942. Tilt buckets for measuring runoff and erosion. Agric. Engr. 23:161-162.

Kennedy, E.J. 1985. Discharge ratings at gaging stations. United States Geological Survey, TWI

3-A10, 59 pp.

Kennedy, E.J. 1990. Levels at streamflow gaging stations. United States Geological Survey, TWI

3-A19, 27 pp.

Kilpatrick, F.A., et al. 1983. Use of flumes in measuring

discharge. United States Geological Survey, TWI

3-A14, 46 pp.

Kilpatrick, F.A., et al. 1985. Measurement of discharge

using tracers. United States Geological Survey,

TWI 3-A16, 52 pp.

Klemm, D.J., P.A. Lewis, F. Fulk, and J.M. Lazorchak.

1990. Macroinvertabrate field and laboratory

methods for evaluating the biological integrity of

surface waters. Office of Research and Development, Washington, DC, EPA/600/4-90/030.

Kohnke, H., and R.B. Hickok. 1943. An automatic

aliquot runoff sampler. Soil Sci. Soc. Amer. Proc.

8:444-447.
Part 614

National Water Quality Handbook

Chapter 10 Station Type

10–24 (450–VI–NWQH, September 2003)

Laenen, A. 1985. Acoustic velocity meter systems.

United States Geological Survey, TWI 3-A17, 38

pp.

McGuire, P.E., T.C. Daniel, D. Stoffel, and B. Andraski.

1980. Sample intake position and loading rates

from nonpoint source pollution. Envir. Mgmt.

4(1):73-77.

National Park Service, Water Resources Field Support

Laboratory. 1983. Automatic water samplers for

field use. U.S. Dept. of the Int. Natl. Park Serv.,

Water Resourc. Field Sup. Lab. Rep. No. 83-1,

Fort Collins, CO.

Plafkin, J.L., M.T. Barbour, K.D. Porter, .S.K. Gross,

and R.M. Hughes. 1989. Rapid bioassessment

protocols for use in streams and rivers: Benthic

macro-invertebrates and fish. U.S. EPA EPAl444/

4-89001, Off. of Water. Washington, DC.

Replogle, J.A., and A.J. Clemmens. 1981. Measuring

flumes of simplified construction. Trans. Amer.

Soc. Agric. Eng. pp. 362-366.

Russell, M.B. 1945. A portable runoff measuring device. J. Amer. Soc. Agron. 37(8):589-594.

Schulz, E.F. 1976. Problems in applied hydrology.

Water Resourc. Publ., Fort Collins, CO.

Schwer, C.B., and J.C. Clausen, 1989. Vegetative filter

treatment of dairy milkhouse wastewater. J.

Environ. Qual. 18(4):446-451.

Schwoerbel, J. 1970. Methods of hydrobiology.

Pergamon Press, New York, NY.

Skougstad, M.W., et al. 1979. Methods for determination of inorganic substances in water and fluvial

sediments. United States Geological Survey, TWI

5-A1, 626 pp.

Smith, C.N., D.S. Brown, J.D. Dean, R.S. Parrish, R.F.

Carsel, and A.S. Donigian, Jr. 1985. Field agricultural runoff monitoring (FARM) manual. EPA/

600/385/043, Environ. Res. Lab., Athens, GA.

Terrell, C.R., and P.B. Perfetti. 1989. Water quality

indicators guide: Surface waters. USDA Soil

Conserv. Serv. SCS-TP-161, Washington, DC.

United States Department of Agriculture. 1979. Field

manual for research in agricultural hydrology.

Agric. Handb. 224, Washington, DC.

United States Department of Interior, Bureau of Reclamation. 1977. Water measurements manual. 2nd

edition.

United States Environmental Protection Agency. 1973.

Biological field and laboratory methods for

measuring the quality of surface waters and

effluents. USEPA 670/4-73-001. Off. Res. & Dev.,

Cincinnati, OH.

United States Geological Survey. 1977. Methods for

collection and analysis of aquatic biological and

microbiological samples. Edited by P.E. Greeson,

et al., TWI 5-A4, 332 pp.

United States Geological Survey. 1977. National handbook of recommended methods for water-data

acquisition. Chapter 1: Surface water, Off. Water

Data Coord., Reston, VA.

United States Geological Survey. 1987. Methods for the

determination of organic substances in water and

fluvial sediments, edited by R.L. Wershaw, et al.,

TWI 5-A3, 80 pp.

United States Weather Bureau. 1970. Weather Bureau

observing handbook No. 2. Substation observations. U.S. Dep. Com., Environ. Sci. Serv. Admin.,

Silver Spring, MD.

World Health Organization. 1978. Water quality surveys—A guide for the collection and

interpretation of water quality data. IHD-WHO

Working group on water quality. UNESCO/WHO,

Geneva, Switzerland.
(430–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resource

Conservation

Service

Part 614

National Water Quality Handbook

Chapter 11 Sample Collection

and Analysis
(430–VI–NWQH, September 2003) 11–i

Chapter 11 Sample Collection

and Analysis

Contents: 614.1100 Introduction 11–1

614.1101 Sample Collection 11–1

614.1102 Sample preservation and transport 11–4

614.1103 Methods of laboratory analysis 11–5

614.1104 Field test kits 11–5

614.1105 Quality assurance 11–6

614.1106 Quality control 11–6

614.1107 Quality assessment 11–7

(a) Precision ...................................................................................................... 11–7

(b) Accuracy ...................................................................................................... 11–8

(c) Representativeness ..................................................................................... 11–8

(d) Comparability ............................................................................................. 11–8

(e) Completeness .............................................................................................. 11–8

614.1108 Sample custody procedures 11–9

614.1109 Calibration procedures and preventative maintenance 11–9

614.1110 Performance and systems audits 11–11

(a) Calculation ................................................................................................ 11–11

614.1111 Corrective action 11–11

614.1112 Field QA 11–12

(a) Field equipment ........................................................................................ 11–12

(b) Field logs ................................................................................................... 11–12

(c) Field QC samples ...................................................................................... 11–13

614.1113 References 11–13
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11–ii (430–VI–NWQH, September 2003)

Tables Table 11–1 Recommended methods for sample collection 11–2

and preservation

Table 11–2 Water quality variables for which field test kits 11–5

are available

Table 11–3 Partial list of manufacturers of field test kits 11–5

Table 11–4 Components of a quality control program 11–6

Table 11–5 Components of a quality assessment program 11–7

Table 11–6 Quality control samples 11–7

Figures Figure 11–1 Outline of a quality assurance plan 11–6

Figure 11–2 Laboratory chain of custody sheet 11–10

Figure 11–3 Example daily field log 11–12
(430–VI–NWQH, September 2003) 11–1

Chapter 11 Sample Collection and Analysis

614.1100 Introduction

Obtaining high quality data requires following appropriate techniques for obtaining water quality samples

and analyzing them for their constituents. Equally

important is the need to describe in detail how the

work is being conducted so that others can duplicate

the information. This chapter describes suggested

techniques for collecting a water sample, and recommended quality assurance and quality control procedures for both the lab and the field. Two references

may be helpful for volunteer monitoring (US EPA

1990, Simpson 1991)

614.1101 Sample collection

Different sample collection procedures should be

followed depending upon the type of sample (grab,

automatic) and whether the system is a lake, stream,

or ground water. Generally, a bottle used for a grab

sample should be rinsed with the sample water two or

three times before filling unless the bottle contains a

preservative, in which case there should be no rinsing

(APHA 1989). If samples are collected from pipes

under pressure, make sure that the system has been

flushed for a sufficient period to guarantee that new

water is being sampled. Bacteria samples are collected

in sterilized bottles.

Collection of samples from wells can be complicated.

Water within the well may be stagnant and not representative of surrounding ground water. The well

should be purged for a sufficient amount (3 to 10 wellbore volumes) to ensure that the sample is representative of the ground water. More than 5 minutes may be

required to remove over 80 percent of the well-bore

volume when pumped at 1.3 gpm. Some recommend

that well purging should be conducted at the rate of

well replenishment. This would not be the case for

well-mixed aquifers. Sampling for volatile organics

may require special precautions and possibly no purging.

Sampling of volatile substances requires special sampling equipment in wells. The release of gases during

pumping can change the pH of the water and. therefore, the solubility of metals. Oxidation of the sample

during pumping can influence organics, sulfur, iron,

ammonium, and manganese (Driscoll 1986).

Generally, all samples should be collected so that the

bottle is completely full. This reduces volatilization

losses. An exception to this would be if the sample

was to be frozen, in which case room for expansion

upon freezing should be left in the container. Sampling

of toxic substances require extra precautions, including gloves, coveralls, aprons, eye protection, and in the

case of toxic vapors, a respirator may be necessary.
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Table 11–1 Recommended methods for sample collection and preservation (USEPA 1983)

Measurement Vol. req. Container Preservative Maximum holding time

(mL) P=plastic; G=glass

Physical properties

Color 50 P,G1/ Cool, 4 °C 48 hrs

Conductance 100 P,G Cool, 4 °C 28 days

Hardness 100 P, G HNO3 to pH < 2 6 mos

Odor 200 G only Cool, 4 °C 24 hrs

pH 25 P,G None req. Analyze immediately

Residue

 Filterable 100 P,G Cool, 4 °C 7 days

 Nonfilterable 100 P,G Cool, 4 °C 7 days

 Total 100 P,G Cool, 4 °C 7 days

 Volatile 100 P,G Cool, 4 °C 7 days

Settleable matter 1,000 P,G Cool, 4 °C 18 hrs

Temperature 1,000 P,G None req. Analyze immediately

Turbidity 100 P,G Cool, 4 °C 48 hrs

Metals

Dissolved 200 P,G Filter on site 6 mos

HNO3 to pH <2

Suspended 200 Filter on site 6 mos

Total 100 P,G HNO3 to pH <2 6 mos

Chromium 200 P,C Cool, 4 °C 24 hrs

Mercury dissolved 100 P,G Filter 28 days

HNO3 to pH <2

Total 100 P G HNO3 to pH <2 28 days

Inorganics, nonmetallics

Acidity 100 P,G Cool, 4 °C 14 days

Alkalinity 100 P,G Cool, 4 °C 14 days

Bromide 100 P,G None req 28 days

Chloride 50 P,G None req 28 days

Chlorine 200 P,G None req Analyze immediately

Cyanides 500 P,G Cool, 4 °C 14 days

NaOH to pH >12

0.6g ascorbic acid6

Fluoride 300 P,G None req 28 days

Iodide 100 P,G Cool, 4 °C 24 hrs

The quantity of sample to collect is dependent upon

the type of analyses to be conducted. Suggested volumes are given in table 11–1. The total volume should

include a summation of the recommended volumes

plus amounts for the quality assurance program. In

addition, the analysis of a sample may need to be

repeated. Therefore, it is generally recommended that

the total recommended volume be doubled (Shelley

1977).
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Chapter 11 Sample Collection and Analysis

(430–VI–NWQH, September 2003) 11–3

Table 11–1 Recommended methods for sample collection and preservation (USEPA 1983)—Continued

Measurement Vol. req. Container Preservative Maximum holding time

(mL) P=plastic; G=glass

Inorganics, nonmetallics (continued)

Nitrogen

 Ammonia 400 P,G Cool, 4 °C 28 days

H2SO4 to pH <2

 Kjeldahl, total 500 P,G Cool, 4 °C 28 days

H2SO4 to pH <2

 Nitrate plus Nitrite 100 PG Cool, 4 °C 28 days

H2SO4 to pH <2

 Nitrate 100 P,G Cool, 4 °C 48 hrs

 Nitrite 50 P,G Cool, 4 °C 48 hrs

Dissolved oxygen

 Probe 300 G bottle & top None req. Analyze immediately

 Winkler 300 G bottle & top Fix on site 8 hrs

and store in dark

Phosphorus

 Ortho-phosphate 50 P,G Filter on site 48 hrs

 Dissolved Cool, 4 °C

 Hydrolyzable 50 P,G Cool, 4 °C 28 days

H2SO4 to pH <2

 Total 50 P,G Cool, 4 °C 28 days

H2SO4 to pH <2

 Total dissolved 50 P,G Filter on site 24 hrs

Cool, 4 °C

H2SO4 to pH <2

silica 50 P only Cool, 4 °C 28 days

sulfate 50 P,G Cool, 4 °C 28 days

sulfide 500 P,G Cool, 4 °C 7 days

add 2 mL zinc

acetate plus NaOH

to pH >9

sulfite 50 P,G None req. Analyze immediately

Organics

BOD 1,000 P,G Cool, 4 °C 18 hrs

COD 50 P,G Cool, 4 °C 28 days

H2SO4 to pH <2

Oil & grease 1,000 G only Cool, 4 °C 28 days

H2SO4 to pH <2

Organic carbon 25 P,G Cool, 4 °C 28 days

H2SO4 / HCl to pH < 2

Phenolics 500 G only Cool, 4 °C 28 days

H2SO4 to pH <2

MBAS 250 P,G Cool, 4 °C 48 hrs

NTA 50 P,G Cool, 4 °C 24 hrs
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Chapter 11 Sample Collection and Analysis

11–4 (430–VI–NWQH, September 2003)

614.1102 Sample preservation and transport

Once a sample is collected, it has the opportunity to

change its composition through chemical, physical,

and biological processes. Some changes may not be

preventable, so rapid analysis is recommended in

those situations (USEPA 1983).

Examples of physical changes include settling of

solids, adsorption of certain cations on container

walls, and loss of dissolved gases. Chemical changes

could include precipitation, dissolution from sediments, complexation with other ions, and changes in

valence state. Biological reactions could result in both

the uptake and release of certain constituents. Microbial activity may change the species of nitrogen

present (APHA 1989).

Preservation techniques are aimed at slowing biological activity, hydrolysis, volatility, and absorption. The

primary preservation methods are acidification, refrigeration, filtration, and preventing light from reaching

the sample (USEPA 1983; APHA 1989). Recommended

preservation methods for most chemical properties of

water are summarized in table 11–1. The appropriate

sample volume, type of sampling container, and maximum holding time also are listed. A similar listing is

given in the "Standard methods for the examination of

water and wastewater" (APHA 1989).

Using a sample bottle that has the preservative already

added may be useful for composite sampling. The

sample becomes preserved immediately upon collection. Preservation of biological samples is also important (Klemm, et al. 1990). Without preservation predation within the sample may occur or the specimens

may degrade. Generally, adding an equal volume of 95

percent ethanol to the sample results in an ethanol

strength of 70 percent, which is adequate to preserve

the sample (USEPA 1973). Plankton can be preserved

with Lugol's solution (APHA 1989).

The sample container is also important. Glass containers may leach sodium and silica, and plastic containers

may sorb organics (APHA 1989). Certain pesticides

may adsorb to silicone rubber and tygon, but not highdensity polyethylene or acrylic plastic (Topp and

Smith 1992). Teflon and stainless steel are appropriate

containers in certain cases.

Transportation to the laboratory should be direct.

Transport should be done following some methods of

preservation, such as cooling and keeping in the dark.

Using dry ice for cooling is not recommended (APHA

1989).
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Chapter 11 Sample Collection and Analysis

(430–VI–NWQH, September 2003) 11–5

614.1103 Methods of laboratory analysis

It is not within the scope of this handbook to describe

methods of laboratory analysis for water quality variables. Two important references on this subject are

Standard Methods for the Examination of Water and

Wastewater (APHA 1989) and Methods for Chemical

Analysis of Water and Wastes (USEPA 1983).

614.1104 Field test kits

Many test kits are available for field analysis of a wide

variety of water quality variables (tables 11–2 & 11–3).

These kits range in level of sophistication and price.

Field test kits are not considered as accurate as laboratory analyses, but may be useful in many situations

(Kunkle & Ricketts 1984).

Kits function in one of three ways.

• Color comparator kits use the addition of a

reagent to a sample, which results in a color

development. The intensity of the color is compared to a color wheel or color tubes.

• Colorimeter and spectrophotometer kits use

color development, which is read in battery

powered colorimeters. Colorimeter kits are the

most expensive kit.

• Titration kits use the addition of a reagent until

a color change occurs.

Electric meters for field pH, conductivity, and dissolved oxygen are also available.

Table 11–3 Partial list of manufacturers of field test kits

Manufacturers

Bausch and Lomb (716) 338-8317

CHEMetrics, Inc. (703) 788-9026

Ecologic Instrument (516) 567-9000

EM Science (609) 423-6300

Hach Company (303) 669-3050

Hellige, Inc. (516) 222-0300

In-Situ, Inc. (307) 742-8213

Kahl Scientific (619) 444-2158

LaMotte Chemical (301) 778-3100

Millipore Corp. (617) 875-2050

Soiltest, Inc. (312) 869-5500

Solomat (203) 849-3111

Spectrum Technologies, Inc. (815) 436-4440

Taylor Chemicals, Inc. (301) 472-4776

Table 11–2 Water quality variables for which field test

kits are available (Kunkle & Ricketts 1984)

Water quality variables

Alkalinity, hardness

Ag, Al, Ba, Ca, Cd, Co, Cr, Cu,

Fe, Hg, K, Mg, Mn, Na, Ni, Pb, Zn

Ammonia, nitrate, nitrite

Total phosphorus, ortho-phosphate

Acidity, COD, color, pH, salinity

Dissolved oxygen, carbon dioxide

Turbidity, dissolved solids

Arsenic

Bromine

Chloride, chlorine

Cyanide chromate

DEEA

Detergents

EDTA/NTA

Fluoride

Formaldehyde

Gasoline

Hydrogen peroxide

Hydrogen sulfide

Iodine

Lignin

Molybdate

Ozone

pH

Phenol

Silica

Sulfate, sulfide

Tannin

Temperature
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National Water Quality Handbook

Chapter 11 Sample Collection and Analysis

11–6 (430–VI–NWQH, September 2003)

Figure 11–1 Outline of a quality assurance plan

(USEPA 1988)

614.1105 Quality assurance

Quality Assurance (QA) is the total integrated program

for assuring the reliability of monitoring and measurement data (USEPA 1988). Quality assurance programs

should allow determining statistical limits of confidence in the data (Taylor 1984). The program also

should document the procedures that are followed

(Dillaha, et al. 1988). Quality assurance is composed of

quality control and quality assessment. Quality Control

(QC) refers to activities conducted to provide high

quality data (Lawrence and Chau 1987). Quality assessment refers to techniques used to evaluate the effectiveness of the program (Taylor 1984).

An overall outline for a quality assurance plan is given

in figure 11–1.

1. Cover page

2. Table of contents

3. Project description

a. Objectives and scope

b. Data usage

c. Design and rationale

d. Monitoring parameters and collection

frequency

e. Parameter table

4. Project organization and responsibility

5. Data quality requirements

a. Precision

b. Accuracy

c. Representativeness

d. Comparability

e. Completeness

6. Sampling and laboratory procedures

7. Sample custody procedures

8. Calibration procedures and preventive

maintenance

9. Documentation, data reduction and reporting

10. Data validation

11. Performance and system audits

12. Corrective action

13. Reports

14. Literature cited

614.1106 Quality control

Table 11–4 summarizes the major components of a

quality control program. Good Laboratory Practices

(GLPs) refer to general practices, such as glassware

cleaning and preparation. Standard Operating Procedures (SOPs) are recipes for conducting analyses.

These would include standard methods (APHA 1989)

and approved methods (USEPA 1983). SOPs would

also exist for sample handling (chain of custody

records) and calibration and maintenance procedures.

Education and training refer to procedures used to

support and verify the training of sampling and analysis personnel. This is especially important for safety

training. Supervision includes the monitoring and

review of techniques and data to allow for timely

corrective actions.

Table 11–4 Components of a quality control program

(after Taylor 1984)

Good Laboratory Practices (GLPs)

Standard Operating Procedures (SOPs)

Education/training

 sample custody procedures

 calibration and maintenance

Supervision
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Chapter 11 Sample Collection and Analysis

(430–VI–NWQH, September 2003) 11–7

614.1107 Quality assessment

Quality assessment allows feedback on how well the

quality control program is operating. Table 11–5 summarizes the components of a quality assessment

program, and table 11–6 shows the indicators of quality data. Indicators of data quality include:

• precision

• accuracy

• representativeness

• comparability

• completeness

A description of each indicator follows.

Table 11–5 Components of a quality assessment program

Internal

Duplicate samples

Standard additions (spikes)

Tests of sampling frequency

Tests of reason with comparable data

Missing analysis records

Standard curves

Internal audit

External

Exchange sample with other lab

External known materials

External audit

(a) Precision

Precision is a measure of the closeness by which

repeated measures of a given sample agree with each

other. The Relative Standard Deviation (RSD) of

duplicate samples provides the overall precision of the

study, including random sampling errors and errors

associated with sample preparation and analysis.

(1) Frequency

Duplicate analysis should be performed for every 20th

sample collected for which there is sufficient quantity

for splitting or at least one per analytical run.

(2) Calculation

The relative standard deviation, which also is the

coefficient of variation, between the duplicates can be

calculated as follows:

 RSD S

X

= ×100 [11–1]

where:

 S = standard deviation

X = the mean

(3) Acceptance

An RSD of more than 10 percent could require notification of the onsite QA officer.

Table 11–6 Quality control samples

Indicator Sample type Frequency Measure Acceptance criteria (%)

Precision Duplicate 1/20 RSD 10

Accuracy Spike 1/20 % recovery 90-110

Representative Multiple Initial n ±20

Completeness All Annual % missing <10

Performance audit EPA known 4/yr % recovery 90-110
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(b) Accuracy

Accuracy (bias) is the degree of agreement between

measured and true values. The percentage recovery of

known standard additions to a sample provides the

measure of accuracy for the study. The amount added

should be sufficient to double the concentration.

(1) Frequency

Every 20th sample collected in sufficient quantity for

splitting should be spiked.

(2) Calculation

Chemical recovery is calculated as follows:

 % Recovery= A

B C+

×100 [11–2]

where

A = measured concentration of spiked sample

B = measured concentration of unspiked sample

C = concentration of known addition

(3) Acceptance

A recovery of 90 to 110 percent is considered acceptable. Recovery less than this limit requires corrective

action.

(c) Representativeness

Representativeness refers to how well the results

represent the sample and how well the samples represent the population. Representativeness can be assessed by examining the variability among samples.

For example, to determine whether individual composite samples are sufficient to develop a weekly composite, the required number of samples could be calculated. Methods for calculating the number of samples

are presented in chapter 9 and repeated here.

(1) Calculation

Compute the required number of samples as follows:

 n

t S

d

>

2 2

2 [11–3]

where:

n = number of samples

t = students 't' at a given confidence level

S = sample standard deviation

d = acceptable difference from the mean

(d) Comparability

Certain data from the study can be compared to results obtained from other similar studies.

(e) Completeness

Completeness can be measured as the percentage of

total samples collected that were analyzed. Sufficient

water volumes should be collected to allow re-analysis

of a sample if beyond a standard curve or if lost in a

laboratory accident. A measure of completeness is the

percentage of missing data obtained in the study. The

number of samples needed is governed by the study

design.
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(430–VI–NWQH, September 2003) 11–9

614.1108 Sample custody

procedures

Each sample should be dated and coded according

to site, sample type, station number, and sample

sequence. The actual sample containers should be

labelled with a sample number for identification.

Transfer of sample custody takes place upon delivery

of samples to the laboratory. At the time of delivery,

the person delivering the samples signs over custody

to a laboratory person receiving the samples. This

transaction is recorded on forms for that purpose, and

the records are maintained in the laboratory

(fig. 11–2).

As part of the process of sample receipt, each sample

is assigned a unique identification number that can

include specific information on location, date, composite, and yearly sequence. For example, a sample numbered 10-011891-24-566 represents a sample taken at

station 10, on January 18, 1991, a 24-hour composite,

and is the 566th sample received by the laboratory in a

calendar year. This final number, representing the

sample received in a year, serves as the shorthand

sample number and is used for overall tracking in the

laboratory.

The sample number should be used in all laboratory

books to identify the sample. Sample transfer forms

may be needed for some studies where samples are

sent to other labs. Some agencies employ the practice

of prelabeling bottles before they go to the field.

614.1109 Calibration procedures and preventative

maintenance

The primary pieces of laboratory equipment should be

described in a quality assurance plan together with the

calibration and maintenance procedures and schedules. Standard curves, using from 8 to 10 standards

including blanks, should be developed the same day of

analysis for most analyses. Each analytical run should

include a set of standards.

The maintenance schedule should be included in a

quality assurance plan. The options available if equipment breakdown occurs should be described.
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11–10 (430–VI–NWQH, September 2003)

Figure 11–2 Laboratory chain of custody sheet

Lab

No.

Sample

Description

Procedure completed (indicate with date)

Acid Filter Digest TKN NH3 NO3 TP CL TSS

Remarks:

Custody sheet for samples collected on (date)____________

Relinquished by___________

Received by_____________

Samples held until:

(+ 28 days)
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Chapter 11 Sample Collection and Analysis

(430–VI–NWQH, September 2003) 11–11

614.1110 Performance and

systems audits

The project should be subject to both performance

audits and systems audits. The performance audit

could consist of unknown samples submitted quarterly

to the laboratory.

(a) Calculation

Reported results are compared to known values. The

percentage recovery for the known is calculated as:

 % Recovery= R T

T

− ×100 [11–4]

where

R = reported value

T = true value

Performance within ± 25 percent should be acceptable. Performance beyond ± 25 is considered an outof-control situation calling for corrective action.

Project supervisors should make unscheduled performance audits of all laboratory personnel to detect any

deviations from standard operating procedures. A

checklist of the audit should remain on file in the

supervisor’s office.

A systems audit consists of an onsite review of the

entire project.

614.1111 Corrective action

Data quality assurance procedures should be designed

to ensure that project personnel are able to quickly

identify and correct analytical problems. Data failing

to meet quality control requirements should be subject

to repeated analysis where sufficient volume exists to

retest the sample.
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Chapter 11 Sample Collection and Analysis

11–12 (430–VI–NWQH, September 2003)

614.1112 Field quality

assurance

(a) Field equipment

Calibration of field equipment is necessary. In situ

analysis of temperature, pH, dissolved oxygen, conductivity, and other ions use field instruments requiring maintenance and calibration. Some instruments,

such as pH and dissolved oxygen meters, require daily

or more frequent calibration. A record should be

maintained of all calibrations.

Stage recorders should be calibrated against a permanent outside staff gage at every visit. The staff gages

should be surveyed to a benchmark at least annually.

Precipitation gages should be calibrated annually, and

checked weekly. Well pressure transducers should be

calibrated when they do not equal staff gage readings.

Well top elevations should be surveyed annually to a

temporary benchmark. Stage-discharge relationships

should be constructed during the first year of the

project by at least 15 discharge measurements using

the velocity-area method. Annually, the stage-discharge relationship should be checked with at least

five ratings. Annual runoff coefficients should be

calculated as the percentage of precipitation that left

the watershed as discharge. These coefficients could

be compared to runoff coefficients calculated from

U.S. Geological Survey water resources data collected

from other watersheds in the same general area of the

state.

(b) Field logs

Daily field logs should be kept for each field visit.

These logs record operating status, calibration checks,

manual readings, and the name of the field visitor.

They are often 1-page sheets (fig. 11–3) and are tailored to the individual project. A personal notebook

(survey book) maintained by each field worker may be

useful. Each field visit is recorded and additional notes

are made on work to be done.

Figure 11–3 Example daily field log

Station 1 Station 2 Station 3 Comments

Time of visit

Weir clear/chop

Solar panels Ok?

Batterries Ok?

Sample volume Ok?

Intake line Ok?

Dessicant Ok?/replace

Line in bottle?

Sampler on?

Recorder stage (ft)

Staff stage (ft)

Point gage (ft)

Display

Enough paper?

Daily Field Log

Checked

Date

General Sampler Stage
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Chapter 11 Sample Collection and Analysis

(430–VI–NWQH, September 2003) 11–13

(c) Field quality control samples

The four types of samples needed to assess field

quality control include (Burger 1987):

• Field duplicate—Samples collected simultaneously at a location used to determine the

variability associated with sample collection.

• Trip blank—Sample container taken to field and

filled with distilled or deionized water and returned. This sample assesses contamination

during transport or storage.

• Sampler blank—Sample obtained by passing

deionized water through a nondedicated sampler,

such as a portable pump. This blank is used to

test contamination by a sampler.

• Filtration blank—Sample collected by field

filtering apparatus using deionized water. This

blank tests contamination by a filter and apparatus.

(d) Field chain of custody

The sample custody procedures actually begin in the

field. Proper labeling of sample bottles is critical.

Some laboratories use pre-numbered bottle labels

(Burger 1987).

614.1113 References

American Public Health Association. 1989. Standard

methods for the examination of water and wastewater. 17th Ed., American Public Health Assoc.,

Washington, DC.

Burger, Robert M. 1987. Design and implementation of

a successful quality control program for ground

water sampling events. Symp. on monitoring,

modeling, and mediating water quality, pp. 49-58,

Amer. Water Resour. Assoc.

Dillaha, T.A., S. Mostaghimi, C.D. Eddleton, and P.W.

McClellan. 1988. Quality control/quality assurance for water quality monitoring. Amer. Soc.

Agric. Eng. Pap. No. 88-2648, St. Joseph, MI.

Driscoll, F.G. 1986. Ground water and wells. 2nd. Ed.

Johnson Div., St. Paul, MN.

Klemm, D.J., P.A. Lewis, F. Fulk, and J.M. Lazorchak.

1990. Macroinvertabrate field and laboratory

methods for evaluating the biological integrity of

surface waters. Office of Research and Development, Washington, DC, U.S. Environmental

Protection Agency/600/4-90/030.

Kunkle, S.H., and T.E. Ricketts. 1984. Portable kits for

water chemistry reconnaissance in the field.

WRFSL Rep No. 84-2, Water Resour. Field Sup.

Lab., Natl. Park Serv., Fort Collins, CO.

Lawrence J., and A.S.Y. Chau. 1987. Quality assurance

for environmental monitoring. Symp. on monitoring, modeling, and mediating water quality, pp.

165-175. Amer. Water Resour. Assoc.

Shelley, P.E. 1977. Sampling of water and wastewater.

US EPA-600/4-77-039. Off. Res. and Dev., Cincinnati, OH.

Simpson, J.T. 1991. Volunteer lake monitoring: a methods manual. US EPA 440/4-91-002. Off. Water.

Washington, DC.
Part 614

National Water Quality Handbook

Chapter 11 Sample Collection and Analysis

11–14 (430–VI–NWQH, September 2003)

Taylor. J.E. 1984. Essential features of a laboratory

quality assurance program. In Statistics in the

environmental sciences, S.M. Gertz and M.D.

London (Eds.). Amer. Soc. for Test. and Mat. pp.

66-73.

Topp, E., and W. Smith. 1992. Sorption of the herbicide

Atrazine and Metolachlor to selected plastics and

silicone rubber. J. Environ. Quality 21:316-317.

United States Environmental Protection Agency. 1973.

Biological field and laboratory methods for

measuring the quality of surface waters and

effluents. EPA 670/4-73-001, Off. Res. and Dev.,

Cincinnati, OH.

United States Environmental Protection Agency. 1983.

Methods for chemical analysis of water and

wastes. EPA600/4-79-020, Off. Res. and Dev.,

Cincinnati, OH.

United States Environmental Protection Agency. 1988.

Guide for the preparation of quality assurance

project plans for the national estuary program.

EPA 556/2-88-001, Off. Marine and Estuarine

Prot., Washington, DC.

United States Environmental Protection Agency. 1990.

Volunteer water monitoring: a guide for state

managers. EPA 440/4-90-010. Off. Water. Washington, DC.
(450-VI-NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

National Water Quality Handbook

Chapter 12 Land Use and Management

Monitoring
(450–VI–NWQH, September 2003) 12–i

Chapter 12 Land Use and Management

Monitoring

Contents: 614.1200 Introduction 12–1

614.1201 Methods of monitoring 12–1

(a) Personal observations ................................................................................ 12–1

(b) Field logs ..................................................................................................... 12–2

(c) Personal interviews .................................................................................... 12–2

(d) Remote sensing ........................................................................................... 12–4

614.1202 Management of land treatment data 12–4

(a) Ad hoc files .................................................................................................. 12–4

(b) Spreadsheets/data bases ............................................................................ 12–4

(c) Geographic information system ................................................................ 12–5

614.1203 Relationship between land use/treatment and water quality 12–7

614.1204 References 12–8

Tables Table 12–1 Frequently used data layers for a GIS 12–6

Table 12–2 Land use and management data generated from a GIS 12–7

Figures Figure 12–1 Example of a field log 12–3

Figure 12–2 Geographic information systems data layers 12–5
(450-VI-NWQH, September 2003) 12–1

Chapter 12 Land Use and Management

Monitoring

614.1200 Introduction

An essential element of water quality monitoring is the

tracking of land use and management activities in the

watershed being monitored. Land use and management data are needed to explain any water quality

changes that may occur. The water quality changes

must be attributed to the management practice and

not to other confounding influences, such as climate

or a point source. For watershed scale monitoring, the

proximity of the land practices to the monitoring

location can directly influence the water quality observed. A poor practice near the watershed outlet or

downgradient can mask the influence of good practices upstream or upgradient.

This chapter presents methods for monitoring and

managing land use and management data and provides

checklists of recommended activities to monitor for

the major sources of the nonpoint pollutant.

614.1201 Methods of

monitoring

The four basic approaches for monitoring land treatment data are personal observations, field logs, personal interviews, and remote sensing. Any one project

may use some or all of these approaches to track

activities on the land, depending on the scale and

complexity of the project.

Land treatment data can be either static or dynamic,

point or diffuse. Static land treatment data do not

change with time. Examples of this type data include

soil type and slope. Dynamic land treatment data can

vary with time and include the number of animals,

cover crop, nutrient applications, and irrigation schedules. Most land treatment activities are considered

diffuse or nonpoint. However, some activities, such as

feedlots, manure stacks, and silage bunkers, can be

viewed as potential point sources from a watershed

scale perspective.

(a) Personal observations

For small scale projects, such as plots or individual

fields, tracking may best be accomplished by project

personnel using personal observations. Routine site

visits can include an analysis of the site conditions at

the time of the visit. The type of information that can

be collected through personal observations includes

counts, timing of certain activities, site characteristics,

and tests. Some examples are:

Counts Site characteristics

• Number of animals • Slope

• Crop type • Slope length

• Soil type

Timing Tests

• Planting date • Yield test

• Harvest date • Soil test

• Tillage dates • Application rates

• Fertilizer applications

• Pesticide applications

• Irrigation schedules
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A form for recording personal observations is highly

recommended. It should include required check-offs to

assure certain questions are not overlooked.

The windshield survey is another type of personal

observation. This survey is useful in identifying land

uses for areas where ownership is unknown and

information is difficult to collect from traditional

methods.

(1) Advantages

A major advantage of the personal observation is that

the quality of the data is controlled by the observer.

This means that the timing of the visit can be scheduled as well. Personal observation-type data are relatively inexpensive to obtain.

(2) Disadvantages

Timing is critical to certain types of land use observations. For example, pesticide applications occur on a

short time frame and will most likely be missed by less

frequent than daily visits. Also, the amount of an

application, such as nutrient loading, can only be

determined by being present during the application.

The potential for "judgment bias" in personal observations is great. Different individuals will most likely

make different observations. Bias also can be introduced by personal schedules. Quantitative and randomized observations may help to reduce bias. Generally, a reliance on personal observation alone results in

an incomplete data set of land treatment activities.

(b) Field logs

The term field log is meant to include the various

forms that would be left with the landowner or manager. The manager ideally would keep a record of

activities. A copy of a manure/fertilizer log used in the

St. Albans Bay RCWP is shown in figure 12–1. This

particular log was given to each cooperating and

noncooperating farm producer in the watershed. The

log was placed inside a checkbook cover with a farm

map showing numbered fields. The field logs were

recovered twice yearly.

Some states require that the producer maintain a field

log as part of a permit condition.

(1) Advantages

The major advantage of the field log is that the person

performing the activities is keeping the records. This

person is often the only one who knows when certain

activities occur and how much occurred. Picking up a

field log allows for additional interaction with the

producer.

(2) Disadvantages.

A 100 percent compliance in good record keeping in

the watershed is unlikely. Some producers will not fill

out the log. Others will not complete the log with the

level of detail or precision needed. For example,

instead of indicating the exact date of a manure application on field No. 10, a producer may indicate “early

spring.”

(c) Personal interviews

A personal interview or one-on-one contact is an

effective way to obtain land treatment data. A direct

visit is preferred over a telephone interview. A form is

recommended as a guide for the interview. Based on

experience obtained in the St. Albans Bay RCWP, two

visits per year yields much more reliable data than an

annual visit. Meetings with producers were timed with

less busy periods on the farm (e.g., mid-summer and

mid-winter).

(1) Advantages

The major advantage of the personal interview is that

the data is obtained from the person responsible for

the land activity. Also, the interview facilitates obtaining information on subtle land use changes, such as

rental lands, field boundary changes, and shifts in

animal numbers.

(2) Disadvantages

A major disadvantage of the personal interview is that

the quality of data obtained varies with both the interviewer and the interviewee. Some people are adept at

questioning farm producers, while others are not.

Similarly, some farm producers are reluctant to share

management information. Another disadvantage is that

the personal interview relies on "reconstructed" data

based on the memories of the person interviewed.
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Chapter 12 Land Use and Management Monitoring

(450-VI-NWQH, September 2003) 12–3

Figure 12–1 Example of a field log

A. Manure application

Date Field ID Amount applied Date incorporated Time Comments

(see map) (full spreader load) (approx.)

Example 3b 1 1/2 4/23 10:30 am • Evenly spread except wet spot on NE

4/23/82 corner

• Planted corn 4/28

B. Commercial fertilizer application (including lime)

Date Field ID Formulation Amount applied/ac How applied Comments

Example 21 10-20-10 4 lb/ac broadcast disced on 4/23

4/23/82 (or all corn

fields)
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(d) Remote sensing

For certain types of land use and treatment data,

remote sensing techniques may serve as a primary

data source or verification of other data sources. For

example, the 35mm slides of cropland areas taken

annually by FSA can provide a source of land cover

information on a field basis. Satellite data would

generally not be sufficient for monitoring land treatment, although it has been used to assess critical areas

(Sivertun, et al. 1988).

(1) Advantages

Remotely sensed data can give a permanent visual and

spatial record of certain types of land use data, including land cover. Certain types of critical sources of

nonpoint pollution, such as erosion, may be observable

using remote sensing. Data that can be obtained by

remote sensing eliminate reliance on the memories of

individuals.

(2) Disadvantages

Remotely sensed data have limited applications. Low

level air photos can be used to distinguish some crop

covers, but it is difficult to distinguish between others,

such as forest and residential. Remotely sensed data

will not provide timing information, such as manure or

fertilizer applications.

614.1202 Management of

land treatment data

The method employed to keep track of land use data

varies with the situation, but the method used must be

defined at the beginning of the project. Without attention to management of land treatment data, records

will most likely be insufficient and full of gaps. The

three methods for management of land treatment and

land use data are ad hoc files, spread sheets/data

bases, and geographic information systems.

(a) Ad hoc files

A good filing system can be effectively used to track

land use and treatment data. It is important that the

results of land treatment monitoring be reported

routinely and often. Failure to do so will result in data

gaps remaining hidden, possibly until the end of the

project when it will be too late to recover the data.

Spatial data from ad hoc files should be transferred to

and displayed on maps as a quality control check on

how much information is actually being obtained.

(b) Spreadsheets/data bases

Various computer spreadsheet and data base programs

can be used to track land treatment data. Such programs are particularly efficient in attaching attributes

to field IDs. The EPA has developed a PC software

program, the Nonpoint Source Management System

(NPSMS), to track management activities and water

quality and implementation data (US EPA 1991).

NPSMS actually has several separate files for tracking

information. The management file stores information

about the water quality problem and project goals. The

monitoring plan file holds descriptions of the monitoring design, including stations, variables, and frequencies. The annual report file includes the annual

water quality and implementation data. The system

also includes the water body system for identifying the

individual body of water involved.

Data bases, in particular, allow relating data between

different files, such as land treatment files and water

quality files.
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Chapter 12 Land Use and Management Monitoring

(450-VI-NWQH, September 2003) 12–5

(c) Geographic information

system (GIS)

Geographic information systems are "...systems that

integrate layers of spatially oriented information,

whether manually or automatically..." (Walsh 1985). A

GIS is ideally suited to track land use and treatment

data. The primary advantage is that land treatment

data can be displayed spatially and combined with

other water quality related information.

GIS data can be stored as values for uniform grids

(raster) or as strings of coordinates representing

points, lines, and areas, including polygons (vector).

Land treatment data, such as land cover, can be overlaid on stream courses, soil types, and topography

(fig. 12–2). A GIS also allows displaying and calculating new information from the combined data layers,

such as where and how much animal waste was applied within 50 feet of a stream or where and how

much animal waste was applied on soil hydrologic

group D.

Because all the files in a GIS are relational, that is,

two-dimensional tables can be related to each other

based on a common characteristic, such as field ID, a

GIS also serves as a data base for managing and reporting land treatment data.

Figure 12–2 Geographic information systems data layers

Topography

Streams

Fields

Land cover

Soils
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Chapter 12 Land Use and Management Monitoring

12–6 (450-VI-NWQH, September 2003)

(1) Data entry

The most difficult aspect of using a GIS for managing

land treatment data is the initial digitizing of the spatial data layers. Quality control is an important consideration in GIS data entry, just as it is for water quality

analysis. Digitized information should go through an

error checking system to make sure that the layer has

been appropriately geo-referenced and lines and

points are properly located. Just closing polygons is

insufficient quality control. Other information added

should also receive error checking (see chapter 13).

Once the data layers have been entered, attributes are

easily added and data management is enhanced and

powerful. Although the appropriate data layers would

vary with each situation, several useful data layers are

given in table 12–1 along with suggested priorities for

most water quality monitoring situations.

Farm and field boundaries are almost essential as a

data layer. Such data can be obtained from the farm

plan photos with verification from the farm operator.

Stream courses can be digitized as lines or bands,

polygons, or grids, or a proximity zone to the watercourse can be used. For example, Sivertun, et al.

(1988) used proximity bands of 0 to 150, 150 to 650,

650 to 3,300, and >3,300 feet to help identify critical

areas in a watershed.

Soils data could be entered as the soil series or as

some more general textural class either as a separate

layer or as a field attribute. However, a separate soils

layer is recommended. Topography could be entered

as a data layer, either as points, polygons, or grid

information, or the percent slope could be entered

either as an attribute of the field boundary or the soil

series. Topographic information is not necessary to

track land use data, but is useful for displaying results

in a 3-D format and identifying critical areas.

Land cover could be entered as a separate data layer;

however, it is best entered as an attribute of a farm

field because it is easily updated. Good land cover/land

use maps are not readily available. Therefore, these

maps are often developed from aerial photo interpretations, satellite imagery, or on-the-ground observations.

For the St. Albans Bay RCWP, a land use/land cover

data layer was created from individual farm 9 by 9

1:660 scale farm plan photos, verifications from the

farm operator, supplemental ASCS 35mm slides, and

ground truthing of gaps in the data layer.

The use of satellite results is not accurate enough at

this time to determine land use/land cover for water

quality monitoring purposes. However, satellite data

may be very useful when determining critical areas of

high pollution potential (Guilliland and Baxter-Potter

1987).

Precipitation is an appropriate data layer when highly

variable across the watershed in some cases. Irrigation

networks may be useful in certain areas (Walsh 1985).

For ground water projects, information on ground

water withdrawals and piezometric surfaces may be

important management information.

Table 12–1 Frequently used data layers for a GIS

Priority Data layer

1 quadrangle basemap

1 farm and field boundaries

1 stream courses and other water bodies

 (or proximity class)

1 watershed boundary

1 soil series (or attribute of field)

2 topography or slope (or attribute of soil)

2 land cover/land use

3 transportation

3 geology

3 political boundaries

4 archeology

4 precipitation (where variable)
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Table 12–2 Land use and management data generated

from a GIS

Units

Land treatment data

Critical area under BMP %, ac.

Animal units under BMP %, No., No/ac

Fields under nutrient management %, ac.

Fields under irrigation management %, ac.

Area of land use (pasture, etc.) %, ac.

Erosion control %, ac.

Animal waste data

Manure from storage %

Manure incorporated %

Barnyard management No.

Milkhouse management No.

(2) Analysis

After the data layers have become part of the GIS data

base, attributes of dynamic data layers can be updated. For example, cover crop can be changed annually. The additions of nutrients, either as animal waste

or fertilizers, can be updated on a weekly, monthly, or

annual basis. From this data base, several types of

land use and management information can be generated (table 12–2).

614.1203 Relationship

between land use/treatment

and water quality

The purpose in collecting land use and management

information is to use that data to establish causal

relationships with water quality. Causality involves

several steps:

1. An association should exist between the water

quality and land treatment data.

2. This association should be consistent across

different data sets so that a general statement

may be made about the relationship.

3. The association should be tested to make sure

that one variable is responsive to the other

variable. This responsiveness may require experimentation.

4. There must be a mechanism that logically explains the process that results in the relationship.

This section will focus on developing associations

between land treatment and water quality data.

When developing a program for monitoring land treatment data for the purpose of relating that data to

water quality, both temporal and spatial scales must

be decided.

Water quality data are often collected at a much more

frequent rate than land treatment data. For example, in

the St. Albans Bay RCWP, water quality samples were

collected every 8 hours, but land treatment information was collected twice a year. In one analysis associations were made of weekly phosphorus and manure

application data (Hopkins & Clausen 1985). However,

the danger in such associations is that they are confounded by the timing of agricultural practices. For

example, animal waste is not applied to agricultural

lands during wet seasons, but nutrient concentrations

in streams are highest during the same wet periods.

Thus a confounded association of manure applications

and stream concentrations could exist. To resolve this

problem, Meals (1992) used annual data for the associations.
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12–8 (450-VI-NWQH, September 2003)

The spatial scale of land treatment data also is important. Watershed-wide summaries were most useful in

establishing land treatment-water quality relationships

in Vermont (Meals 1992). However, an association of

land use (corn, pasture, hay) and certain water quality

variables for data summarized were within 150 feet of

the streams for each watershed. Schlagel (1992) also

pointed out that the spatial pattern within watersheds

of changes in land treatment practices is important

and could mask water quality changes.

The primary methods for establishing associations are

described in part 615 of this handbook. Correlations

serve as an initial tool.

When developing the monitoring plan, a list of land use

and management data that will be used to relate to

water quality data also should be developed. This list

will obviously vary with the project.

614.1204 References

Gilliland, M.W., and W. Baxter-Potter. 1987. A geographic information system to predict non-point

source pollution potential. Water Resourc. Bull.

23(2):281-291.

Hopkins, R.B., Jr., and J.C. Clausen. 1985. Land use

monitoring and assessment for nonpoint source

pollution control In Perspectives on nonpoint

source pollution, EPA 440/5-85-001, Washington,

DC, pp. 25-29.

Meals, D.W. 1992. Relating land use and water quality

in the St. Albans Bay watershed, Vermont. Proc.

Natl. RCWP Symp., EPA pp. 131-143.

Schlagel, J.D. 1992. Spatial and temporal change in

animal waste application in the Jewett Brook

watershed, Vermont: 1983-1990. Proc. Natl.

RCWP Symp., EPA pp. 145-150.

Silvertun, A., L.E. Reinelt, and R. Castensson. 1988. A

GIS method to aid in non-point source critical

area analysis. J. Geogr. Inf. Sys. 2(4):365-378.

United States Environmental Protection Agency. 1991.

Watershed monitoring and reporting for section

319 national monitoring program projects. Office

of Water Washington, DC.

Walsh, S.J. 1985. Geographic information systems for

natural resource management. J. Soil and Water

Conserv. pp. 202-205.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

National Water Quality Handbook

Chapter 13 Data Management
(450–VI–NWQH, September 2003) 13–i

Chapter 13 Data Management

Contents: 614.1300 Introduction 13–1

614.1301 Data acquisition 13–1

614.1302 Data storage 13–2

614.1303 Data validation 13–3

614.1304 Data retrieval 13–3

614.1305 Data manipulation 13–4

614.1306 Data reporting 13–4

614.1307 References 13–5

Figures Figure 13–1 Data management system 13–1

Figure 13–2 Example data entry sheets 13–1
(450-VI-NWQH, September 2003) 13–1

Chapter 13 Data Management

614.1300 Introduction

Data management in water quality monitoring projects

refers to a series of steps for handling data (fig. 13–1).

The management of data has become increasingly

important because efficient means are needed to deal

with a large amount of numbers and the integrity of

those numbers must be guaranteed. The processes in a

data management system include acquisition, storage,

validation, retrieval, manipulation, and reporting of

data (Canter 1985; Sanders, et al. 1983; Ward, et al.

1990). The interpretation of data will be further described in part 615 of this handbook.

Advances in computers and software have made the

process of data management much easier. Therefore

computer applications will be described in this chapter.

614.1301 Data acquisition

The acquiring of data is meant to include its collection

and entry into the data management system. Entry

may begin indirectly from data entry sheets (fig. 13–2),

which could be completed by either field or laboratory

personnel. More direct entry of data has been made

possible via the use of data loggers. This latter process

bypasses the steps of manually entering data and

therefore avoids transcription errors. Data from a data

logger can be input using storage modules, cassette

tapes, or telecommunication devices that have an

interface with a computer system.

Figure 13–1 Data management system Figure 13–2 Example data entry sheets

Data acquisition

Data validation

Data storage

Data retrieval

Data manipulation

Reporting

STA Date

MM/DD/YY

Hours Lab

No.

Concentration (mg/l)

TKN NH3 NO2/NO TP

Streams

Data entry sheet

riparian zone restoration project
Part 614

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Chapter 13 Data Management

13–2 (450-VI-NWQH, September 2003)

614.1302 Data storage

The storage of data should be viewed as a multilevel

effort using manual and computerized technologies.

Manual efforts should include safe storage of original

laboratory notebooks, field notebooks, daily field logs,

and any paper tapes and strip charts. A manual copy of

all computerized data files should be printed on high

quality paper and placed in safe storage. Smoke destroys a floppy disk, but not paper.

Laboratory notebooks should be considered a permanent record of data. The notebooks should be bound

with numbered pages so that pages cannot be substituted or deleted. Pages should be dated and signed by

operators. Entries should be made in ink. Errors

should be crossed out so that they are legible, but not

erased. The correction should be initialed and dated.

Large blank spaces in the notebooks should have lines

drawn through them. Standard curves should be

drafted within the lab notebook.

Computerized data storage also is highly recommended. In the past, computerized data management

systems were developed specifically for individual

projects onsite, and could not be transferred to other

locations. The availability of general spreadsheet

software, such as Lotus 1-2-3, Quattro Pro, or Excel,

has greatly changed the need to develop individual

data management systems. In addition, data base

management software is available. The following are

recommendations for computerized spreadsheets and

data base management systems use:

• Store data in ASCII format, preferably formatted

in columns.

• Store data on floppy disks, not hard drives.

• Backup disks are essential; maintain one set

onsite and one set offsite (at home).

• Store data in files of “convenient” blocks of data,

such as annually. One disk could represent 1 year

of data.

• Plan file naming conventions. A file name could

include such information as project or study

area, data type, data manipulations, and project

year. For example, the file “SAQ23.S85” refers to

the St. Albans Bay RCWP project (SA), flow data

(Q), for the Level 2 tributary stations (2), for the

third quarter of the year (3), sorted by station

number and date (S), and for project year 1985.

For this study separate formatted ASCII files

were created for flow (Q) files, concentration

data (C), mass data (M), stage data (S), and

precipitation data (P) using the same file naming

convention. Because knowing that the data files

have been error checked is important, checking

was done quarterly. However, many spreadsheets use their own filename extensions, such

as XXXXXXXX.WQ1 for Quattro.

• Decide how to record missing data in the computer files. A -9.0 could be a code for missing

data in cases where negative data does not exist

(e.g., concentration, flow). The statistical package SAS uses a single period, ‘.’ as an indicator of

missing data.

Geo-referencing the location of water quality sampling

stations by latitude and longitude (degrees, minutes,

seconds) is further recommended. Such referencing is

required by some data storage systems, such as

STORET.

Data that are below detection limits are termed censored data. Data should be entered in the data management system that codes the data as below the detection limit. For example, a -8.0 could be used where

negative data is not possible. The elimination of data

below detection limits or the entry of the below detection limit data as either a 0, half the limit, or the limit

itself is not recommended (Newman, et al. 1989).
Part 614

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Chapter 13 Data Management

(450-VI-NWQH, September 2003) 13–3

614.1303 Data validation

All data reported should receive a 100 percent error

check. Transcription errors can be checked by entering the data twice, preferably by two individuals. A

computer program can compare the two data files and

flag any inconsistencies for correction.

Also, the COMP command in DOS allows the comparison of the contents of two files in either the same or

different directories. If the COMP command finds any

mismatches, an error statement will be displayed.

Laboratory notebook calculations should be checked

by a supervisor, who initials the notebooks as verified.

Sample custody sheets should be reviewed to ensure

that holding times, preservation, sample integrity, and

equipment calibration requirements have been met.

Additional tests of reason can be applied to concentration values. For example, ammonia concentrations

cannot exceed total Kjeldahl nitrogen values, and

ortho-phosphorus cannot exceed total phosphorus

values. Also, limits can be used as flags in the data set.

For example, appropriate limits for pH are 0 to 14. A

maximum limit for total phosphorus might be 5 mg/L

for a lake. Standard laboratory curves should be analyzed for warning and control limits as described in

Standard Methods (APHA 1989).

Data not meeting the requirements described above

could be rejected and noted in the data files as missing

data.

614.1304 Data retrieval

The retrieval of data from the data management system must consider the form of retrieval (paper report,

data file, graph) as well as the intended use (statistical,

quality control, share with others). Good records must

be maintained on format for data storage so that

others can review the data files. Readme.txt files

stored on disks containing the data files are highly

recommended.
Part 614

National Water Quality Handbook

Chapter 13 Data Management

13–4 (450-VI-NWQH, September 2003)

614.1305 Data manipulation

Data generally require some form of manipulation

before being reported. Common manipulations include:

• calculations of average values or mass exports

• sorting

• graphical presentations

• statistical analysis/ transformations

Common spreadsheet and data base programs facilitate the calculation of averages and mass exports. For

example, Quattro Pro and Lotus allow entering a

formula, i.e., equation, to apply to stored data or the

use of functions (internal formulas) to apply to the

data. These functions include mathematical, statistical, and logical operations.

The sorting of data is a common manipulation in a

data management system. Frequently, data must be

arranged by date or station number to report the

results, input to a graph, or perform statistical analysis. Most spreadsheets have sorting commands. It may

be desirable to search through the data system as well

as sort the data.

Graphical presentations also are facilitated by spreadsheets, or a number of graphics packages are available.

Statistical manipulation of data will be very specific to

the study design. However, most data receive routine

univariate analysis, including the number of samples,

mean, maximum, minimum, and standard deviation.

These simple statistics can be determined in most

spreadsheets. More sophisticated statistical analysis

may require the use of other statistical packages.

If censored (below detection limits) data are in the

data set, the mean and standard deviation for the data

are strongly influenced by the manner in which the

censored data is handled and the percentage of data

that is censored. This is described further in part 615.

614.1306 Data reporting

Reporting data at the end of a monitoring study may

seem obvious, but reporting during the progress of the

study is very important for several reasons. Interim

reporting encourages (requires) identifying data errors

and data gaps. Frequent reporting aids in solving

problems. Although it seems like it takes too much

time, reporting should be at a minimum of quarterly

either formally or informally. Progress reports should

include data that have been screened, analyzed statistically, summarized and plotted. A few copies of the

raw data should be made available to project sponsors

and cooperators. The data could be shared as ASCII

files on diskettes.

Guidelines for preparing reports are beyond the scope

of this handbook. However, following the guidelines of

an appropriate professional journal, especially regarding tables and figures, is recommended.
Part 614

National Water Quality Handbook

Chapter 13 Data Management

(450-VI-NWQH, September 2003) 13–5

614.1307 References

American Public Health Association. 1989. Standard

methods for the examination of water and wastewater. 17th ed., American Public Health Assoc.,

Washington, DC.

Canter, L.W. 1985. River water quality monitoring.

Lewis Pub., Inc. Chelsea, MI.

Newman, M.C., P.M. Dixon, B.B. Looney, and J.E.

Pinder, III. 1989. Estimating mean and variance

for environmental samples with below detection

limit observations. Water Resourc. Bull.

25(4):905-916.

Sanders, T.G., R.C. Ward, J.C. Loftis, T.D. Steele, D.D.

Adrian, and V. Yevjevich. 1983. Design of networks for monitoring water quality. Water

Resourc. Pub., Littleton, CO.

Ward, R.C., J.C. Loftis, and G.B. McBride. 1990. Design

of water quality monitoring systems. Van

Nostrand Reinhold. New York, NY.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

National Water Quality Handbook

Appendixes
(450–VI–NWQH, September 2003)

Appendixes

Contents: Appendix A Distribution of Z A–1

Appendix B Distribution of t A–2

Appendix C Significance of r A–3
Part 614

National Water Quality Handbook

Appendixes

(450–VI–NWQH, September 2003) Appendixes–1

Appendix A Distribution of Z 1

Probability of a random value of Z = (X – μ)/s being greater than the values tabulated in the margins

Z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09

.0 .5000 .4960 .4920 .4880 .4840 .4801 .4761 .4721 .4681 .4641

.1 .4602 .4562 .4522 .4483 .4443 .4404 .4364 .4325 .4286 .4247

.2 .4207 .4168 .4129 .4090 .4052 .4013 .3974 .3936 .3897 .3859

.3 .3821 .3783 .3745 .3707 .3669 .3632 .3594 .3557 .3520 .3483

.4 .3446 .3409 .3372 .3336 .3300 .3264 .3228 .3192 .3156 .3121

.5 .3085 .3050 .3015 .2981 .2946 .2912 .2877 .2843 .2810 .2776

.6 .2743 .2709 .2676 .2643 .2611 .2578 .2546 .2514 .2483 .2451

.7 .2420 .2389 .2358 .2327 .2296 .2266 .2236 .2206 .2177 .2148

.8 .2119 .2090 .2061 .2033 .2005 .1977 .1949 .1922 .1894 .1867

.9 .1841 .1814 .1788 .1762 .1736 .1711 .1685 .1660 .1635 .1611

1.0 .1587 .1562 .1539 .1515 .1492 .1469 .1446 .1423 .1401 .1379

1.1 .1357 .1335 .1314 .1292 .1271 .1251 .1230 .1210 .1190 .1170

1.2 .1151 .1131 .1112 .1093 .1075 .1056 .1038 .1020 .1003 .0985

1.3 .0968 .0951 .0934 .0918 .0901 .0885 .0869 .0853 .0838 .0823

1.4 .0808 .0793 .0778 .0764 .0749 .0735 .0721 .0708 .0694 .0681

1.5 .0668 .0655 .0643 .0630 .0618 .0606 .0594 .0582 .0571 .0559

1.6 .0548 .0537 .0526 .0516 .0505 .0495 .0485 .0475 .0465 .0455

1.7 .0446 .0436 .0427 .0418 .0409 .0~01 .0392 .0384 .0375 .0367

1.8 .0359 .0351 .0344 .0336 .0329 .0322 .0314 .0307 .0301 .0294

1.9 .0287 .0281 .0274 .0268 .0262 .0256 .025n .0244 .0239 .0233

2.0 .0228 .0222 .0217 .0212 .0207 .0202 .0197 .0192 .0188 .0183

2.1 .0179 .0174 .0170 .0166 .0162 .0158 .0154 .0150 .0146 .0143

2.2 .0139 .0136 .0132 .0129 .0125 .0122 .0119 .0116 .0113 .0110

2.3 .0107 .0104 .0102 .0099 .0096 .0094 .0091 .0089 .0087 .0084

2.4 .0082 .0080 .0078 .0075 .0073 .0071 .0069 .0068 .0066 .0064

2.5 .0062 .0060 .0059 .0057 .0055 .0054 .0052 .0051 .0049 .0048

2.6 .0047 .0045 .0044 .0043 .0041 .0040 .0039 .0038 .0037 .0036

2.7 .0035 .0034 .0033 .0032 .0031 .0030 .0029 .0028 .0027 .0026

2.8 .0026 .0025 .0024 .0023 .0023 .0022 .0021 .0021 .0020 .0019

2.9 .0019 .0018 .0018 .0017 .0016 .0016 .0015 .0015 .0014 .0014

3.0 .0013 .0013 .0013 .0012 .0012 .0011 .0011 .0011 .0010 .0010

3.1 .0010 .0009 .0009 .0009 .0008 .0008 .0008 .0008 .0007 .0007

3.2 .0007 .0007 .0006 .0006 .0006 .0006 .0006 .0005 .0005 .0005

3.3 .0005 .0005 .0005 .0004 .0004 .0004 .0004 .0004 .0004 .0003

3.4 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0002

3.6 .0002 .0002 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001

3.9 .0000

1/ Steel, R.G.D., and J.H. Torrie. 1960. Prnciples and procedures of statistics. McGraw-Hill, Inc., New York, NY. (Reproduced with permission

of the McCraw-Hill Companies.)
Part 614

National Water Quality Handbook

Appendixes

Appendixes–2 (450–VI–NWQH, September 2003)

Appendix B Distribution of t (two-tailed) 1

Degrees of - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - Probability of a Larger Value, Sign Ignored - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -

Freedom 0.500 0.400 0.20 0.10 0.050 0.025 0.010 0.005 0.001

1 1.000 1.376 3.078 6.314 12.706 25.452 63.657

2 0.816 1.061 1.886 2.920 4.303 6.205 9.925 14.089 31.598

3 .765 0.978 1.638 2.353 3.182 4.176 5.841 7.453 12.941

4 .741 .941 1.533 2.132 2.776 3.495 4.604 5.598 8.610

5 .727 .920 1.476 2.015 2.571 3.163 4.032 4.773 6.859

6 .718 .906 1.440 1.943 2.447 2.969 3.707 4.317 5.959

7 .711 .896 1.415 1.895 2.365 2.841 3.499 4.029 5.405

8 .706 .889 1.397 1.860 2.306 2.752 3.355 3.832 5.041

9 .703 .883 1.383 1.833 2.262 2.685 3.250 3.690 4.781

10 .700 .879 1.372 1.812 2.228 2.634 3.169 3.581 4.587

11 .697 .876 1.363 1.796 2.201 2.593 3.106 3.497 4.437

12 .695 .873 1.356 1.782 2.179 2.560 3.055 3.428 4.318

13 .694 .870 1.350 1.771 2.160 2.533 3.012 3.372 4.221

14 .692 .868 1.345 1.761 2.145 2.510 2.977 3.326 4.140

15 .691 .866 1.341 1.753 2.131 2.490 2.947 3.286 4.073

16 .690 .865 1.337 1.746 2.120 2.473 2.921 3.252 4.015

17 .689 .863 1.333 1.740 2.110 2.458 2.898 3.222 3.965

18 .688 .862 1.330 1.734 2.101 2.445 2.878 3.197 3.922

19 .688 .861 1.328 1.729 2.093 2.433 2.861 3.174 3.883

20 .687 .860 1.325 1.725 2.086 2.423 2.845 3.153 3.850

21 .686 .859 1.323 1.721 2.080 2.414 2.831 3.135 3.819

22 .686 .858 1.321 1.717 2.074 2.406 2.819 3.119 3.792

23 .685 .858 1.319 1.714 2.069 2.398 2.807 3.104 3.767

24 .685 .857 1.318 1.711 2.064 2.391 2.797 3.090 3.745

25 .684 .856 1.316 1.708 2.060 2.385 2.787 3.078 3.725

26 .684 .856 1.315 1.706 2.056 2.379 2.779 3.067 3.707

27 .684 .855 1.314 1.703 2.052 2.373 2.771 3.056 3.690

28 .683 .855 1.313 1.701 2.048 2.368 2.763 3.047 3.674

29 .683 .854 1.311 1.699 2.045 2.364 2.756 3,.038 3.659

30 .683 .854 1.310 1.697 2.042 2.360 2.750 3.030 3.646

35 .682 .852 1.306 1.690 2.030 2.342 2.724 2.996 3.591

40 .681 .851 1.303 1.684 2.021 2.329 2.704 2.971 3.551

45 .680 .850 1.301 1.680 2.014 2.319 2.690 2.952 3.520

50 .680 .849 1.299 1.676 2.008 2.310 2.678 2.937 3.496

55 .679 .849 1.297 1.673 2.004 2.304 2.669 2.925 3.476

60 .679 .848 1.296 1.671 2.000 2.299 2.660 2.915 3.460

70 .678 .847 1.294 1.667 1.994 2.290 2.648 2.899 3.435

80 .678 .847 1.293 1.665 1.989 2.284 2.638 2.887 3.416

90 .678 .846 1.291 1.662 1.986 2.279 2.631 2.878 3.402

100 .677 .846 1.290 1.661 1.982 2.276 2.625 2.871 3.390

120 .677 .845 1.289 1.658 1.980 2.270 2.617 2.860 3.373

× .6745 .8416 1.2816 1.6448 1.9600 2.2414 2.5758 2.8070 3.2905

1/ Snedecor, G.W., and W.G. Cochran. 1980. Statistical methods, 7th ed. Iowa State Univ. Press, Ames. (No part of this appendix may be

reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopying, recording, or

otherwise—without the prior written permission of the publisher.)
Part 614

National Water Quality Handbook

Appendixes

(450–VI–NWQH, September 2003) Appendixes–3

Appendix C Significance of r 1

df 10% 5% 2% 1%

3 0.805 0.878 0.934 0.959

4 .729 .811 .882 .917

5 .669 .754 .833 .874

6 .622 .707 .789 .834

7 .582 .666 .750 .798

8 .549 .632 .716 .765

9 .521 .602 .685 .735

10 .497 .576 .658 .708

11 .476 .553 .634 .684

12 .458 .532 .612 .661

13 .441 .514 .592 .641

14 .426 .497 .574 .623

15 .412 .482 .558 .606

16 .400 .468 .542 .590

17 .389 .456 .528 .575

18 .378 .444 .516 .561

19 .369 .433 .503 .549

20 .360 .423 .492 .537

25 .323 .381 .445 .487

30 .295 .349 .409 .449

35 .275 .325 .381 .418

40 .257 .304 .358 .393

45 .243 .288 .338 .372

50 .231 .273 .322 .354

60 .211 .250 .295 .325

70 .195 .232 .274 .302

80 .183 .217 .256 .283

90 .173 .205 .242 .267

100 .164 .195 .230 .254

150 .134 .160 .189 .208

200 .116 .138 .164 .181

300 .095 .113 .134 .148

400 .082 .098 .116 .128

500 0.073 0.088 0.104 0.115

1/ Snedecor, G.W., and W.G. Cochran. 1980. Statistical methods,

7th ed. Iowa State Univ. Press, Ames. (No part of this appendix

may be reproduced, stored in a retrieval system, or transmitted

in any form or by any means—electronic, mechanical, photocopying, recording, or otherwise—without the prior written

permission of the publisher.)
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 614

National Water Quality Handbook

Index
(450-VI-NWQH, September 2003) Index–1

Index

A

Analysis 1–2, 1–7, 1–12, 1–13,

4–9, 4–12, 8–1, 8–4, 8–6

data 4–3, 4–6, 4–11, 4–12,

11–11, 12–7, 13–4

sample 10–13, 11–2, 11–7

samples 7–4

Aquifer 8–6

confined 8–6

unconfined 8–6

water table 7–2

B

Baseline 1–2, 1–12, 4–5, 5–1,

7–1, 9–1

Bedload 10–24

Bedrock 8–8

Biological monitoring 1–5, 1–9,

1–11, 8–1, 8–4

BMP 1–7, 1–8, 1–9, 4–5, 5–1,

5–5, 5–6, 9–1, 12–7

C

Compliance 1–3, 1–12, 4–13,

5–1, 5–5, 7–1, 8–1, 9–1, 12–2

Composite sample 7–1, 7–2,

10–13, 11–8

Computer 1–12, 12–4, 13–1,

13–2, 13–3

Continuous monitoring 7–4

Cost in analysis 6–1

Cost of analysis 6–8

Costs of analysis 6–8

Critical area 1–3, 4–1, 4–7,

5–1, 5–5, 7–1, 8–1, 9–1,

12–4, 12–6, 12–7

D

Data

acquisition 10–17, 11–1,

12–2, 13–1

analysis 2–2, 6–11, 9–2, 9–4

collection 4–11, 9–4, 9–5,

11–12, 12–2, 12–4, 12–6, 12–7

management 12–1, 12–2,

12–4, 12–5, 12–6, 12–7,

13–1, 13–2, 13–3, 13–4

verification 11–6, 12–4,

12–6, 13–1

vertification 13–3

Data collection 1–13

Data Management 1–16

Data management 1–12, 1–16

Decisionmaking 1–4

Discharge 1–16, 5–5, 5–6, 6–2,

6–3, 6–4, 6–5, 6–6, 6–7,

6–10, 7–1, 7–2, 7–3, 8–2,

8–3, 10–1, 10–2, 10–3,

10–4, 10–9, 10–10, 10–11,

10–14, 11–12

E

Erosion 4–3, 5–4, 12–4, 12–7

F

Fate 1–2, 5–1, 5–2, 5–4, 7–1,

8–1, 9–1

Field scale 1–3, 1–8, 5–4

Flow 1–8, 1–15, 4–2, 4–6,

4–7, 5–2, 5–3, 5–4, 5–5,

5–6, 6–2, 6–4, 6–8, 7–2,

7–3, 8–2, 8–3, 8–4, 8–6,

9–5, 10–1, 10–3, 10–4,

10–10, 10–14, 10–16, 13–2

Flume 5–4, 7–3, 10–2, 10–3,

10–12, 10–14

G

Geographic Information System

1–12

Geographic information system 12–4, 12–5

Goal 1–5, 1–13, 3–1, 4–2,

6–12, 9–2, 9–4, 9–5, 12–4

Grab sample 5–6, 7–1, 7–2,

8–4, 8–9, 10–13, 11–1

Ground water 1–15, 4–3, 8–2,

8–7

flow 8–6

monitoring 4–1, 4–2, 4–3,

5–2, 5–4, 5–5, 7–3, 8–1,

8–6, 9–1, 11–1, 12–6

wells 5–1

H

Hydraulic jump 10–4

Hydrograph 5–6, 10–11

I

Integrated sample 7–1, 7–3,

8–5, 10–14, 10–16

L

Laboratory analysis 11–5

Lake 2–2, 4–1, 4–2, 5–1, 5–2,

5–4, 5–5, 8–1, 8–2, 8–5,

9–1, 9–4, 9–5, 9–6, 11–1, 13–3

Lakes 6–2, 6–13, 7–2, 7–3,

10–13, 10–24

Land use 12–1, 12–2, 12–4,

12–5, 12–6, 12–7, 12–8

Land use data 1–5, 1–12, 4–11

Leachate 6–5

Limnocorral 5–1, 5–2

M

Management objectives 3–2,

3–3, 4–1

Mesocosm 5–1, 5–2

Model

evaluaiton 5–4

evaluation 5–1, 5–2, 7–1, 9–1

Monitoring

objective 5–2, 5–4

objectives 3–1, 3–2, 3–3,

4–10, 4–11, 5–1, 5–5, 7–1,

8–1, 9–1, 10–17

purpose 8–1, 8–6, 8–7,

8–8, 10–12, 12–6, 12–7

purposes 02–2, 4–1, 4–6,

5–5, 7–4, 8–1, 10–1

Monitoring objectives 1–7

Monitoring purposes 1–2

N

Nonpoint Source 12–4

Nonpoint source 1–3, 1–7, 6–

1, 6–3, 6–4, 6–5, 7–4
Part 614

National Water Quality Handbook

Index

Index–2 (450-VI-NWQH, September 2003)

O

Objectives

attributes 3–1, 3–3

constraints 3–1, 6–1

forming 3–1, 6–1

monitoring 2–2, 3–1, 3–2, 7–1

tree 3–2, 3–3

Objectives

attibutes 9–1

attributes 8–5

constraints 5–1, 8–6

forming 5–5, 8–1

monitoring 9–1

Overland flow 5–2, 5–3, 5–4, 10–1

P

Paired regression 1–7, 4–12

Plot 2–2, 8–1, 8–2, 10–1,

10–2, 10–14, 10–21, 12–1

Plots 4–3, 5–1, 5–2, 5–3, 5–5

Pollution 1–2, 1–3, 1–13, 4–1,

4–2, 7–4, 12–4, 12–6

Precipitation 1–8, 1–12, 1–13,

1–16, 4–3, 4–5, 4–12, 5–1,

5–4, 5–5, 10–1, 10–17,

10–19, 11–4, 11–12, 12–6,

13–2

Problem 2–1, 2–2, 4–1, 5–1,

6–1, 6–3, 6–8, 6–9, 6–10,

6–11, 7–1, 7–4, 8–2, 8–7,

8–10, 9–1, 10–1, 10–3,

10–4, 10–21, 11–11, 12–4,

12–7, 13–4

Program 4–1, 5–1, 6–2, 6–10,

7–1, 7–4, 8–1, 8–4, 8–8,

9–1, 9–3, 10–5, 10–17,

11–2, 11–6, 11–7, 12–4,

12–7, 13–3, 13–4

Purpose of monitoring 2–2, 8–7

Q

Quality assurance 1–12,

10–17, 11–1, 11–2, 11–6,

11–9, 11–11

Quality Control 11–6

Quality control 11–1, 11–6,

11–7, 11–11, 11–13, 12–4,

12–6, 13–3

R

Reconnaissance 1–2, 1–3, 1–7

River 1–13, 8–4, 8–5

Runoff 4–9, 4–10, 5–2, 5–4,

5–5, 6–4, 6–6, 8–1, 10–1,

10–2, 10–3, 10–14, 10–17,

10–24, 11–12

S

Sample 7–2

analysis 4–6, 4–10, 5–1,

6–8, 9–1, 9–4, 9–6, 10–14,

11–7, 11–11, 13–4

collecgtion 10–13

collectin 10–19

collection 4–1, 4–2, 4–6,

4–10, 5–1, 5–4, 5–6, 7–1,

7–2, 7–3, 7–4, 8–1, 8–3,

8–4, 8–5, 8–6, 9–1, 9–2,

9–3, 9–5, 10–1, 10–12,

10–13, 10–14, 10–16,

10–19, 10–20, 10–21,

10–22, 10–24, 11–1, 11–2,

11–4, 11–5, 11–9, 11–13,

12–7

size 4–10, 6–1, 8–1, 9–2,

9–3, 9–4, 9–5

Sampling

duration 4–10, 5–1, 9–1,

9–2, 10–17

frequency 4–1, 4–2, 4–7,

4–10, 5–1, 8–1, 9–1, 11–7

locatin 8–6

location 4–1, 4–2, 7–3, 8–1,

8–2, 8–3, 8–4, 8–5, 8–6,

8–8, 8–9

station 4–1, 8–3, 8–4,

10–14, 13–2

well 8–6, 8–7

wells 11–1

Scale of study 5–5

Sediment 1–4, 1–7, 1–8, 2–1,

2–2, 4–5, 5–2, 5–4, 5–5,

5–6, 6–3, 6–5, 6–9, 6–11,

7–1, 8–3, 8–4, 8–5, 8–6,

10–1, 10–2, 10–3, 10–13,

10–14, 10–21, 10–23,

10–24, 11–4

Seepage meter 5–2

Site selection criteria 1–9, 8–1,

8–2

Soil solution 5–2, 5–3, 10–20

Soil water 4–3, 6–2, 9–1,

10–1, 10–20

Stage 4–5, 7–2, 7–3, 8–2, 8–3,

8–6, 10–3, 10–4, 10–5,

10–6, 10–9, 10–10, 10–11,

10–14, 10–15, 10–17,

11–12, 13–2

Stage-discharge 8–2, 11–12

Stage-discharge relationship

7–3, 10–9

Standard 8–5, 13–2, 13–3,

13–4

Standards 1–3, 6–1, 6–12,

11–9

Stream 11–1, 12–1, 12–5,

12–6, 12–7, 12–8

Streams 1–11, 4–2, 4–10,

4–11, 5–2, 5–5, 5–6, 7–3,

9–1, 9–4, 10–3, 10–11, 10–

16, 10–17, 10–21

Study design 1–4, 4–1, 4–9,

6–1, 8–1, 11–8, 13–4

Suspended sediment 1–7,

7–1, 10–14, 10–24

T

Transport 1–2, 4–3, 5–1, 5–2,

5–4, 7–1, 8–1, 9–1, 10–24,

11–4, 11–13

Trend 1–2, 1–7, 1–13, 1–15,

4–11, 4–12, 5–1, 7–1, 9–1,

9–2, 9–4, 9–5

analysis 4–11, 4–12, 5–6, 8–1

V

Vadose zone 5–4

Vadose zone 5–1, 5–2, 10–20

Variables 11–5

prioritizing 6–1, 6–10, 6–12,

8–5

selection 4–3, 4–6, 6–1,

6–2, 6–3, 6–5, 6–8, 6–10,

6–11, 7–4, 11–5

Velocity 7–1, 7–3, 7–4, 8–3,

8–4, 10–3, 10–9, 10–21, 11–12
Part 614

National Water Quality Handbook

Index

(450-VI-NWQH, September 2003) Index–3

W

Wasteload allocation 1–3, 5–1,

5–5, 7–1, 8–1, 9–1

Water quality 8–5

defined 2–1, 2–2

management 4–1, 9–1

monitoring 2–2, 4–1, 4–2,

4–5, 4–6, 4–7, 4–9, 4–10,

4–11, 5–1, 5–3, 5–6, 6–1,

6–2, 7–1, 7–2, 7–4, 8–1,

9–2, 10–1, 10–17, 10–20,

12–1, 12–6

problem 2–1, 2–2, 4–1, 6–1,

6–3, 10–21, 12–4

Water sampling 8–7, 10–5, 10–20

Watershed 1–3, 1–5, 1–6, 1–7,

1–8, 1–10, 1–13, 1–15, 2–2,

4–1, 4–3, 4–5, 4–6, 4–7,

4–8, 4–9, 4–10, 4–11, 5–1,

5–2, 5–3, 5–4, 5–5, 5–6,

6–10, 8–1, 8–2, 8–6, 9–1,

10–1, 11–12, 12–1, 12–2,

12–6, 12–8

scale 5–1, 5–5, 12–1

Watershed scale 5–4, 5–5,

5–6, 12–1

Weirs 10–4

Well 4–2, 11–1

Wells 1–11, 5–1, 7–3, 7–4,

8–6, 8–7
United States

Department of

Agriculture

Natural

Resource

Conservation

Service

National Water Quality Handbook

Part 615

WQM Data Analysis

Part 615 Water Quality Monitoring

Data Analysis
(450–VI–NWQH, September 2003)

Part 615 Analysis of Water

Quality Monitoring

Data

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

National Water Quality Handbook
(450–VI–NWQH, September 2003) i

The purpose of part 615 of the National Water Quality Handbook (NWQH)

is to provide guidance in the statistical analysis of water quality data that

have been collected according to the designs described in part 614. Part 615

is concerned with the statistical analysis of monitoring results.

Part 615 of the National Water Quality Handbook was written by John C.

Clausen, Ph.D., College of Agriculture and Natural Resources, University of

Connecticut. The concept for this project was developed by James N.

Krider, former national environmental engineer, Natural Resources Conservation Service (NRCS), Washington, DC. Technical leadership was

provided by Bruce J. Newton, limnologist, NRCS National Water and

Climate Center, Portland, Oregon.

The following people contributed to the review of this document:

Richard H. McCuen, University of Maryland, College Park, Maryland

Carl DuPoldt, agricultural engineer, NRCS, Somerset, New Jersey

Barbara M. Vining, pesticide and nutrient specialist, formally with NRCS,

Indianapolis, Indiana

Howard Thomas, (retired) economist, Portland, Oregon

Robert C. Feurer, Philadelphia Suburban Water Company, Bryn Bawr,

Pennsylvania

Lynn Sampson, biologist, NRCS, East Lansing, Michigan

William H. Boyd, environmental engineer, NRCS National Water Management Center, Little Rock, Arkansas

James C. Wood, water quality specialist, NRCS, Burlington, Vermont

Richard Croft, water quality specialist, NRCS Watershed Science Institute,

Burlington, Vermont

Jorge A. Delgado, USDA-Agricultural Research Service

Ron Schierer, resource conservationist, Greely, Colorado

Joseph A. Neafsey, water quality specialist, Storrs, Connecticut, was the

contract project officer. Mary R. Mattinson, editor, and Wendy R. Pierce,

illustrator, NRCS National Cartographic and Geospatial Center, Fort Worth,

Texas, provided editorial and graphic support.

The National Water Quality Handbook is the result of a collaborative effort

of the NRCS Science and Technology Consortium. Special thanks to the

following individuals for their leadership and support in the development

and publishing of this essential technical reference:

Wil Fontenot, natural resource specialist, Lafayette, Louisianna

Jon Werner, national hydrologist, Conservation Engineering Division,

Washington, D.C.

Roy Mann, (retired) resource conservationist, Portland, Oregon

Ken Pfeiffer, pest management specialist, National Water and Climate

Center, Portland, Oregon

Bruce Newton, acting director, National Water and Climate Center, Portland, Oregon

Lynn Betts, communications director, Wildlife Habitat Management Institute, Des Moines, IA

Purpose

Preface

Acknowledgments
ii (450–VI–NWQH, September 2003)
(450–VI–NWQH, September 2003) iii

Contents:

Part 615 Analysis of Water Quality

Monitoring Data

Chapter 1 Introduction

Chapter 2 Basic Statistics

Chapter 3 Exploratory Data Analysis

Chapter 4 Statistical Assumptions

Chapter 5 Causality

Chapter 6 Hypothesis Testing

Chapter 7 Plot Designs

Chapter 8 Single Watershed

Chapter 9 Above and Below Watersheds

Chapter 10 Paired Watersheds

Chapter 11 Multiple Watersheds

Chapter 12 Trend Analysis

Chapter 13 Statistical Packages

Appendixes

Index
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 1 Introduction
(450–VI–NWQH, September 2003) 1–i

Chapter 1 Introduction

615.0100 General 1–1

615.0101 Steps in statistical analysis 1–1

615.0102 References 1–4

Tables Table 1–1 Summary of statistical procedures use in Part 615, 1–2

by subpart

Table 1–2 Summary of purpose of statistical procedures used 1–3

in Part 615

Figure Figure 1–1 Steps in data analysis for a water quality monitoring 1–1

study

Contents:
(450–VI–NWQH, September 2003) 1–1

Chapter 1 Introduction

615.0100 General

In National Water Quality Handbook (NWQH), part

614, the 12 steps for designing a water quality monitoring study were described. The overall purpose of part

615 is to provide assistance in how to analyze water

quality data that have been collected according to the

designs described in part 614. It is not the intention

that part 615 replace a basic course or textbook on

statistics; actually the reader would be much better

prepared for this part of the handbook having had

such a course.

Chapters 2 to 5 provide background information on

statistical analysis; chapters 6 to 12 provide guidance

on how to analyze data obtained from particular monitoring designs; and chapter 13 describes information

on several available computer packages for statistics.

The chapters include several examples that use both

hand calculations and computer-generated output.

Many computerized statistical packages are available

today, and to save time and effort, the user is encouraged to invest in a package. Chapter 13 provides

guidance on how to select statistical analysis software.

The Statistical Analysis System (SAS) software for a

PC is used for illustration purposes throughout part

615 of the NWQH.

Table 1–1 summarizes the statistical procedures used

in part 615 and indicates the chapter where that procedure is best described. Table 1–2 summarizes the

purpose of the various statistics and statistical tests

used in part 615 of the handbook.

615.0101 Steps in

statistical analysis

As in part 614, there are several steps in conducting

the statistical analysis of water quality data (fig. 1–1).

The analysis of data begins with Exploratory data

analysis (EDA), which is intended for the analyst to

become familiar with the data (Tukey 1977). The next

step is to test the appropriate assumptions for the

statistical tests to be performed. The assumptions may

include randomness, the type of distribution, the

homogeneity of variances, and independence. The

next step is to determine the appropriate hypotheses

to test. This step may have already been completed as

part of designing the study. The next step would be to

conduct the actual statistical tests. Finally, the conclusions regarding the data are constructed. The following chapters are intended to assist the analyst through

these steps of data analysis.

Figure 1–1 Steps in data analysis for a water quality

monitoring study

Data

EDA

Assumptions

Hypotheses

Statistical tests

Conclusions
Part 615

National Water Quality Handbook

Chapter 1 Introduction

1–2 (450-VI-NWQH, September 2003)

Table 1–1 Summary of statistical procedures used in Part 615, by chapter

Procedure - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Chapter - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

2345678910 11 12

Basic statistics:

Mean X X

Median X X

Mode X

Variance X

Standard deviation X

Standard error X X

Coefficient of variation X

Coefficient of skewness X X

Kurtosis X

Shapiro-Wilk W-statistic X

Autocorrelation coefficient X

Statistical tests:

t-test X X

Mann-Whitney U (nonparametric) X

Wilcoxon paired sample (nonpar) X

F ratio X X

Analysis of variance X X X

one-way X

Kruskal-Wallis one-way (nonpar)

two-way X

Tukey's multiple comparisons X X

Regression X X

Coefficient of determination X

Confidence intervals X

Analysis of covariance X

Kendall tau X
Chapter 1

(450-VI-NWQH, September 2003) 1–3

Introduction Part 615

National Water Quality Handbook

Table 1–2 Summary of purpose of statistical procedures used in Part 615

Procedure Purpose

Basic statistics:

Mean measure of central tendency

Median measure of central tendency

Mode measure of central tendency

Variance measure of dispersion of a random variable

Standard deviation measure of dispersion

Standard error measure of dispersion of a statistic

Coefficient of variation standardized measure of dispersion

Coefficient of skewness measure of symmetry

Kurtosis measure of long tailedness (peakedness) of dispersion

Shapiro-Wilk W-statistic test for normality

Autocorrelation coefficient measure of independence of observations on a single random variable

Statistical tests:

one-sample t-test comparison of a single mean to a standard

two-sample t-test comparison of two sample means

Mann-Whitney U (nonparametric) nonparametric comparison of unpaired two-sample ranks

Wilcoxon paired sample (nonpar) nonparametric comparison of paired ranks of differences

F ratio test of homogeneity of variances

Analysis of variance comparison of several means

one-way comparison of several means for one factor

Kruskal-Wallis one-way (nonpar) comparison of several means for one factor, nonparametric

two-way comparison of several means for two factors

Tukey's multiple comparisons determine which means are different for a rejected ANOVA test

Regression relationship between two variables

Coefficient of determination fraction of variation explained by relationship

Confidence intervals measure of accuracy of a statistic

Analysis of covariance comparison of regression slopes and intercepts among groups

Kendall tau nonparametric measure of correlation for trend detection
Part 615

National Water Quality Handbook

Chapter 1 Introduction

1–4 (450-VI-NWQH, September 2003)

615.0102 References

Tukey, J.W. 1977. Exploratory data analysis. AddisonWesley Publ. Co., Reading, MA.

United States Department of Agriculture, Natural

Resources Conservation Service. 1996. Design of

water quality monitoring systems. National

Water Quality Handbook, Part 514.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 2 Basic Statistics
(450–VI–NWQH, September 2003) 2–i

Chapter 2 Basic Statistics

615.0200 Introduction 2–1

615.0201 Purpose of statistics 2–1

615.0202 Statistical terms 2–2

615.0203 Data types 2–2

615.0204 Frequencies 2–3

615.0205 Measures of central tendency 2–6

(a) Mean ............................................................................................................... 2–6

(b) Median ........................................................................................................... 2–7

(c) Mode .............................................................................................................. 2–7

615.0206 Measures of dispersion 2–8

615.0207 References 2–11

Tables Table 2–1 Raw algae counts from St. Albans Bay, Vermont, 1985 2–4

Table 2–2 Frequency table of algal counts in St. Albans Bay, 2–4

Vermont

Table 2–3 Measures of central tendency for data types 2–6

Contents:
Part 615

National Water Quality Handbook

Chapter 2 Basic Statistics

2–ii (450–VI–NWQH, September 2003)

Figures Figure 2–1 Frequency histogram of algal counts in St. Albans Bay, 2–4

Vermont

Figure 2–2 Cumulative frequency of algal counts in St. Albans Bay, 2–5

Vermont

Figure 2–3 Normal distribution 2–8

Figure 2–4 Distributions showing skewness and kurtosis 2–9

Examples Example 2–1 Measures of central tendency 2–6

Example 2–2 Measures of dispersion 2–10
(450-VI–NWQH, September 2003) 2–1

Chapter 2 Basic Statistics

615.0200 Introduction

The understanding of basic statistics is important to

the analysis of water quality data. For many, chapter 2

is a review of some of the foundations of statistics.

Included in this chapter is the purpose of statistics,

some statistical terms, definitions of data types, frequencies, measures of central tendency, and measures

of dispersion.

615.0201 Purpose of

statistics

In water quality monitoring, the use of statistics is

important. For example, if our measurement of the

quality of water averaged three this year and six next

year, has the water quality really doubled in a year? In

other words, is the number three different from the six

and how confident can I be that they are or are not

different?

Almost all water quality data collected are a sample.

That is, we sample a certain portion of the entire

population of water quality data available. For example, if we sample a well weekly from 2003 to 2008

for nitrate-N, that also means that we are not sampling

the well during all other times. Assuming it takes at

most 30 minutes to sample a well, we are sampling

only 0.3 percent of the time during the week. We also

are sampling between 2003 and 2008. We are not

sampling before 2003 nor after 2008, which are times

that also may be part of the entire population of water

quality data. Therefore, the real purpose of statistics is

to be able to make conclusions from a sampling of

data for the entire population. Because we usually

cannot measure the entire population, a sample is

necessary. Statistics provide a systematic framework

for analysis and summarization of the sample data.
Part 615

National Water Quality Handbook

Chapter 2 Basic Statistics

2–2 (450–VI–NWQH, September 2003)

615.0202 Statistical terms

A number of statistical terms used throughout this

chapter are defined in this section.

Observation—A record representing a characteristic

of a real-world object (EPA 1973). The record is generally a single number; for example, a chemical concentration or the number of macroinvertebrates found in a

sample. The observation is the data you collect.

Population—The population is all possible values of

a variable and is synonymous with universe (Steel and

Torrie 1960).

Sample—A part of the population that should be

representative of the population (Steele and Torrie

1960). A sample is a set of observations from the

population.

Random sample—A sample that has an equal chance

of being selected (Snedecor and Cochran 1980). Usually such a sample is collected to eliminate bias in the

data.

615.0203 Data types

The two types of random variables that can be collected in water quality monitoring projects are continuous and discrete. The type of data selected influences the statistics applied and depends on the type of

information being collected.

Continuous data means that all values within some

range are possible (Steel and Torrie 1960). An example

of continuous data would be concentrations. A nearly

infinite number of values are possible within some

range. More values become possible as detection

equipment becomes more precise.

Discrete data means that the possible values can be

only a certain set of numbers (Snedecor and Cochran,

1980). Examples include counts, categories, and binary data. The number of fish collected would be

discrete data.

In addition to the continuous and discrete data, several

scales can be used to measure water quality data. They

include nominal, ordinal, interval, and ratio scales.

Nominal data include categories without ranking

among the categories. The term nominal means that

the category is called a name. Often, nominal data are

binary, such as presence or absence. An example of

nominal data would be taxa of macroinvertebrates

present in a stream.

Ordinal data imply ordering (Ward et al. 1990). Ordinal variables measure the degree of something

(Horowitz 1981). Trophic status—oligotrophic, mesotrophic, and eutrophic—is an example of an ordinal

scale. However, the differences among the categories

do not have to be equal.

Interval data also use ordering, but intervals between

the categories are equal. Intervals or categories are

used to describe the data. Interval data are used for

data sets that do not have a true zero. For example,

the intervals for temperature could be <25, 25–50,

50–75, and >75 degrees Fahrenheit. Intervals also are

used to describe size classes of fish, such as <10,

10–20, 20–30, and >30 centimeters.
Chapter 2

(450–VI–NWQH, September 2003) 2–3

Basic Statistics Part 615

National Water Quality Handbook

Ratio data are similar to interval data except that a

true zero exists. Therefore, 500 is 5 times greater than

100. Concentration and flow data are ratio data. 615.0204 Frequencies

Water quality data can be presented in many ways.

They include tables of raw data or frequencies, seasonal tables, and graphical pie charts or frequency

diagrams. A raw data table is given in table 2–1 for

algal counts in St. Albans Bay, Lake Champlain,

Vermont.

This raw data can be summarized in a frequency table

by establishing intervals in the data. For example, the

raw algal data in table 2–1 were grouped into intervals

of 2,500 organisms per milliliter and are summarized in

table 2–2. The frequency is the number of observations

for that class interval.

The frequency table can also be displayed as a frequency histogram. A histogram graphs frequency as a

function of class intervals as rectangles on a graph

(fig. 2–1).

Such data may also be presented as a cumulative

frequency histogram. The cumulative frequency is the

summation of all the frequencies up to and including

the class interval plotted (fig. 2–2). The points are

joined with a line forming a cumulative frequency

polygon (Zar 1996).

The frequency histogram and the cumulative frequency polygon can be converted to relative frequency. This is done by changing the Y-axis to either a

decimal or percentage scale by dividing the frequencies by the total sample size.

Frequency plots have several values, including:

• help assess the distribution type

• detect characteristics of the data (e.g., central

tendency, dispersion)

• identify potential outliers

• assess the range of data

Although these forms of data presentation are useful,

there are other ways to describe the data. They include describing a measure of central tendency and a

measure of dispersion of the data.
Part 615

National Water Quality Handbook

Chapter 2 Basic Statistics

2–4 (450–VI–NWQH, September 2003)

Figure 2–1 Frequency histogram of algal counts in St. Albans Bay, Vermont

Table 2–1 Raw algal counts (organisms/mL) from St.

Albans Bay, Vermont, 1985

Date Count Date Count

1/23 25 8/6 1,564

3/19 125 8/13 6,384

4/23 410 8/20 10,062

5/14 1,883 8/27 6,305

5/30 770 9/4 39,861

6/11 2,229 9/10 6,755

6/18 519 9/17 15,074

6/25 899 9/25 36,823

7/2 882 10/1 29,448

7/9 565 10/8 45,283

7/16 826 10/15 1,336

7/23 299 11/5 1,000

7/30 547 12/4 56

Table 2–2 Frequency table of algal counts in St. Albans

Bay, Vermont

Interval Frequency Interval Frequency

0 – 2,500 17 25,000 – 27,500 0

2,500 – 5,000 0 27,500 – 30,000 1

5,000 – 7,500 3 30,000 – 32,500 0

7,500 – 10,000 0 32,500 – 35,000 0

10,000 – 12,500 1 35,000 – 37,500 1

12,500 – 15,000 0 37,500 – 40,000 1

15,000 – 17,500 1 40,000 – 42,500 0

17,500 – 20,000 0 42,500 – 45,000 0

20,000 – 22,500 0 45,000 – 47,500 1

22,500 – 25,000 0

20

15

10

5

0

2,500 7,500 12,500 17,500 22,500 27,500 32,500 37,500 42,500 47,500

5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000

Algae-organisms/mL

Frequency
Chapter 2

(450–VI–NWQH, September 2003) 2–5

Basic Statistics Part 615

National Water Quality Handbook

Figure 2–2 Cumulative frequency of algal counts in St. Albans Bay, Vermont

30

25

15

20

5

10

0

0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000

2,500 7,500 12,500 17,500 22,500 27,500 32,500 37,500 42,500

Algae-organisms/mL

Cumulative frequency
Part 615

National Water Quality Handbook

Chapter 2 Basic Statistics

2–6 (450–VI–NWQH, September 2003)

Example 2–1 Measures of central tendency

Given: The algal count data from St. Albans Bay in table 2–1.

Determine: The mean, geometric mean, median, and mode.

Solution:

Mean: X = + + ++ = 25 125 410 56

26

8 074 K , organisms/mL

Geometric mean: X anti

X

n g anti

i

i

n

== = =

∑

log log . , 1 3 2343 1 715 organisms/mL

Median—Because the data contain an even number of data values (n=26), the median is the

mean of the two middle values.

Median = + = 1 336 1 000

2

1 168 , , , organisms/mL

Mode—No value occurred more than once in table 2–1; therefore, the mode does not exist for

this data set.

615.0105 Measures of

central tendency

Several measures of central tendency for a data set are

available. The appropriate measure varies with the

type of data (table 2–3). Example 2–1 illustrates the

different measures of central tendency.

(a) Mean

The most commonly used measure is the arithmetic

mean or average. The mean ( X ) is the sum of the

observations ( X ∑ i ) divided by the number of observations (n):

X

X

n

i = ∑ [2–1]

The mean is appropriate for interval and ratio data, but

not nominal or ordinal types of information. Arithmetic means may not be the best measure of central

tendency when distributions are skewed (long tail) left

or right. If the data are censored, that is, there are

observations below detection limits, the calculation of

the mean is more rigorous. The mean for a censored

distribution can be calculated from (Newman et al.

1989):

X X k

n k

f

F = − −

( )

( ) σ

ε

ε

[2–2]

Table 2–3 Measures of central tendency for data types

Scale Measure Example

nominal mode taxa

ordinal median trophic state

interval mean fish age class

ratio mean concentrations
Chapter 2

(450–VI–NWQH, September 2003) 2–7

Basic Statistics Part 615

National Water Quality Handbook

where:

n = total number of observations

k = number of observations below the detection

limit

X = mean of all the values above the detection

limit

σ = standard deviation

f(ε) = distribution function for the normal

distribution

F(ε) = cumulative distribution function for the

normal distribution

ε is obtained from:

ε μ

σ = DL − ˆ [2–3]

where:

DL = detection limit

μˆ = mean

In water quality data a geometric mean is often calculated. The geometric mean X G is the nth root of the

product of n values (Landwehr 1978, Zar 1996):

X XX X G = 1 2 n ... [2–4]

The geometric mean is also obtained as the antilog of

the mean of the log of the values, which is the typical

manner of calculating the geometric mean:

X anti

X

n G

i

i

n

= =

∑

log 1 [2–5]

The geometric mean is only used when all the values

are positive and is typically used as the measure of

central tendency for log transformed data.

(b) Median

A second measure of central tendency is the median

( Xm). The median is the value for which 50 percent of

observations are greater and 50 percent are lesser. It is

the midpoint of a frequency distribution. The median is

an appropriate measure of centrality for ordinal data

and is often used when the data are highly skewed. If a

distribution is symmetrical, then the mean and the

median will be the same.

 X

X

m X X

n

=  n n +





























( ) +

+

1

2

2

1

2

2

if n is odd

 if n is even 















[2–6]

(c) Mode

The mode is the final measure of central tendency. It is

the value that occurs most frequently. The mode is the

only appropriate measure of central tendency for

nominal data and quickly describes the most commonly occurring value.
Part 615

National Water Quality Handbook

Chapter 2 Basic Statistics

2–8 (450–VI–NWQH, September 2003)

615.0106 Measures of

dispersion

Measures of dispersion are useful to further understand a water quality data set. They indicate how

spread out from the central tendency are the observations. The common measures of dispersion include the

range, the variance (standard deviation is square root

of variance), the standard error (standard deviation of

a statistic, such as the mean), and the coefficient of

variation.

A normal distribution has a preponderance of values

around the mean and fewer observations at the extremes of the range of values. Such a distribution

forms the typical bell-shaped curve (fig. 2–3).

The range is the distance from the smallest value to

the largest value in the data set. It is the most simple

of the measures of dispersion, but is subject to extreme values.

The sample variance is the sum of the squares of the

deviations from the mean divided by the number of

observations minus 1. Another term for variance is the

mean square, which is the sums of squares divided by

the degrees of freedom (n-1). The sample variance is

represented by s2, and the population variance is

represented by σ2.

Figure 2–3 Normal distribution

The sample variance is calculated from:

s

X

X

n

n

i

i

2

2

2

1 =

− ( )

−

∑ ∑ [2–7]

where:

Xi = value of the observation

n = number of observations

The population variance is the sum of the squares of

the deviations from the mean divided by the number of

observations, rather than the number of observations

minus one. The population variance is rarely used in

water quality studies because sampling is almost

always being conducted. Some calculators compute

the wrong variance.

The standard deviation (s) is the square root of the

variance ( s 2 ). The standard deviation carries the

same units as the original data. The s is also called the

root mean square. For normal distributions, one standard deviation on either side of the mean includes 68

percent of the observations and two standard deviations include 95 percent (fig. 2–3).

The standard error of the mean (SE), also termed the

standard deviation of the mean, indicates the variability about the estimate of the mean:

SE s

n = [2–8]

where:

s = standard deviation

n = number of observations

The standard error of the mean can be shown as an

error bar in graphs summarizing mean values.

The coefficient of variation (CV) is a measure of the

relative dispersion about the mean. It is defined as the

standard deviation expressed as a percent of the mean:

CV s

X = 100 ×

[2–9]

where:

s = standard deviation

X = mean

34% 34%

Mean

s

x-s x+s

One

standard

deviation

Y

X
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National Water Quality Handbook

The advantage of the coefficient of variation is that it

allows direct comparison of variations between variables or among studies.

The coefficient of skewness indicates how equally

distributed or symmetrical the data are about the

mean. It is defined as the cube of the deviations about

the mean (SAS 1985):

g

n XX

n ns

i

1

3

3 1 2 = ( ) −

( ) − ( ) −

∑ [2–10]

The coefficient of skewness is normally distributed

with a mean of 0 and a standard deviation of:

6 1

213

05

n n

nnn

( ) −

( ) − ( ) + ( ) +





 





.

[2–11]

If g1 is greater than four times the standard deviation

of the skewness coefficient, then the data are skewed.

Snedecor and Cochran (1980) provide a table for

determining the significance of the skewness coefficient (appendix B). The sign of the skewness coefficient indicates whether the data are positively skewed

(upper tail extended) or negatively skewed (lower tail

extended) (fig. 2–4).

Kurtosis is a measure of the long tailedness of the

distribution. It is defined as the average of the deviations from the mean raised to the 4th power divided by

the standard deviation to the 4th power (SAS 1985):

g

nn X X

n n ns

n

n n

i

2

4

4

2 1

123

3 1

2 3 = ( ) + ( ) −

( ) − ( ) − ( ) − − ( ) −( ) − ( ) −

∑ [2–12]

The kurtosis is normally distributed with a mean of –3

and a standard deviation of:

24

n

If the ratio of g2 to standard deviation is less than –2,

then the distribution has shorter tails than a normal

distribution. If the ratio is more than 2, then the distribution has longer tails than a normal distribution (fig.

2–4). Snedecor and Cochran (1980) provide a table for

testing the kurtosis based on the sample size and level

of confidence desired.

Figure 2–4 Distributions showing skewness and kurtosis

Median

a b

c d

Mean Median

Mean

Positive skewness Negative skewness

Leptokurtic kurtosis Platykurtic kurtosis

X X

X X

Y Y

Y Y
Part 615

National Water Quality Handbook

Chapter 2 Basic Statistics

2–10 (450–VI–NWQH, September 2003)

Example 2–2 Measures of dispersion

Given: Algal data in table 2–1

Determine: Range, variance, standard deviation, standard error, coefficient of variation, skewness, and

kurtosis values.

Solution: Range: 45,283 – 25 = 45,258 organisms/mL

Variance: s2

2

6 334 495 000 209 930

26

26 1 = 185 590 000

− ( )

− =

,,, ,

, ,

Standard deviation: s organisms mL = = 185 590 000 13 623 ,, , /

Standard error: SE organisms mL = = 13 623

26

2 672 , , /

Coefficient of variation: CV = ( ) = 100 13 623

8 074

169 ,

, %

Skewness: g

E 1 3

26 0 110873 15

25 24 23 13 623 = 1 90 ( )( ) +

( )( )( )( ) = .

, .

Since the skewness coefficient is positive, the upper tail is extended. Based upon a table

provided by Snedecor and Cochran (1980) (appendix B), this skewness is significant at a

probability (p) = 0.01.

Kurtosis:

g

E 2 4

2

26 27 0 38816 19

25 24 23 13 623

3 25

24 23 = ( )( )( ) +

( )( )( )( ) − ( )

( )

.

, ( )

= 2 335 .

The standard deviation of the kurtosis is:

24 24

26

0 9607

0 9607

2 4

2

n

g

= =

=

.

. .

Since the ratio of g2 to the standard deviation is greater than 2, the algae data have longer tails

than a normal distribution (fig. 2–1).
Chapter 2

(450–VI–NWQH, September 2003) 2–11

Basic Statistics Part 615

National Water Quality Handbook

615.0107 References

Horowitz, G. 1981. Sadistic statistics. Avery Publishing

Group, Inc., Wayne, NJ.

Landwehr, J.M. 1978. Some properties of the geometric mean and its use in water quality standards.

Water Resources Research 14(3):467-473.

Newman, M.C., P.M. Dixon, B.B. Looney, and J.E.

Pinder, III. 1989. Estimating mean and variance

for environmental samples with below detection

limit observations. Water Resources Bulletin

25(4):905-916.

SAS Institute, Inc. 1985. SAS procedures guide for

personal computers. SAS Institute, Inc. Cary, NC

27511.

Snedecor, G.W., and W.G. Cochran. 1980. Statistical

methods. 7th Ed. The Iowa State Univ. Press,

Ames.

Steele, R.G.D., and J.H. Torrie. 1960. Principles and

procedures of statistics. McGraw-Hill Book Co.,

Inc., New York.

United States Environmental Protection Agency. 1973.

Biological field and laboratory methods for

measuring the quality of surface waters and

effluents. EPA-670/4-73-001. Office of Research

and Development. Cincinnati, OH.

Ward, R.C., J.C. Loftis, and G.B. McBride. 1990. Design

of water quality monitoring systems. Van

Nostrand Reinhold. New York.

Zar, J.H. 1996. Biostatistical analysis. 3rd Ed. Prentice

Hall, Upper Saddle River, NJ 07458.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 3 Exploratory Data Analysis
(450–VI–NWQH, September 2003) 3–i

Chapter 3 Exploratory Data Analysis

Contents: 615.0300 Introduction 3–1

615.0301 Writing numbers 3–1

615.0302 Stem-and-leaf diagrams 3–2

615.0303 Schematic summaries 3–2

(a) Box-and-whisker plot ................................................................................... 3–2

615.0304 Transformations 3–4

615.0305 Comparisons 3–6

615.0306 Plots of relationship 3–6

615.0307 Smoothing data 3–7

615.0308 References 3–8

Figures Figure 3–1 Stem-and-leaf diagram for algal data from SAS® output 3–2

Figure 3–2 Box-and-whisker plot 3–3

Figure 3–3 Boxplot for the algal data from SAS® output 3–3

Figure 3–4 Boxplot for the algal data from JMP output 3–3

Figure 3–5 The mean as a function of the size of the constant 3–4

added in a log transformation

Figure 3–6 Boxplots for two annual sets of phosphorus data 3–6

Figure 3–7 Relationship of observed to predicted runoff (*=p=0.05) 3–7

Figure 3–8 Time plot of raw data 3–7
Part 615

National Water Quality Handbook

Chapter 3

3–ii (450-VI-NWQH, September 2003)

Exploratory Data Analysis

Figure 3–9 Smoothed data using medians of three 3–7

Figure 3–10 Smoothed data using the eye 3–8

Figure 3–11 Smoothed data using blurring 3–8

Examples Example 3–1 Log transformations with zero values 3–4

Example 3–2 Transformations 3–5
(450–VI–NWQH, September 2003) 3–1

Chapter 3 Exploratory data analysis

615.0300 Introduction

The first step in water quality data analysis is exploratory data analysis (EDA). For most data sets, EDA is

a necessary step. The basic purpose for EDA is to

better become familiar with the data. EDA is "detective work" that examines the data for how it appears

(Tukey 1977). EDA, as proposed by Tukey, relies

heavily on pictures. It is intended to provide indications rather than confirmations of a specific test. The

actual procedure used varies with the type of data

being explored, whether univariate, bivariate, or

multivariate. Not all techniques are appropriate for all

data; however, a number of steps are often examined

for routine EDA. They include writing the numbers,

stem-and-leaf diagrams, schematic summaries, transformations, comparisons, plots of relationships, and

smoothing data.

Chapter 3 explains the various approaches to EDA. It

presents examples of each of the routine methods

used in EDA.

615.0301 Writing numbers

The process of writing numbers may be as simple as

the listing of the raw data in a table. Tukey (1977)

suggests using colors to highlight differences in the

numbers making visual inspection easier.

Table 2–1 in chapter 2 is an example of writing numbers. In this case the numbers were written according

to date. An alternative presentation would be to write

the numbers from lowest to highest.
Part 615

National Water Quality Handbook

Chapter 3

3–2 (450–VI–NWQH, September 2003)

Exploratory data analysis

615.0302 Stem-and-leaf

diagrams

Stem-and-leaf diagrams summarize the data visually in

a sideways frequency diagram. Each line in the diagram is a stem, and each data point is a leaf on the

stem. The stem represents the first digit of an observation in the data set. The leaves indicate the number of

observations at that stem and the digits for those

observations. Significant figures to the right of the

leaves often are dropped. Stem-and-leaf diagrams are

presented in many ways. Such a diagram, as presented

in output from the Statistical Analysis System software

(SAS®) for the algal data in table 01–1, is given in

figure 3–1.

In this diagram, each stem is a multiple of 10,000;

indicated by a 10**+4 by SAS®. The 4 represents

40,000, 3 represents 30,000 and so on. The leaf of 05

indicates that there are two numbers of 40,000 or

greater, after rounding to the nearest 1,000. The data

are skewed toward the low values (Stem = 0). There

are more values for the leaf column at the stem of 0

than other stem values. SAS® output indicates the

number of leaves in each stem by a # column. SAS®

output also gives a multiplication factor for the

Stem.Leaf data if needed.

615.0303 Schematic

summaries

The stem-and-leaf diagram can also be summarized

using five numbers: the median, maximum, minimum,

and upper and lower hinges. The rank of the median

can be determined from:

median rank=1+count

2 [3–1]

The hinges are half-way from the extremes to the

median and are determined by:

hinge=1+median rank

2 [3–2]

The hinges are so-named because they represent folds

in the data between the median and the extremes

(Tukey 1977). Another way to characterize the lower

and upper hinges is as the 25th and 75th percentile

values. The upper hinge is the value that is three/

fourths of the way along the values when ranked from

lowest to highest.

These five numbers can be provided in a box, as below:

Med

Hlow Hhigh

Min Max

For example, using the algae data from table 2–1, the

five-number summary would be:

1,168

547 6,755

25 45,283

(a) Box-and-whisker plot

Another more common schematic summary is the boxand-whisker plot. This is really a five-number summary

in graphical form. The box extends from lower hinge

to upper hinge and is crossed with a bar at the median

(fig. 3–2). The 75th percentile means that 75 percent of

all values are below that value. The whiskers extend

from each end of the box to the respective extreme.

Figure 3–1 Stem-and-leaf diagram for algal data from

SAS® output

Stem Leaf #

4 05 2

37 1

29 1

1 05 2

0 00000111111111222667 20

++++

Multiply Stem.Leaf by 10**+4

- - -

-

- - -

-

- - -

-

- - -

-
Chapter 615.3

(450–VI–NWQH, September 2003) 3–3

Exploratory data analysis Part 615

National Water Quality Handbook

In some cases it is desirable to show some data values

as farther out than others. H-spread is a term given to

the differences between the hinges. A step is 1.5 times

the box length (H-spread). An inner fence can be

placed at one step outside the hinges; an outer fence is

located at two steps outside the hinges.

The values located inside the inner fence, but closest

to the inner fence are termed adjacent. Values between the inner and outer fences are termed outside.

And values beyond the outer fences are far out.

The box-and-whisker plot is useful in conveying a

concept of how even is the data above and below the

median. In some cases the whisker may end at the

adjacent values.

Boxplots are included in SAS® output using PROC

UNIVARIATE PLOT (SAS® 1985). The boxplot for the

algal data is shown in figure 3–3. Another boxplot from

the output of JMP (SAS® Institute, Inc.) is given in

figure 3–4.

The boxplots show that the data are highly skewed to

the low values. The bottom and top of the box represent the 25th and 75th percentiles (hinges). The center

horizontal line is drawn at the median, and a + is given

at the mean (SAS® output). In the example, all these

lines are so close that they are printed on the same

line (fig. 3–3). The whiskers in SAS® extend to 1.5 the

inter-quartile range (H-spread). Values more extreme,

but within three interquartile ranges, are indicated

with a zero. Values outside are indicated with an

asterisk. For the example in figure 3–3, the three

asterisks indicate three extreme values outside three

interquartiles. The JMP outlier boxplot uses dots for

points beyond the whiskers. The diamond indicates

the 95 percent confidence intervals about the mean.

Figure 3–2 Box-and-whisker plot

Figure 3–3 Boxplot for the algal data from SAS® output

1.5 H-spread

75th percentile

Median

25th percentile

1.5 H-spread

H-spread

Figure 3–4 Boxplot for the algal data from JMP output

*

*

*

+++ -- --
Part 615

National Water Quality Handbook

Chapter 3

3–4 (450–VI–NWQH, September 2003)

Exploratory data analysis

615.0304 Transformations

Transformations of the data are sometimes needed to

normalize the data or stabilize the variance. Transformations also change the appearance of the data into a

form that may be more readily understandable (Tukey

1977). Some basic rules for different transformations

have been described by Tukey (1977):

• Amounts and counts can never be less than zero,

but can be large. A transformation may be useful

if the ratio of the largest value to the smallest

value is large (i.e., 100 or more). If the ratio is

small (i.e., 1), the transformation will not modify

the appearance of the data.

• Balances, values which can be both positive and

negative, are usually not improved by

transformations.

• Fractions and percentages may be better expressed with transformations.

• Grades, such as A, B, C, D, also may respond to

complex transformations.

A common transformation for water quality data is the

use of logarithms. The log distribution for concentration data makes sense because negative values do not

exist, many values exist at lower concentrations, and a

few values will exist at much higher concentrations

(positively skewed). If plotted in a frequency diagram,

the typical exponential decay curve results. Logs also

are appropriate when the standard deviation in the

data is likely to be proportional to the mean or for data

that are proportional rather than additive on a linear

scale (Snedecor and Cochran 1980, Sokal and Rohlf

1969). Logs tend to squeeze the data together and

make it more symmetrical. A log transformation of

zero does not exist; zeros can exist in a data set of

mass export values. Also, when the data values are

less than one, a log transformation gives negative

numbers. In such cases the addition of a constant,

such as log(X+1), is recommended (Steel and Torrie

1960, Zar 1984). However, the size of the constant

added influences the estimate of the mean for the data

set, as shown in example 3–1.

Example 3–1 Log transformations with zero values

A log10 transformation was applied to the following values of X:

0.25 5.0

0.5 8.0

0.8 14.0

1.0 50.0

1.2 100.0

Additional transformations were made by adding

the following constants: 10.0, 1.0, 0.1, 0.01, and

0.00001. The mean was obtained for each transformed data set as the antilog of the mean of the

logged data minus the added constant. The

results from these transformations are plotted in

figure 3–5. These transformations indicate that

adding smaller constants results in mean values

that approach the true mean for the data set.

Figure 3–5 The mean as a function of the size of

the constant added in a log transformation

10

8

6

0

2

4

X X+0.01 X+0.1 X+1.0 X+10.0 X+0.00001

Log of:

ALog (mean)-C
Chapter 615.3

(450–VI–NWQH, September 2003) 3–5

Exploratory data analysis Part 615

National Water Quality Handbook

Counts, such as for bacteria data, can be re-expressed

with logs and square roots, with root counts more

often used (Tukey 1977). When the data numbers are

small (<10) the square root transformation is recommended (Steel and Torrie 1960). If the counts are

small, Snedecor and Cochran (1980) recommend the

square root (X + 1) transformation.

Percentage data, based on counts, where the data

range from 0 to 20 percent or 80 to 100 percent may be

transformed with a square root (Steel and Torrie

1960). Percentage or decimal data based on binomial

data can be re-expressed using an arc sine or inverse

sine transformation.

For data that are skewed to the left, a value squared

transformation has been recommended (Zar 1984).

Generally, when transformations are made, the mean

is transformed back to the original scale, but variances

or standard deviations should not be transformed back

to the original scale (Steel and Torrie 1960).

Example 3–2 illustrates the transformation of the St.

Albans Bay data from chapter 2.

Example 3–2 Transformations

A log10 transformation was made of the St.

Albans Bay algal data in table 2–1. The stem-andleaf diagram for the transformed data indicates

that the transformation removed much of the

skewness in the algal count data, as compared to

figure 3–1.

Stem Leaf #

4 5667 4

4 02 2

3 888 3

3 001233 6

2 56778999 8

21 1

17 1

14 1

- - - -+- - - -

The box-and-whisker plot of the log10 transformed

data also shows that the data are now more evenly

distributed above and below the median as compared with figure 3–3. The absence of zeros and

asterisks in the whiskers indicates that there are

no values more extreme than three interquartile

ranges. This shape is characteristic of a normal

distribution.

|

|

+----+

*--+--*

+----+

|

|
Part 615

National Water Quality Handbook

Chapter 3

3–6 (450–VI–NWQH, September 2003)

Exploratory data analysis

615.0305 Comparisons

Different groups of data can be compared in several

ways. They include side-by-side stem-and-leaf displays,

tables of means or medians, and box-and-whisker

plots. Transformations of scale often aid in the comparison among groups. For example, the box plots in

figure 3–6 indicate that the phosphorus concentrations

for 1990 were lower and less variable than for 1980.

The width of the box can be used to reflect the sample

size when comparing samples of different sizes (R.H.

McCuen 1998, personal communication).

615.0306 Plots of relationship

Plots can be used to describe a relationship between a

response variable (dependent) and a factor (independent) (Tukey 1977). The independent variable is usually shown as the abscissa (horizontal X-axis), and the

dependent variable is shown as the ordinate (vertical

Y-axis). Although default values in computer graphics

programs make many decisions for us, there are some

general rules that are useful in plotting relationships.

These rules include guidance regarding the scale,

shape, grid, and labeling of axis.

If comparing different plots with similar information,

all plots should be at the same scale even though your

graphics program may not default in this manner.

The shape of the plot is another important consideration. Plots can be taller than wide, wider than tall,

and of equal dimensions. Taller than wide plots are

useful for growth or decay phenomenon. Wider than

tall plots facilitate reading from left to right and might

be useful for scatter diagrams or time plots. Square

plots may be useful in situations where the same units

are plotted on each axis and the 45 degree line, representing Y = X, has some meaning. Figure 3–7 provides

an example of such a graph—the comparison of observed data to data simulated by a model (Jamieson

and Clausen 1988).

Figure 3–6 Boxplots for two annual sets of phosphorus

data

Total P (mg/L)

1980 1990

Figure 3–7 Relationship of observed to predicted runoff

(*=p=0.05)

x

x

x

x

xxx

Y=X

0

0

50

100

150

200

250

50 100 150

Simulated runoff (mm)

Observed runoff (mm)

200 250

Y=6.00 X-.59

r2=.86*
Chapter 615.3

(450–VI–NWQH, September 2003) 3–7

Exploratory data analysis Part 615

National Water Quality Handbook

The type of grid chosen for the graph influences the

interpretation of the graph. Data that are extremely

variable, such as suspended solids concentrations,

might better be graphed using a log scale rather than a

linear scale. Also, exponential relationships are

straightened by plotting them on a log-log scale. If the

data contain zero values, they cannot be plotted on a

log scale unless a constant is added, as described in

the previous section on transformations.

The labeling of axis, both in terms of the use of values

and tick marks, influences interpretations from the

graph. Generally, the number of tick marks and values

shown on the graph are minimized because they can

be distracting to the eye. An exception would be when

the graph is used to pick off points. The origin of the

graph, where Y = X, is generally zero to show the real

magnitude of the values. This guidance is often abused

in the media (e.g., stock market) to indicate larger

variations than are really occurring.

One of the more common abuses of plots of relationship is termed spurious correlation (Kite 1989). This

occurs when both axes have a variable in common.

For example, a plot of mass export as a function of

stream discharge is almost always guaranteed to show

a positive relationship. This occurs because the values

for the variable discharge are included in both axes. In

regression, this would also violate the assumption of

independence.

615.0307 Smoothing data

Smoothing data allow definition of general trends

without looking at too much detail (Tukey 1977).

Generally, the Y data are smoothed and the X data

become intervals. Several techniques are used in

smoothing. They include running medians or averages,

eye smoothing, blurring, and splitting. An example of a

water quality data set where smoothing might be

useful is a time plot of concentration data (fig. 3–8).

The data as they appear are quite rough, and general

trends are difficult to interpret. To use running medians or averages, take adjacent Y values and calculate a

new smoothed point. Running implies that a central

estimate is made for each point as opposed to creating

intervals and deriving a central estimate for each

interval. A running 3-day average of daily data is computed by determining the average of the days around

Monday, then around Tuesday, and so on. For example, the median of three values running was used to

develop the points for figure 3–9. The first three points

were: 3, 7, and 10, which would result in a median of 7.

New medians are calculated for the second set of

three values by skipping the first number. In this case

using the medians of a larger number of points may

have provided a smoother picture of the data. The

mean could be used rather than the median for

smoothing. This method is also called the moving

average method.

Figure 3–8 Time plot of raw data

Jan Jul

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990

Jan Jul Jan Jul Jan Jul Jan JulJan Jul Jan Jul Jan Jul Jan Jul Jan Jul

Suspended solids (mg/L)

0

20

40

60

80

100

Time

Figure 3–9 Smoothed data using medians of three

Jan Jul

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990

Jan Jul Jan Jul Jan Jul Jan JulJan Jul Jan Jul Jan Jul Jan Jul Jan Jul

Suspended solids (mg/L)

0

20

40

60

80

100

Time

Smoothed
Part 615

National Water Quality Handbook

Chapter 3

3–8 (450–VI–NWQH, September 2003)

Exploratory data analysis

Figure 3–10 Smoothed data using the eye

Jan Jul

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990

Jan Jul Jan Jul Jan Jul Jan JulJan Jul Jan Jul Jan Jul Jan Jul Jan Jul

Suspended solids (mg/L)

0

20

40

60

80

100

Time

Smoothed

Figure 3–11 Smoothed data using blurring

Eye smoothing is drawing a smooth curve through the

data. However, smoothing by eye allows bias to be

used to meet the need or intent of the analyst. For

example, figure 3–10 shows two curves fit to the

smoothed data that are quite different from each

other. Both lines are smoothing of the data. One line

attempts to follow the peaks and valleys; the other

suggests an even more general trend. This trend is

contingent upon when monitoring began. Note that if

the sampling began in 1983, a different trend might be

suggested.

Blurring is a method of smoothing where the data

points are replaced with vertical lines of some length

showing their variability. In figure 3–11, the raw data

have been blurred, which suggests a band of data

rather than a line or a series of points.

Jan Jul

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990

Jan Jul Jan Jul Jan Jul Jan JulJan Jul Jan Jul Jan Jul Jan Jul Jan Jul

Suspended solids (mg/L)

0

20

40

60

80

100

Time

Smoothed

615.0308 References

Jamieson, C.A., and J.C. Clausen. 1988. Test of the

CREAMS model on agricultural fields in Vermont. Water Resourc. Bul. 24(6):1219-1226.

Kite, G. 1989. Some statistical observations. Water

Resourc. Bul. 25(3):483-490.

SAS Institute, Inc. 1985. SAS procedures guide for

personal computers, Version 6 edition, SAS

Institute, Inc., Cary, NC.

Snedecor, G.W., and W.G. Cochran. 1980. Statistical

methods. 7th Ed., The Iowa State Univ. Press,

Ames, IA.

Sokal, R.R., and F.J. Rohlf. 1969. Introduction to biostatistics. W.H. Freeman and Co., San Francisco,

CA.

Steel, R.G.D., and J.H. Torrie. 1960. Principles and

procedures of statistics. McGraw-Hill Book Co.,

Inc., New York, NY.

Tukey, J.W. 1977. Exploratory data analysis. AddisonWesley Publ. Co., Reading, MA.

Zar, J.H. 1984. Biostatistical analysis. Prentice-Hall,

Inc., Englewood Cliffs, NJ.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 4 Statistical Assumptions
(450–VI–NWQH, September 2003) 4–i

Chapter 4 Statistical Assumptions

Contents: 615.0400 Introduction 4–1

615.0401 Assumptions 4–1

(a) Randomness .................................................................................................. 4–1

(b) Normal distribution ...................................................................................... 4–2

(c) Homogeneity of variances ........................................................................... 4–3

(d) Independence ................................................................................................ 4–4

(e) Additivity ....................................................................................................... 4–4

615.0402 Residual plots 4–5

615.0403 Missing data 4–5

615.0404 Extreme outliers 4–6

615.0405 Summary 4–7

615.0406 References 4–7

Table Table 4–1 Statistical assumptions and tests 4–7

Figures Figure 4–1 Examples of frequency distributions 4–2

Figure 4–2 Residual plots for linear regression 4–5

Examples Example 4–1 Cumulative frequency distributions for St. Albans 4–2

Bay algal data from SAS output

Example 4–2 Test of normality for the St. Albans Bay algal data 4–3
(450–VI–NWQH, September 2003) 4–1

Chapter 4 Statistical Assumptions

615.0400 Introduction

When applying statistical analyses to water quality

data, such as analysis of variance, we must be familiar

with several underlying assumptions. It is important to

know how to test if these assumptions have been

violated and what to do if they are violated. All assumptions are difficult to meet exactly. It is more

important to understand whether the violation of an

assumption has a serious consequence on the probability statements made based on the assumption

(Glass, et al. 1972). The main assumptions are: randomness, normality, homogeneity of variances, independence, and additivity.

Chapter 4 describes the various statistical assumptions

made when performing statistical tests. The consequences of failing to exactly meet these assumptions

are presented for each assumption. The usefulness of

residual plots in evaluating assumptions is also detailed as is how to deal with missing data and extreme

outliers.

615.0401 Assumptions

(a) Randomness

The first assumption is that the water quality data are

sampled randomly. Randomness means that the probability of obtaining a sample remains the same for all

possible samples (Steel and Torrie 1960). The purpose

of randomization is to design bias out of the study and

increase the accuracy of the study (Hurlbert 1984). For

example, if a stream was sampled only during

stormflow periods, the study would be biased toward

higher concentrations than if the stream were sampled

mostly during low-flow periods. Water quality data

have both random and deterministic components

(Moser and Huibregtse 1976). Random components

are introduced by precipitation events that are themselves random in most parts of the United States.

Nonrandom components are related to trends or

seasonality in the data (part 614, ch. 7, fig. 7–1).

Water quality samples may not be truly random for

several reasons. Sampling is not randomized over all

possible observations. For example, if sampling were

done from 1980 to 1990, the sampling ignores what the

water quality may have been for all time before 1980.

By sampling within a shorter window than all time,

there is a possibility that a nonrandom component is

dominating water quality.

The lack of randomness may result in producing a lack

of independence, heterogeneous variances, or nonnormal distributions (Sokal and Rohlf 1969). No specific test of randomness is available; however, proper

design of the sampling program should ensure an

appropriate level of randomness.

Sampling methods to maintain randomness are described in part 614 of this handbook in chapters 8 and

9.
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National Water Quality Handbook

Chapter 4 Statistical Assumptions

4–2 (450–VI–NWQH, September 2003)

(b) Normal distribution

A second assumption is that the data come from a

population with a particular frequency distribution of

values, usually a normal distribution. Several methods

are available for examining the normality of the data.

They include graphical and statistical methods. The

graphical approach is to plot the data in a cumulative

frequency distribution. Normal data plot as a straight

line on such a graph (fig. 4–1a). Data that are skewed

(long tail) to the left have a cumulative frequency

distribution that is concave upward (fig. 4–1b). Data

that are skewed right have a cumulative frequency

distribution that is concave downward (fig. 4–1c).

Within the Statistical Analysis System, a normal probability plot can be obtained from:

PROC UNIVARIATE PLOT;

In addition to the normal probability plot, a stem-andleaf plot and a boxplot are automatically produced.

Example 4–1 illustrates the cumulative frequency

distributions for St. Albans Bay algal data in table

2–1 using the SAS® output. The log transformed data

produces a straighter line on the normal probability

plot than the untransformed data. This finding implies

that the data follow a log normal distribution, and a log

transformation should be used in subsequent statistical analysis.

Among the statistical approaches for evaluating the

normality of the data is the use of univariate statistics,

such as the mean, median, skewness, and kurtosis.

Generally, if the median and the mean are very different, the data may not be normally distributed. In

addition, tests of either the skewness or the kurtosis

will provide information regarding the normality of the

distribution (see chapter 2).

Several statistical tests have been used for testing

normality. One common test is the Chi-square goodness of fit (Snedecor and Cochran 1980; Sokal and

Example 4–1 Cumulative frequency distributions for St.

Albans Bay algal data from SAS® output

Untransformed (ALGAE):

45,000

25,000

5,000

-2 -1 0 +1 +2

* * * * **** ********* ****

* * *

*

+ ++++++ ++ ++++++++++++++

St. Albans Bay Algae Data 8:10 Wednesday, January 1,

Univariate Procedure

Normal Probability Plot

Algae

Log Transformed (LALGAE):

 

1.25

4.57

-2 -1 0 +1 +2

+ ++ ++ * * * **** ********* ***** * ** *

* + ++ ++ + + ++ + ++ + ++ +++ ++++

St. Albans Bay Algae Data

8:10 Wednesday, January 1,

Univariate Procedure

Normal Probability Plot

Lalgae

Figure 4–1 Examples of frequency distributions

a Normal

b Skewed left

c Skewed right

Frequency distribution

Cumulative frequency distribution
Chapter 4

((450–VI–NWQH, September 2003) 4–3

Part 615

National Water Quality Handbook

Statistical Assumptions

Rohlf 1969; Zar 1984). This tests the hypothesis that

the sample came from a specific theoretical distribution.

The goodness of fit also may be tested using the

Kolmogorov-Smirnov test (Zar 1984). Finally a test for

normality can be accomplished by using the ShapiroWilk W-statistic. The W statistic has values ranging

from 0 to 1; small values for W are significant and

indicate nonnormality (Shapiro and Wilk 1965). The

decision whether to use the Kolmogorov-Smirnov test

is dependent on the sample size. For samples less than

2,000, the Shapiro-Wilk test should be used (SAS 1985).

For larger samples, the Kolmogorov-Smirnov test

should be used. Example 4–2 illustrates the test of

normality using the Shapiro-Wilk W-statistic.

SAS® output provides the W statistic and its probability using the following command:

PROC UNIVARIATE NORMAL;

Failure to exactly meet the assumption of normality is

generally not considered to be a major problem (Glass,

et al. 1972, Sokal and Rohlf 1969). The significance

levels for t-tests and F-tests do not appear to be affected by nonnormality. That is to say that the probability of the Type I error is not increased significantly

by failure to meet the assumption of normality (chapter 6). This is especially true for large data sets and

when equal numbers of values are being compared.

Skewed populations can affect the level of significance

for one-tailed tests (Glass, et al. 1972). It is not considered necessary to use nonparametric approaches

simply because the assumption of normality has not

been exactly met. However, an appropriate transformation to better approximate normality is recommended.

(c) Homogeneity of variances

In uses involving more than one data set, the equality

of variances is an important assumption for several

statistical tests. If there are two sample data sets that

are being compared, the test of the homogeneity of

variances is made by computing an F as the ratio

between the larger variance divided by the smaller

variance (Snedecor and Cochran 1980, Sokal and Rohlf

1969). The computed F is compared to a critical value

for F from an F table (appendix C).

If three or more sample data sets are compared,

Bartlett's test may be used. The ratio of the test statistic, B, to a correction factor is compared to the chisquare statistic (Snedecor and Cochran 1980, Zar

1984). For nonnormal distributions, some prefer the

Levene's test for homogeneity of variances (Snedecor

and Cochran 1980). The statistical program BMDP

(Biomedical Computer Programs P-Series) computes

both the Bartlett's test (BMDP9D) and the Levene's

test (BMDP7D) (Dixon and Brown 1979).

A quick test is the Fmax test for which an F ratio is

computed from S2

max/S2min and compared to a critical

value for F that is given in various tables (appendix C)

(Sokal and Rohlf 1969, Peterson and Hartley 1954).

The consequence of failing to meet the assumption of

equal variances can be serious, especially when the

sample sizes from the two groups are of unequal size

(Glass, et al. 1972). When the sample sizes of the

groups are equal, there is little effect on the probability

Example 4–2 Test of normality for the St. Albans Bay

algal data

Untransformed Log

transformed

Mean 8075. 3.234

Median 1168. 3.063

Skewness 1.900 –0.039

Kurtosis 2.334 –0.389

W:Normal 0.626 0.959

Prob<W 0.0001 0.4018

For the St. Albans Bay algal data, the small W

for the untransformed data indicates that the

W is significant and nonnormal. The logtransformation of this data resulted in a large,

nonsignificant W. The hypothesis that the data

come from a normal distribution cannot be

rejected. Therefore, the log transformed data are

assumed to be normally distributed. Note also

that the mean and median are closer and the

skewness and kurtosis are smaller for the log

transformed, as compared to the untransformed

data.
Part 615

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Chapter 4 Statistical Assumptions

4–4 (450–VI–NWQH, September 2003)

level of committing a Type I error (chapter 6). When

the sample sizes of the groups being compared are

unequal and the variances are heterogeneous, the

probability of committing a Type I error may be seriously affected. The probability level may be underestimated when a smaller number of samples come from

the more variable population. It may be overestimated

when a smaller number of samples come from the less

variable population (Glass, et al. 1972).

Transformations often help remove heterogeneous

variances. If a transformation does not eliminate the

problem, perhaps the data could be aggregated so that

the number of samples among groups could be equalized. If this is not possible, a nonparametric approach

may be desirable.

(d) Independence

Another assumption is that the experimental errors are

independently distributed (Sokal and Rohlf 1969, Steel

and Torrie 1960). That is, if the data are arranged in

some logical sequence, such as in the order of collection, the errors should follow each other randomly.

Randomization in sampling helps reduce the correlation of observations and their errors over time. This is

a special concern in water quality sampling where high

values are more likely to follow high values and low

values follow low values.

If the errors are not independent, the F-test in analysis

of variance (ANOVA) and the t-test results can be

questioned. With positive serial correlations, the

probability level of the Type I error is increased progressively with the size of the correlation. With negative correlations, the probability level of the Type I

error is much lower than it really should be (Glass, et

al. 1972).

If the sampled data are serially correlated, there is

little that can be done. Randomization in the design of

the experiment was insufficient. One alternative may

be to aggregate the serial data in some logical manner,

such as computing means or totals. For example,

serially correlated weekly data could be aggregated to

monthly data that may not be correlated. Another

option would be to use Time Series Analysis (Vandaele

1983). This analysis assumes that the errors are not

independent and are, in fact, correlated according to

some time step. Although time series analysis has

certain applications in water quality monitoring, such

as trend analysis, it is a sophisticated statistical technique requiring special training.

Serial or auto correlation of the residuals can be

determined from:

r

y yy y

y y k

t t tk

N k

t t

N = ( ) − ( ) −

( ) −

= −

−

=

∑

∑

1

2

1

[4–1]

where:

rk = autocorrelation coefficient for any lag k

y = observation at any time step t

N = total number of observations

In SAS® the autocorrelation coefficient may be obtained by:

PROC REG;

 MODEL Y=X / DW;

The DW stands for the Durbin-Watson d statistic that

is a test of the hypothesis that autocorrelation is zero

(SAS 1985).

(e) Additivity

The assumption of additivity (also termed linearity) is

normally applied to ANOVA and means that the effects

of the treatment are additive, not multiplicative (Sokal

and Rohlf 1969, Steel and Torrie 1970, Zar 1984). One

way of viewing additivity is by writing the model for an

ANOVA. A typical one-way ANOVA model would take

the form:

χ μα ε ij i ij =+ +

This equation states that an observed value (χij) equals

the sum of an overall mean (μ), a treatment deviation

(αI), and a random error term (εij) (Snedecor and

Cochran 1980). The three factors in the equation are

additive rather than multiplicative. Thus there would

be no interaction in this particular model.

A test for nonadditivity has been suggested by Tukey

(Snedecor and Cochran 1980). Log transformations of

multiplicative effects promote additivity in the data.
Chapter 4

((450–VI–NWQH, September 2003) 4–5

Part 615

National Water Quality Handbook

Statistical Assumptions

615.0402 Residual plots

When using linear regression, an examination of a plot

of the residuals, as a function of the independent

variable, helps in the assessment of several of the

assumptions including equal variances, independence,

as well as the adequacy of the linear regression model

(Afifi and Azen 1979, Draper and Smith 1981, Ponce

1980, Zar 1984). A residual is the deviation of a datum

point from the regression line. For example, if the

residuals are independent and of constant variance,

then they should be scattered evenly about the horizontal line where the residual is zero (fig. 4–2a). If, on

the other hand, the residuals appear to increase or

decrease as X increases (fig. 4–2b), the variance may

not be constant. A nonconstant variance implies that

the regression model is inadequate.

615.0403 Missing data

Missing data are common in water quality sampling.

Sometimes samples are missing because they were not

collected. Possible reasons for not collecting samples

include equipment failure, frozen conditions, or missing an event. Water samples that must be analyzed in a

laboratory are subject to accidents or a quality assurance program that may render the sample as in error.

Missing data are important for some water quality

monitoring designs, but not for all designs. Missing

values may not be important for paired and unbalanced unpaired tests where the number of samples is

adequate. The missing value merely eliminates a pair

from the analysis and reduces the sample size. However, missing data may have important consequences

on trend analysis.

As a cautionary note, the analyst must be aware of

how missing data are coded when using computer

statistical packages. Some packages read a blank as a

zero. If a special value is used, such as –9, the computer may include that in calculations unless specifically informed otherwise. Each statistical package

may have different requirements. SAS® for example

recognizes a '.' as missing. One should also be aware

that for some packages a missing value within a line

(or case) may result in the elimination of the entire

case.

Several techniques are used to estimate missing water

quality data. They include linear interpolation, regression with another station or flow, and the use of several stations. In addition, more sophisticated measures

are needed for missing blocks in randomized block

designs (Snedecor and Cochran 1980, Zar 1984).

Linear interpolation uses the existing values adjacent

to the missing value(s) and assumes that the missing

value(s) is proportional to the difference between the

known values.

For water quality data that are highly correlated to

either other water quality data or flow data, missing

values could be predicted using a regression equation.

For missing flow data, a relationship with precipitation

or with flow at a nearby station may provide an adequate predictor of the missing information.

Figure 4–2 Residual plots for linear regression

X

X

+

-

+

-

0

0

a Constant

 variance

b Changing

 variance

Residual Residual
Part 615

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Chapter 4 Statistical Assumptions

4–6 (450–VI–NWQH, September 2003)

Another approach is that several stations could be

used to predict a single missing value if such data are

available. For example, the concentration at a fourth

station could be determined from the concentrations

observed at three other stations and the means at all

stations using the equation:

C C

C

C C

C

C C

C 4 C 4

1

1

4

2

2

4

3

3

1

3

= ×+ ×+ × 



 



 [4–2]

where:

C = concentration at stations 1, 2, 3, and 4

C = mean for the respective station

615.0404 Extreme outliers

Water quality data sets generally contain values that

appear to be extreme outliers. The initial response

should be to verify that no mistake has been made in

recording the observation. Upon occasion, an error

has been made, but the true value cannot be determined. In this case the data could be declared missing.

Several methods are available for determining whether

certain observations are outliers (e.g., Dunn and Clark

1987). For example, the maximum normed residual

(MNR) can be calculated from:

MNR

Max x x

x x

= −

∑( ) 1 − 2 [4–3]

where:

x = outlier to be tested (Snedecor and Cochran

1980).

The calculated MNR is compared to a tabular MNR,

which varies with the sample size and probability

level. If the calculated MNR is less than the tabular

MNR, the value is expected to occur more often than

the probability level, and thus is not considered an

extreme outlier.
Chapter 4

((450–VI–NWQH, September 2003) 4–7

Part 615

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Statistical Assumptions

615.0405 Summary

Table 4–1 provides a summary of the standard assumptions for parametric statistical tests and the appropriate methods for testing the assumption.

Table 4–1 Statistical assumptions and tests

Assumption Test

Randomness Sampling design

Normality Graphical

Shapiro-Wilk

Kolmogorov-Smirnov

Equal variances F ratio

Bartlett's

Levene's

Independence Residual plot

Autocorrelation

Additivity Tukey's

615.0406 References

Afifi, A.A., and S.P. Azen. 1979. Statistical analysis: a

computer oriented approach. (2nd ed). Academic

Press. New York, NY.

Dixon, W.J., and M.B. Brown (Eds.). 1979. BMDP

biomedical computer programs P-series. Univ.

CA Press, Los Angeles, CA.

Draper, N.R., and H. Smith. 1981. Applied regression

analysis. (2nd ed.) John Wiley and Sons. New

York, NY.

Dunn, O.J., and V.A. Clark. 1987. Applied statistics:

Analysis of variance and regression (2nd ed.)

John Wiley and Sons, New York, NY.

Glass, G.V., P.D. Peckham, and J.R. Sanders. 1972.

Consequences of failure to meet assumptions

underlying the fixed effects analyses of variance

and covariance. Rev. Educ. Research 42(3):237-

288.

Hurlbert, S.H. 1984. Pseudoreplication and the design

of ecological field experiments. Ecological Monographs 54(2):187-211.

Moser, J.H., and K.R. Huibregtse. 1976. Handbook for

sampling and sample preservation of water and

wastewater. U.S. EPA 600/4-76-049.

Peterson, E.S., and H.O. Hartley. 1954. Biometrika

tables for statisticians. (Vol I.) Cambridge Univ.

Press.

Ponce, S.L. 1980. Statistical methods used in water

quality data analysis. WSDG Tech. Pap. WSDGTP-00001. Watershed Systems Development

Group, USDA Forest Service, Fort Collins, CO.

SAS Institute, Inc. 1985. SAS procedures guide for

personal computers. (Ver. 6 ed.) Cary, NC.

Shapiro, S.S., and M.B. Wilk. 1965. An analysis of

variance test for normality (complete samples).

Biometrika 52:591-611.
Part 615

National Water Quality Handbook

Chapter 4 Statistical Assumptions

4–8 (450–VI–NWQH, September 2003)

Snedecor, G.W., and W.G. Cochran. 1980. Statistical

methods. (7th ed.) The IA State Univ. Press,

Ames, IA.

Sokal, R.R., and F.J. Rohlf. 1969. Introduction to biostatistics. W.H. Freeman and Co., San Francisco,

CA.

Steel, R.G.D., and J.H. Torrie. 1960. Principles and

procedures of statistics. McGraw-Hill Book Co.,

Inc. New York, NY.

Vandaele, W. 1983. Applied time series and BoxJenkins models. Academic Press, Inc., New York,

NY.

Zar, J.H. 1984. Biostatistical analysis. Prentice-Hall,

Inc., Englewood Cliffs, NJ.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 5 Causality
(450–VI–NWQH, September 2003) 5–i

Chapter 5 Causality

Contents: 615.0500 Introduction 5–1

615.0501 Association 5–1

615.0502 Consistency 5–2

615.0503 Responsiveness 5–4

615.0504 Mechanism 5–4

615.0505 Experimental design 5–5

(a) Time scale ...................................................................................................... 5–5

(b) System level................................................................................................... 5–5

(c) Reasonableness of treatment ...................................................................... 5–6

615.0506 References 5–6

Table Table 5–1 Correlations between mean weekly discharge 5–1

concentrations and discharge

Figures Figure 5–1 Jewett Brook phosphorus concentration and manure 5–2

applied in the watershed

Figure 5–2 Mean annual bacteria abundance and the percent 5–3

of BMP animal units for the Jewett Brook watershed

Figure 5–3 Mean annual bacteria abundance and the percent 5–3

of BMP animal units for the Stevens Brook watershed

Figure 5–4 Mean annual bacteria abundance and the percent 5–3

of BMP animal units for the Rugg Brook watershed
Part 615

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Chapter 5

5–ii (450–VI–NWQH, September 2003)

Causality

Figure 5–5 Mean annual bacteria abundance and the percent 5–3

of BMP animal units for the Mill River watershed

Figure 5–6 Mechanism for bacteria decreases 5–5

Examples Example 5–1 Correlation 5–1

Example 5–2 Regression 5–2

Example 5–3 Consistency 5–2

Example 5–4 Responsiveness 5–4

Example 5–5 Mechanism 5–5
(450–VI–NWQH, September 2003) 5–1

Chapter 5 Causality

615.0500 Introduction

Although the reasons for conducting water quality

monitoring are varied (see part 614, chapter 1), many

involve attempting to develop a cause-and-effect

relationship between something that is done on the

landscape (cause) and a response in water quality

(effect). In statistical terms an experimental design is

developed to determine the conclusion desired. An

experimental design is a plan of the experimental

units, treatments including a control, and the replications to achieve some objective. Four concepts provide a useful framework for designing water quality

monitoring studies with causation in mind. These

concepts are association, consistency, responsiveness,

and mechanism (Mosteller and Tukey 1977).

This chapter describes these four concepts of causality. Examples are used to illustrate each of these

requirements. Other features of designing experiments

are also described.

615.0501 Association

An association between variables, such as water

quality and land treatment, implies that these variables

are paired in a related way across the population

(Mosteller and Tukey 1977). An association is necessary, but not sufficient to show causality.

An association may be expressed in several ways

including correlation and regression (Draper and

Smith 1981) or a significance analysis of variance

(ANOVA) model. Regression is appropriate when one

variable is dependent on the other (Zar 1984). When

two variables are associated, but one is not dependent

upon the other, correlation analysis is used. For example, the association between runoff and rainfall is

best analyzed by regression because runoff is dependent upon rainfall. However, the association between

stream order and discharge is best explained by correlation. Discharge would be expected to be greater for

higher order streams although there is no mathematical dependence of discharge on stream order.

Examples 5–1 and 5–2 help to illustrate the meaning of

association.

Water quality monitoring in the Jewett Brook

watershed in Vermont revealed an association

between stream discharge and various water

quality variables (Hopkins and Clausen 1985).

This association is represented by correlation

coefficients of log-transformed data (table 5–1).

The correlations in table 5–1 do not necessarily

imply dependence. Increased discharge may not

cause increased concentrations in streamflow.

Rather, other processes, for example snowmelt,

can cause increases in both discharge and concentrations. Surely, increased stream concentrations do not cause increased discharge.

Example 5–1 Correlation

Table 5–1 Correlations (r) between mean weekly

discharge concentrations (mg/L) and

discharge (m3/s) n=52

Variable Correlation

coefficient

 (r)

Total phosphorus 0.37**

Total kjeldahl nitrogen 0.44**

Total suspended solids 0.61**

** Indicates p=0.01 (see chapter 6).
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5–2 (450–VI–NWQH, September 2003)

Causality

Example 5–2 Regression

For the watershed described in example 5–1,

land treatment data were also collected. These

data included the amount of dairy cow manure

applied in the watershed between each runoff

event. A linear regression was developed between the concentration of total phosphorus in

streamflow and the amount of manure applied in

the watershed (fig. 5–1). This regression was

significant based on analysis of variance for

regression.

This association indicates that total phosphorus

concentrations in the stream increase with

increasing manure applications.

615.0502 Consistency

Another requirement of causation is that the association between the variables is consistent from population to population in both direction and magnitude

(Mosteller and Tukey 1977). To assess consistency,

different data sets are needed of the same association.

Consistency is shown in example 5–3.

Example 5–3 Consistency

Figure 5–2 shows a relationship between either

fecal coliform or fecal streptococcus abundance

in Jewett Brook as a function of the percentage

of the animal units in the watershed that are

being managed with best management practices

(BMPs). The major BMP used in this case was

manure storage during the winter with spring

manure spreading followed by rapid incorporation.

The association for fecal streptococcus was

statistically significant, but the association for

fecal coliform was not. Fecal coliform abundance appeared to be more variable than fecal

streptococcus. To show consistency, compare

this association to that derived from other data

sets. Figures 5–3 through 5–5 show the association between bacteria abundance and the percent of animal units for three other watersheds in

the same vicinity.

In all cases illustrated in figures 5–2 through

5–5, the bacteria abundance in the stream declined as the percentage of animal units being

managed with BMPs increased. The same general

relationship was observed in the LaPlatte River

watershed about 50 miles away (Meals 1990).

Ideally, this relationship should be tested across

the United States to show consistency.

Figure 5–1 Jewett Brook phosphorus

concentration and manure

applied in the watershed

1.0

R=0.60

Y=0.189X0.178

5.0

10.0

0.5

0.0

1 10 100 1,000 10,000

Manure applied (tonnes)

Total phosphorus (mg/L)
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Figure 5–2 Mean annual bacteria abundance and the

percent of BMP animal units for the Jewett

Brook watershed (n=6)

Figure 5–3 Mean annual bacteria abundance and the

percent of BMP animal units for the Stevens

Brook watershed (n=6)

Figure 5–4 Mean annual bacteria abundance and the

percent of BMP animal units for the Rugg

Brook watershed (n=6)

Figure 5–5 Mean annual bacteria abundance and the

percent of BMP animal units for the Mill

River watershed (n=6)

2,000

1,500

1,000

500

0 0 10 20 30 40

+

+

+

+

+

+

50 60 70 80 90 100

Bacteria (No./100 mL)

BMP animal units (%)

+

Fecal coliform

Fecal streptococcus

FC=1,600-12.4(%AU)

FS=648-7.1(%AU)

r2

=0.28

r2=0.68*

350

400

150

200

250

300

100

50

0 0 10 20 30 40

+

++ +

+

+

50 60 70 80 90 100

Bacteria (No./100 mL)

BMP animal units (%)

+

Fecal coliform

Fecal streptococcus

FC=380-3.75 (%AU)

FS=265-4.65 (%AU)

r2

=0.51

r2=0.99***

1,400

600

800

1,000

1,200

400

200

0

0 10 20 30 40

+ + +

+ +

+

50 60 70 80 90 100

Bacteria (No./100 mL)

BMP animal units (%)

+

Fecal coliform

Fecal streptococcus

FC=1,827-32.1 (%AU)

FS=442-7.4 (%AU)

r2=0.89**

r2=0.81*

 * Indicates p=0.05

 ** Indicates p=0.01

 *** Indicates p=0.001

0

50

100

150

200

250

0 10 20 30 40

+ +

+

+ +

+

50 60 70 80 90 100

Bacteria (No./100 mL)

BMP animal units (%)

+

Fecal coliform

Fecal streptococcus

FC=396-4.5 (%AU)

FS=242-3.2 (%AU)

r2

=0.54

r2

=0.90**
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Causality

615.0503 Responsiveness

Causality is also supported by the concept of responsiveness. By performing an experiment, the dependent

variable should respond to manipulation of the independent variables (Mosteller and Tukey 1977). This

concept requires that an experiment is performed

where we intervene and change the x's and note

whether the y's change in a corresponding manner.

Example 5–4 illustrates this concept.

Example 5–4 Responsiveness

For the bacteria example, we learned that the

bacteria abundance in the streams draining

agricultural watersheds was associated to the

percent of the BMP animal units. The percent of

BMP animal units is actually a surrogate variable

for changes that occur in the management of

bacteria from animal wastes. Included in these

changes are longer storage of manure and incorporation of the manure soon after field application.

At a farm in the St. Albans Bay watershed, a

paired watershed study was conducted at a field

scale to determine the effect of best manure

management on bacteria in runoff. During the

calibration period both fields were spread with

manure on top of ice and snow during the winter.

During the treatment period, the upper field

received manure in the winter again, but the

lower field was spread with manure in the spring,

which was immediately incorporated into the

soil. This experiment could determine the change

in bacteria abundance in runoff that resulted

from the BMP of storage and incorporation.

Bacteria abundance in runoff should respond to

the application of manure on frozen ground.

615.0504 Mechanism

The final requirement for causality is adequate description of a mechanism that provides a step-by-step

pathway from the cause to the effect, making the

appropriate linkages along the way (Mosteller and

Tukey 1977). Example 5–5 illustrates this point.
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Causality

615.0505 Experimental

design

Other considerations in analyzing cause and effect

depend, in large part, on how the monitoring study is

conducted. These factors include the time scale,

system level, and reasonableness of treatment.

(a) Time scale

The time scale is important for causality because we

all investigate windows within the continuum of time.

Numerous temporal cycles, such as diurnal, lunar,

seasonal, annual, and astronomical, operate in the

natural environment. All these cycles have the potential of influencing our perception of causality. These

time scales also influence interpretation of trend data.

The timing of flow occurrences during a study can

influence our perception of water quality trends. For

example, if a wet year occurred early in the study,

flow, concentrations, and mass exports would be high

during that year. If that year were followed by several

years of lower flows, a decreasing trend in flow, concentrations, and mass would be likely.

To avoid or account for problems associated with time

scales, the true natural variability must be determined

before treatments are imposed. The response observed may be an increase in the variability rather than

a change in the mean. Reference watersheds (controls) help account for time scale problems. The experimental design must consider time scale cycles.

(b) System level

Biological systems can be studied at the ecosystem,

community, population, individual, cell, and molecular

level. Similarly, watersheds (catchments, drainage

basins) can be investigated at the watershed, field, and

plot level. Because the lower levels of systems are

inherently easier to investigate, the tendency is to

investigate at a lower level than is needed to answer

the question. For example, interest is high in knowing

the effect of implementation of BMPs in a watershed

on water quality. However, the common approach to

investigating cause-and-effect is to look at the effectiveness of an individual BMP on a field or plot basis.

1

Storage

2

Rate

and

timing

3

Incorporation

4

Proximity

Mechanism

Figure 5–6 Mechanism for bacteria decreases

Example 5–5 Mechanism

Figure 5–6 shows a logical mechanism that

explains why bacteria abundance in the example

stream may decline after the animal units begin

to be managed.

Bacteria would have a tendency to die off, or

otherwise decline in abundance, at several points

along the pathway. First, bacteria would die off

in storage in the manure pit or tank faster than in

piled manure (Moore, et al. 1988). Second, the

amount and timing of manure applied would be

managed based on soil and crop needs. Third,

much less manure would be available for runoff

if it were incorporated into the soil. Fourth,

manure would be applied at a safe distance from

the stream off runoff-producing zones. All of

these factors should contribute to lower bacteria

abundance in streams draining agricultural

watersheds that have animal waste BMPs.
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Causality

This approach ignores processes that operate on a

watershed basis, such as stream transport phenomenon. The project scale should be matched with the

objective to avoid misconceptions about the system

level being studied.

(c) Reasonableness of treatment

When studying causality, the type of treatment applied

should be reasonable and consistent with real world

situations. Some treatments may be strong interventions, such as a catastrophe. An example of such

treatment is the clearcut and herbicide treatment at

Hubbard Brook Experimental Forest (Likens, et al.

1970). Following harvesting, the timber was left on the

site and regrowth was prevented with herbicide applications. Stream concentrations increased dramatically

in nitrate and cations. By comparison other treatments

can be more gradual, such as a change in nutrient

management on an agricultural field.

The interaction of the treatment with the environment

may be more important than the main effect of the

treatment. For example, certain erosion control practices may show no effect during small storms, but may

be very effective during the larger, rarer storm events.

A final consideration in causality is understanding the

number of variables contributing to a dependent

variable. Most water quality issues are multivariate

and not univariate. For example, stream phosphorus

concentrations may be influenced by precipitation,

antecedent moisture, previous stream loading of

phosphorus, biological activity, temperature, geologic

formation, land activities, and the time available for

mineralization. Thus the cause of the level of phosphorus in a stream is potentially the effect of numerous

factors that could be considered in the design of the

study.

Some causal variables could be unexpected interferences. For example, the midnight dumping of septage,

an accidental spill, or routine washing practices at a

small point source can create havoc with an experimental design.

615.0506 References

Draper, N.R., and H. Smith. 1981. Applied regression

analysis. (2nd. ed.) John Wiley and Sons, New

York, NY.

Hopkins, R.B., and J.C. Clausen. 1985. Land use monitoring and assessment for nonpoint source

pollution control. In Perspectives on Nonpoint

Source Pollution, U.S. EPA 440/5-85-001, p. 25-29.

Likens, G.E., F.H. Bormann, N.M. Johnson, D.W.

Fisher, R.S. Pierce. 1970. Effects of forest cutting

and herbicide treatment on nutrient budgets in

the Hubbard Brook watershed-ecosystem. Ecological Monographs 40(1):23-47.

Meals, D.W. 1990. LaPlatte River watershed water

quality monitoring and analysis program comprehensive final report. Prog. Rep. No. 12, VT Water

Resourc. Res. Ctr., Univ. VT, Burlington.

Moore, J.A., J. Smyth, S. Baker, and J.R. Miner. 1988.

Evaluating coliform concentrations in runoff

from various animal waste management systems.

Agric. Exp. Sta. Spec. Rep. 817, OR State Univ.,

Corvallis.

Mosteller, F., and J.W. Tukey. 1977. Data analysis and

regression: a second course in statistics.

Addison-Wesley Publ. Co., Reading, MA.

Zar, J.H. 1984. Biostatistical analysis. Prentice-Hall,

Inc., Englewood Cliffs, NJ.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 6 Hypothesis Testing
(450–VI–NWQH, September 2003) 6–i

Chapter 6 Hypothesis Testing

Contents: 615.0600 Introduction 6–1

615.0601 Error types 6–1

615.0602 One-sample hypotheses 6–2

(a) One-tailed ...................................................................................................... 6–2

(b) Two-tailed ...................................................................................................... 6–2

615.0603 Two-sample hypotheses 6–3

615.0604 Paired sample hypotheses 6–4

615.0605 Multisample hypotheses 6–5

615.0606 Nonparametric hypotheses 6–6

615.0607 Statistical significance 6–6

615.0608 Summary 6–7

615.0609 References 6–7

Tables Table 6–1 Error types in statistical decisions 6–2

Table 6–2 Summary of hypotheses by type of data and 6–7

appropriate test

Figure Figure 6–1 Distribution of t showing critical regions 6–2
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Chapter 6

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Hypothesis Testing

Examples Example 6–1 One-sample hypothesis testing—one tailed 6–3

Example 6–2 One-sample hypothesis testing—two tailed 6–3

Example 6–3 Two-sample hypothesis testing—one tailed 6–3

Example 6–4 Two-sample hypotheses testing—two tailed 6–4

Example 6–5 Paired sample hypotheses testing—one tailed 6–4

Example 6–6 Paired sample hypotheses testing—two tailed 6–5

Example 6–7 Multisample hypotheses testing 6–5
(450–VI–NWQH, September 2003) 6–1

Chapter 6 Hypothesis Testing

615.0600 Introduction

Developing a hypothesis and testing that hypothesis

are fundamental steps in data analysis for water quality monitoring studies. A hypothesis is a scientific

statement about an assumption regarding the results

expected from a study. A statistical hypothesis is a

statement about a variable describing the distribution

of the data, such as the mean (Snedecor and Cochran

1980, Steel and Torrie 1960, Zar 1984). Hypotheses are

statements regarding population parameters, not

sample statistics. We use hypotheses to draw inferences regarding the assumed population based on

sample information. A test of a hypothesis, also

termed a test of significance, is a procedure for determining whether a hypothesis should be rejected or

accepted (Afifi and Azen 1979).

A null hypothesis is the primary hypothesis to be

tested and is so termed because it is the hypothesis of

no change. The null hypothesis is noted by Ho. Generally, rejecting the null hypothesis is desirable. An

example of a null hypothesis is:

Ho: mean (year 1) = mean (year 2)

This seemingly reverse logic exists because data can

be collected that can contradict the null hypothesis,

but data cannot be obtained to directly accept the

hypothesis.

An alternative hypothesis, denoted by Ha, is often the

hypothesis of interest and is the statement that we

may want to assume is true. An example of an alternative hypothesis is:

Ha: mean (year 1) • mean (year 2)

or possibly:

Ha: mean (year 1) < mean (year 2)

The various types of hypotheses used in water quality

studies are described in this chapter. In addition, the

consequences of making incorrect hypothesis decisions (error types) and the meaning of statistical

significance are described.

615.0601 Error types

When performing a statistical test of a hypothesis, the

decision can be wrong because probability, or chance,

is involved. Two types of errors can occur. A Type I

error can occur when the Ho is rejected even though it

is true (table 6–1). The probability of a Type I error is

indicated by α, which is usually a small value that

should be decided before the study begins (Steel and

Torrie 1960, Zar 1984). This is also termed the statistical significance of the study. Conversely, accepting the

null hypothesis when it is true (a correct decision) has

the probability of 1–α, which should be a high value.

A Type II error can occur when the Ho is not rejected

when it should be (table 6–1). The probability of a

Type II error is indicated by β. Conversely, the probability of rejecting the null hypothesis when it is false

has the probability of 1–β, which is also called the

power of the test (Steel and Torrie 1960, Zar 1984).

For a given number of samples, α is inversely related

to β. This means that if we reduce the probability of

rejecting the null hypothesis when it is true (α), we

increase the probability of accepting the null hypothesis when it is false (β). Both types of errors can be

reduced by larger sample sizes.

Hypotheses will be used throughout the various chapters contained herein. However, some common hypotheses used and their appropriate applications are

described further. Hypotheses may be categorized by

the number of groups being compared. They are often

distinguished as one-sample, two-sample, pairedsample, and multisample (Zar 1984).
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Hypothesis Testing

615.0602 One-sample

hypotheses

A test involving one sample is used when a population

parameter (e.g., the mean) is compared to a fixed

value that may either be known or hypothesized. Tests

can be either one-tailed or two-tailed, depending upon

the nature of the problem. These tests are termed oneor two-tailed because they refer to a comparison of a

calculated t to a critical region of the t-distribution at a

certain probability. A one-tailed test is used when the

mean is to be compared to a fixed value, such as a

water quality standard. A two-tailed test is used when

the mean could lie on either side of a fixed value.

In figure 6–1a the t-distribution is shown for a onetailed test. If the calculated t is greater than the critical

t (see chapter 8 for a definition of t), the null hypothesis can be rejected at the probability used. This

means that the mean is so different from the fixed

value that it lies in the shaded area and has a very

small probability of occurring if it were part of the

fixed value's population.

The t distribution is used rather than the z distribution

because the population standard deviation (σ) is

unknown.

(a) One-tailed

A one-tailed test is appropriate when the mean or

some other population parameter is to be compared to

some fixed value in a specific direction, such as a

water quality standard (Snedecor and Cochran 1980,

Zar 1984). We may test that the value is either significantly larger or significantly smaller than the fixed

value, but we can only test one direction at a time. See

example 6–1 for more information.

(b) Two-tailed

A two-tailed test is appropriate when there is no

reason to see whether a value is greater than or less

than a fixed value. Therefore, an appropriate null

hypothesis would be that the means are identical, and

the alternative hypothesis would be that the means are

Table 6–1 Error types in statistical decisions

Decision - - - - - - - - - - - - - - - - Reality - - - - - - - - - - - - - - - - -

Ho is true Ho is false

Reject Ho Type I error Correct decision

Prob = α termed Prob = 1– β termed

significance level power

Accept Ho Correct decision Type II error

Prob = 1–α termed Prob = β

confidence level

Figure 6–1 Distribution of t showing critical regions

a. One-tailed

Y

X

X

Y

-3 -2 -1 0 1 2 3

-3 -2 -1 0 1 2 3

b. Two-tailed

Reject Ho Accept Ho

Reject Ho Reject Ho

Accept Ho
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Hypothesis Testing

615.0603 Two-sample

hypotheses

A two-sample hypothesis is used when testing for the

differences between two populations sampled. Often

we are testing for the difference between two means;

although the two variances could be tested as well.

Both one-tailed (example 6–3) and two-tailed (example 6–4) tests are appropriate for two-sample

hypothesis; however, the two-tailed test is more

commonly used.

Example 6–3 Two-sample hypothesis testing—one-tailed

The nutrient management program described in

Example 6–1 could result in a reduced mean

concentration of nitrogen in a stream draining

the treated watershed. Thus we are interested in

detecting a difference in one direction only. The

null hypothesis might be:

Ho: mean (year 2) > mean (year 1)

The alternative hypothesis might be:

Ha: mean (year 2) ≤ mean (year 1)

If we were less certain about the years, this

could be a two-tailed test.

not equal (Steel and Torrie 1960, Zar 1984). In figure

6–1b, the distribution for t is shown for a two-tailed

test. In this case the calculated t can be either positive

or negative.

In some cases the appropriate value to compare to the

mean might be a zero. This may happen when examining the change in something, such as the change in

concentrations before and after some time period. See

example 6–2 for more information.

Example 6–1 One-sample hypothesis testing—one-tailed

Implementation of a nutrient management program on cropped fields might be expected to

result in reduced ground water NO3-N concentrations below the standard of 10 mg/L. An appropriate null hypothesis would be:

Ho: mean NO3–N ≥ 10 mg/L

The alternative hypothesis might be:

Ha: mean NO3–N < 10 mg/L

In this case it is desirable to reject the null hypothesis in favor of the alternative hypothesis.

Example 6–2 One-sample hypothesis testing—two-tailed

When sampling the ground water in a field, we

may be uncertain as to whether the NO3–N in the

ground water is improving or getting worse over

time. An appropriate null hypothesis may be:

Ho: mean (year 1) = mean (year 2)

The alternative hypothesis would be:

Ha: mean (year 1) ≠ mean (year 2)

A two-tailed t-test would be appropriate to test

these hypotheses. If the calculated t-value was

greater than the critical value from a table, then

the null hypothesis would be rejected. This

t-value could be either positive or negative.
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Hypothesis Testing

615.0604 Paired sample

hypotheses

A paired sample hypothesis is appropriate when two

samples are associated in some meaningful way. The

two-sample hypotheses, described in the previous

section, assume that the samples are independent and

not associated in some way. For example, comparing

the means of monthly observations from one year to

the next would be a two-sample test. Months are not

paired well from year to year because of climate

differences. However, comparing the means of

monthly observations from adjacent watersheds for

the same year would be a paired sample test. The two

adjacent watersheds would be similarly affected by

climate from month to month during the year. The

paired t-test is used to test the null hypothesis (chapter

9). Both the one-tailed and two-tailed hypotheses are

used with paired comparisons. These tests are illustrated in examples 6–5 and 6–6.

The hypotheses for paired samples are expressed in

several ways. One method is to assume that the difference between the means is zero. This is equivalent to

stating that the means are equal.

Example 6–5 Paired sample hypotheses testing—one

tailed

An erosion control irrigation study was established to determine whether the newer sprinkler

irrigation technique results in more than a 1 ton

per acre reduction in erosion compared to the

older flooded irrigation. To answer the question,

paired plots were established with one plot from

each pair being irrigated with a sprinkler and the

other flooded. An appropriate null hypothesis is:

Ho: mean (sprink.)–mean (flood)=1 ton/acre reduction

The alternative hypothesis is:

Ha: mean (sprink)–mean (flood)>1 ton/acre reduction

We only wanted to know whether the change in

irrigation practice was going to result in less

erosion, so a one-tailed test was used.

Example 6–4 Two-sample hypotheses testing—two tailed

For long-term trend analysis we may not be

certain as to whether the change from year 1 to

year 2 might be an increase or a decrease. An

appropriate null hypothesis might be:

Ho: mean (year 1) = mean (year 2)

The alternative hypothesis might be:

Ha: mean (year 1) ≠ mean (year 2)

These hypotheses could also be stated in terms

of their differences. The null hypothesis would

be:

Ho: mean (year 1) – mean (year 2) = 0

and the alternative hypothesis would be:

Ha: mean (year 1) – mean (year 2) ≠ 0

A t-test would be used to test the null hypothesis

(chapter 8).
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Example 6–6 Paired sample hypotheses testing—two

tailed

For the above-and-below watershed design,

samples collected at the above and below stations are associated because of the sampling

time; therefore, they should be paired. An appropriate null hypothesis is:

Ho: mean (Lower) – mean (Upper) = 0

The alternative hypothesis would be:

Ha: mean (Lower) – mean (Upper) ≠ 0

The paired t-test would be used to test the null

hypothesis (chapter 8).

615.0605 Multisample

hypotheses

A multisample hypothesis is used when sampling is

from three or more groups. The number of samples

taken from each group is not required to be of equal

size (unbalanced design). However, equal numbers of

samples per group (balanced design) enhance the

chance of rejecting the null hypothesis statistically.

Example 6–7 illustrates a multisample hypothesis. If

two samples are taken, either the t-test or ANOVA can

be used because they yield identical results.

Example 6–7 Multisample hypotheses testing

For a trend study being conducted over several

years, we may be interested in comparing annual

means. An appropriate null hypothesis might be:

Ho: mean (year 1)=mean (year 2)=...mean (year k)

The alternative hypothesis might be:

Ha: mean (year 1)≠mean (year 2)≠...mean (year k)

Analysis of variance (ANOVA) is used to test the

null hypothesis (chapter 11) using the F-statistic.

The test indicates whether all of the population

means are different, but not which of those

means are different. To answer this question, a

multiple comparison test is needed (chapter 11).
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Hypothesis Testing

615.0606 Nonparametric

hypotheses

Nonparametric or distribution-free tests have the

advantage that they do not assume that the populations are normal or have equal variances (Zar 1984).

Nonparametric tests could be used in most cases

where a parametric test may be used. A parametric

test is better to use than a nonparametric test because

it has greater power; that is, the probability of rejecting the null hypothesis is higher when it is false. A

greater probability of a Type II error occurs when

using nonparametric approaches. Nonparametric tests

are described in detail in subsequent chapters.

Most nonparametric approaches require that the data

be ranked from either lowest to highest or highest to

lowest, and values are assigned the rank of 1, 2, and so

forth. The rank, rather than the actual value, becomes

the basis of comparison. Ranking eliminates the impact of outlyers in the tail regions of distributions.

The actual hypotheses stated will be the same as

previously described; however, a nonparametric

statistic is used to test the null hypothesis.

615.0607 Statistical

significance

The significance level is the probability of committing

a Type I error and is denoted as α. By convention, an α

of 0.05 is used because it is considered to be a small

chance of committing a Type I error. However, in

some cases an α of 0.01 is used. The selection of the

significance level is somewhat arbitrary. Reporting the

level of significance helps the reader in making their

own conclusions regarding significance (Zar 1984).

The significance level should be decided when the null

hypothesis is constructed. Because the significance

level is affected by the sample size, a smaller α might

be used for a smaller experiment (Steel and Torrie

1960).

The concept of biological significance has two meanings. The first meaning is that a much higher α is

acceptable in biological systems because we simply

cannot get any better. An α of 0.2 is sometimes acceptable. The second meaning of biological significance is

related to the interpretation of results. For example,

just because the negative correlation is significant

between elevation and abundance of macroinvertebrates, does it mean that high elevation causes lower

abundance? This relationship may not have biological

significance even though it may have statistical significance.
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615.0608 Summary

Table 6–2 provides a summary of the appropriate null

hypotheses and statistical test for various data types.

In most cases we are interested in comparing means.

However, in some cases a comparison of variances

may be of greater interest. For example, we may want

to know if a particular water quality constituent has

become less variable over time.

Table 6–2 Summary of hypotheses by type of data and

appropriate test

Data type Rejection region Null hypothesis Test

One-sample one-tailed x x > o t

two-tailed x x > o t

Two-sample one-tailed x x 1 > 2 t

two-tailed x x 1 = 2 t

σ σ 1 − = 2 0 F ratio

Paired-sample one-tailed xxx 1 − ≤ 2 o t

two-tailed x x 1 − = 2 0 t

σ σ 1 2 − = 0 F ratio

Multisample xxx 1 2 = = k F

σσσ 1 2 = = k Bartlett's

615.0609 References

Afifi, A.A., and S.P. Azen. 1979. Statistical analysis: a

computer oriented approach (2nd ed). Academic

Press. New York, NY.

Snedecor, G.W., and W.G. Cochran. 1980. Statistical

methods (7th ed). The Iowa State Univ. Press.

Ames, IA.

Steel, R.G.D., and J.H. Torrie. 1960. Principles and

procedures of statistics. McGraw-Hill Book Co.,

Inc., New York. NY.

Zar, J.H. 1984. Biostatistical analysis. Prentice-Hall,

Inc., Englewood Cliffs, NJ.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 7 Plot Designs
(450–VI–NWQH, September 2003) 7–i

Chapter 7 Plot Designs

Contents: 615.0700 Introduction 7–1

615.0701 Replications 7–1

(a) Replications per treatment .......................................................................... 7–1

(b) Observations per plot ................................................................................... 7–2

615.0702 Assumptions 7–3

615.0703 One-way ANOVA 7–3

615.0704 Two-way ANOVA 7–6

615.0705 Factorial 7–8

615.0706 Nonparametric ANOVA 7–8

615.0707 Multiple mean comparisons 7–9

615.0708 References 7–9

Tables Table 7–1 Annual NO3-N export from plots receiving different 7–3

methods of N fertilizer applications

Table 7–2 One-way ANOVA 7–4

Table 7–3 One-way ANOVA of fertilizer data 7–5

Table 7–4 Two-way ANOVA 7–6

Table 7–5 Two-way ANOVA of fertilizer data 7–7

Table 7–6 Annual NO3-N export from plots receiving different 7–8

methods of N fertilizer applications (ranks)
Part 615

National Water Quality Handbook

Chapter 7

7–ii (450–VI–NWQH, September 2003)

Plot Designs

Table 7–7 Tukey's multiple comparison test of the N fertilizer 7–10

data

Table 7–8 Nonparametric multiple comparison test of the N 7–10

fertilizer data

Figure Figure 7–1 Layout of plot design for fertilizer study 7–3

Examples Example 7–1 Replications per treatment 7–2

Example 7–2 One-way ANOVA 7–3

Example 7–3 Two-way ANOVA 7–6

Example 7–4 Nonparametric ANOVA 7–8

Example 7–5 Tukey multiple comparison test 7–9

Example 7–6 Multiple comparison using Kruskal-Wallas 7–10

nonparametric ANOVA
(450–VI–NWQH, September 2003) 7–1

Chapter 7 Plot designs

615.0700 Introduction

Plots are generally small areas that are replicated on

the land or water. In a plot design, all plots are treated

alike except for the factors under study. Data from a

plot design are usually organized into multiple data

sets corresponding to control plots and treatment

plots. A further description of the plot design is in part

614, chapter 4, of the National Water Quality Handbook (NWQH).

The principal tool for the analysis of plot data is the

analysis of variance (ANOVA) (Snedecor and Cochran

1980, Sokal and Rohlf 1969, Steel and Torrie 1960, Zar

1984). Normally, more than two plots are used for plot

studies because the treatment applied is replicated.

The ANOVA procedure is needed to test multisample

hypotheses, such as whether the means of several

treatments are different.

When designing a plot study, two of the important

decisions are selecting the treatment(s) to be tested

and the number of replications for each treatment.

Also, the number of observations per plot and whether

blocking will be used need to be determined.

This chapter describes the methods used to analyze

plot data. Hand calculations and SAS® programs are

used to illustrate the statistical methods. Examples of

parametric and nonparametric statistics are provided.

All possible plot designs are not covered in this chapter. A statistical textbook should be consulted for

more complicated designs. These other designs are

mentioned in this chapter.

615.0701 Replications

Replications in plot studies can be of two kinds:

• number of replications (plots) per treatment

• number of observations (samples or subsamples)

per plot

(a) Replications per treatment

One of the most important initial decisions in a plot

study is to determine the number of replications of

each treatment to use. Often this decision is based

upon economic considerations, such as not enough

funding to have more than two replications per treatment. However, such judgments often result in studies

with insignificant findings. It is far better to simplify

the number of treatments tested rather than sacrifice

the number of replications. The number of replications

per treatment that would be desired is a function of

the variability in the data, the precision desired, and

the type of sampling used, as further described in

NWQH, part 614, chapter 9. Example 7–1 illustrates

the selection of the number of replications per treatment.
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National Water Quality Handbook

Chapter 7

7–2 (450–VI–NWQH, September 2003)

Plot designs

(b) Observations per plot

A second decision is to determine the number of

observations per plot. This decision is partly controlled by the objective of the study. For example, only

one annual export value can be obtained from a plot

per year, but sampling the soil generally requires that

several soil samples be obtained per plot. Having more

than one replicate per plot modifies the ANOVA used.

In a randomized block design (for an example see

fig. 4–1, NWQH, part 614, chapter 4) an interaction

term between treatment and block is added, which

represents the experimental error. A within-plot sampling error is also determined. The ANOVA for a randomized block design is discussed in several introductory statistics textbooks. Blocking is used when the

blocks are believed to be significant. For example, soil

type changes across the experimental area could be

blocked if soil types contribute to the variability observed in the data being measured. All treatments

would be assigned to each block. Blocking is further

described in section 615.0704, Two-way ANOVA.

Example 7–1 Replications per treatment

A plot study is being planned to assess the effect

of different N fertilizer treatments on the export

of NO3–N in water. For this example the export

in surface water and ground water are combined

into one number. The methods described in

NWQH, part 614, chapter 9, are used for this

calculation, especially equation 9–1, which is

repeated here:

n

t s

d =

2 2

2 [9–1]

A published study, similar to the one planned

resulted in the following:

mean NO3–N export = 59 kg/ha

standard deviation = 7.05 kg/ha

n =5

The difference (d) for 10 percent from the mean

would be:

d = 0.1 x 59 kg/ha = 5.9 kg/ha

To determine the number of samples needed to

estimate the mean value within 10 percent of the

true mean, two iterations of equation 9–1 are

needed. The t-value would be 2.776 for n–1

degrees of freedom, where n=5 from the published study (appendix A). Using equation 9–1,

the following number of replications needed is

calculated:

First iteration

n = ( )( )

( ) = 2 776 7 05

5 9

11

2 2

2

. .

.

For the second iteration the t-value is 2.228

(appendix A) at 11–1 = 10 degrees of freedom.

Second iteration

n = ( )( )

( ) = 2 228 7 05

5 9

8

2 2

2

. .

.

Based on this previous study, eight replications

of each treatment would be recommended to

estimate a mean value within 10 percent of its

true value. If only a 20 percent difference were

used, n would equal two replications per treatment.
Chapter 7

(450–VI–NWQH, September 2003) 7–3

Part 615

National Water Quality Handbook

Plot designs

615.0702 Assumptions

Because ANOVA is being used to analyze the plot data,

the assumptions associated with ANOVA must be

considered. First, it is assumed that the treatments

have been assigned randomly to the plots. ANOVA also

assumes that the errors are normally distributed, are

independent, and have a common variance. Tests to

determine if the plot data meet these assumptions are

described in detail in chapter 4. In cases where the

data do not meet these assumptions, you should first

try a transformation of the data (chapters 3 and 4). For

example, a log transformation may convert a nonnormal distribution to an approximate normal distribution. If the transformation still does not result in meeting the assumptions of the test, then you should consider the use of nonparametric statistics.

615.0703 One-way ANOVA

In a one-way classification we are interested in only

the effect of one factor on the water quality variable.

To design this type of study, each plot is assigned one

of the treatments at random with approximately the

same number of plots receiving each treatment. This

type of design is also termed a completely randomized

design. Example 7–2 provides the calculations used to

perform a one-way ANOVA of data from this design.

This example has one observation per plot.

C

C

C

C

C

T1

T1

T1

T1

T2

T2

T2

T2

T1

T2 T3

T3

T3

T3

T3

A plot study was conducted to assess the effect

of different N fertilizer treatments on the overall

mass export of NO3–N in water. The treatments

included spring, split, and spring slow-release

applications and a control plot with no fertilizer.

There were five replications of each treatment.

Figure 7–1 displays the plot layout and assignment of treatments. The data are summarized in

table 7–1.

Table 7–1 Annual NO3–N export (kg/ha) from plots

receiving different methods of N fertilizer

applications

 Control Spring Split Slow ΣXj= ΣXj

2=

 release

Block 1 55 64 78 62 259 17,049

Block 2 62 72 91 70 295 22,209

Block 3 49 68 97 67 281 20,923

Block 4 64 77 82 76 299 22,525

Block 5 66 56 85 55 262 17,742

ΣXi

 = 296 337 433 330 1,396 100,448

X = 59 67 87 66

ΣXi

2 = 17,722 22,969 37,723 22,034 100,448

Example 7–2 One-way ANOVA

Figure 7–1 Layout of plot design for fertilizer study
Part 615

National Water Quality Handbook

Chapter 7

7–4 (450–VI–NWQH, September 2003)

Plot designs

Table 7–2 One-way ANOVA

Source of variation Degrees of Sum of Mean F

freedom squares (SS) squares (MS)

Between treatments t–1 X

r

X

rt

ij ij

2 2

∑ ∑− ( ) SS/df

MS

MS

between

within

Within treatments t(r–1) by subtraction SS/df

Total rt–1 X

X

rt ij

2 ij

2

∑ ∑− ( )

The calculations for a one-way ANOVA are

shown in table 7–2. The null hypothesis for this

experiment would be:

HX X X X o : 1234 ===

The alternative hypothesis is:

HX X X X o : 1234 ≠≠≠

For the calculations in table 7–2:

X = observation from table 7–1

i = ith treatment

j = jth replication

t = number of treatments

r = number of replicates per treatment

Hand calculations are shown in most beginning

statistical books (e.g., Snedecor and Cochran 1980,

Sokal and Rohlf 1969, Steel and Torrie 1960, Zar

1984). To perform these calculations by hand,

initially determine ΣXi

, ΣXi

2, and X for each treatment and overall (table 7–1). The additional calculations follow:

Example 7–2 One-way ANOVA—Continued

Sums of squares

Between treatments:

SS

X

r

X

rt Bet ij ij = − ( )

= +++ − ( )

( )( )

∑ ∑ 2 2

2222 2

296 337 433 330

5

1 396

5 4

,

=−= 99 514 8 97 440 8 2 074 ,. ,. .

Total

SS X Total = −ij

=− =

∑ 2 97 440 8

100 448 97 440 8 3 007 2

, .

, ,. ,.

Within treatment

SS SS SS Within Total Bet = −

= −= 3 007 2 2 074 933 2 ,. , .

Mean squares

MS SS

df

MS SS

df

Bet

Bet

Within

Within

= = − =

= = −

2 074

4 1

691 333

933 2

4 5

, .

.

1

58 325 ( ) = .
Chapter 7

(450–VI–NWQH, September 2003) 7–5

Part 615

National Water Quality Handbook

Plot designs

F-ratio

F MS

MS

Bet

Within

=== 691 333

58 325

11 853 .

. .

These calculations are summarized in table 7–3.

To determine whether to reject the null hypothesis

of no difference between treatment means, the

calculated F ratio is compared to the table F ratio

for 3 and 16 degrees of freedom (appendix C). The

table F is 3.24 and 5.29 for the 0.05 and 0.01 probability levels, respectively. Because the calculated F

exceeds the table F, we can reject the null hypothesis with a 99 percent level of confidence. Therefore, the different fertilizer application methods

most likely resulted in a difference in nitrate export.

However, which treatments were different are not

yet known. To determine which treatment means

are different, the methods described in section

615.0707, Multiple mean comparisons, should be

consulted.

Example 7–2 One-way ANOVA—Continued

Using SAS®, the appropriate program would be:

SAS PC Program

data nitrate;

title 'ANOVA of Plot Data';

infile 'a:nitrate.dat';

input treat nitrate;

Proc ANOVA;

class treat;

model nitrate=treat;

run;

Table 7–3 One-way ANOVA of fertilizer data

Source of Degrees of Sum of Mean F

variation freedom squares squares

Between 3 2074.0 691.333 11.853

Within 16 933.2 58.325

Total 19 3,007.2
Part 615

National Water Quality Handbook

Chapter 7

7–6 (450–VI–NWQH, September 2003)

Plot designs

615.0704 Two-way ANOVA

A two-way classification is useful when we are interested in the effect of two factors on the water quality

variable. In plot studies, for example, plots that are

adjacent to one another will have a tendency to give

more similar results than plots located further away

from each other. This may be because of some physical factor, such as soil heterogeneity. Another example

would be if up slope plots have the potential to impact

downslope plots. To account for this variability, the

land can be subdivided into blocks of similar conditions. Blocks are sometimes referred to as replications.

When assigning treatments to the plots, they are

assigned randomly within each block with a new

randomization for each block. This type of design is

termed a randomized complete-block design. The

primary advantage of this design is that the variability

contributed by field differences can be accounted for

and eliminated from the treatment effect. Example

7–3 illustrates a two-way ANOVA.

Table 7–4 Two-way ANOVA

Source of variation Degrees of Sum of Mean F

freedom squares (SS) squares (MS)

Blocks r-1 X

t

X

rt

ij ij

2 2

∑ ∑− ( ) SS/df

MS

MS

block

error

Treatments t-1 j ij X ij

t

X

rt

2 2

∑ ∑− ( ) SS/df

MS

MS

treatment

error

Error (r-1)(t-1) by subtraction

Total rt-1 X

X

rt ij

2 ij

2

∑ ∑− ( )

Example 7–3 Two-way ANOVA

For the N fertilizer experiment described in

example 7–2, the plots were laid out in the field

by placing them across four elevation transects

(fig. 7–1). Treatments were randomly assigned to

plots across each of the transects. In table 7–1,

blocks are represented by rows. The calculations

for a two-way ANOVA are shown in table 7–4.

Sums of squares

SS

X

t

X

rt Blocks ij ij = − ( )

= +++ − ( )

( )

∑ ∑ 2 2

2222 2

259 295 299 262

4

1 396

5

,

4

97 778 97 440 8 337 2

( )

=− = , ,. .
Chapter 7

(450–VI–NWQH, September 2003) 7–7

Part 615

National Water Quality Handbook

Plot designs

Treatments

SS

X

r

X

rt Bet ij ij = − ( )

= +++ − ( )

( )( )

∑ ∑ 2 2

2222 2

296 337 433 330

5

1 396

5 4

,

=−= 99 514 8 97 440 8 2 074 ,. ,. ,

Total

SS X total = −ij

=− =

∑ 2 97 440 8

100 448 97 440 8 3 007 2

, .

, ,. ,.

Error

SS SS SS SS error total block Bet =− −

= −− = 3 007 2 337 2 2 074 596 ,. . ,

Mean squares

MS SS

df

MS SS

df

block

block

Bet

Bet

= = − =

= = − =

337 2

5 1

84 3

2 074

4 1

691

. .

, .333

596

5141

MS 49 667 SS

df error

error

= = ( ) − ( ) − = .

F-ratio

MS SS

df

F MS

MS

block

block

Block

Block

error

= = − =

= =

337 2

5 1

84 3

84 3

4

. .

.

9 667

1 697

691 333

49 667

13 919

. .

.

. .

=

F == = MS

MS treatment

bet

within

These calculations are summarized in table 7–5.

Table 7–5 Two-way ANOVA of fertilizer data

Source of Degrees of Sum of Mean F

variation freedom squares squares

Blocks 4 337.2 84.3 1.697

Treatment 3 2074.0 691.333 13.919

Error 12 596.0 49.667

Total 19 3007.2

Based upon the ANOVA of the N fertilizer data, the

block effect is not significant while the treatment

effect was significant as before. A significant block

effect would indicate that the design has been made

more precise by blocking (Steel and Torrie 1960).

Note that in the two-way ANOVA the error mean

square has been reduced by apportioning some of

the sums of squares to the block effect. This results

in an overall higher treatment effect. If blocks are

not different, they can be pooled into the error

term, which results in an increase in the error

degrees of freedom. However, in this example a

higher significance was obtained with blocking than

without it. Introductory statistical textbooks describe the calculation of the efficiency added by

blocking.

Using SAS®, the appropriate program would be:

SAS PC Program

data nitrate;

title 'ANOVA of Plot Data with Blocking';

infile 'a:nitrate.dat';

input block treat nitrate;

Proc ANOVA;

class block treat;

model nitrate = block treat;

run;

Example 7–3 Two-way ANOVA—Continued
Part 615

National Water Quality Handbook

Chapter 7

7–8 (450–VI–NWQH, September 2003)

Plot designs

615.0706 Nonparametric

ANOVA

If data are found to violate the assumptions of normality and especially homogeneous variances, a nonparametric approach may be used (Zar 1984). The KruskalWallis test can be used for a one-way ANOVA. Other

similar nonparametric tests, such as Friedman's, exist

for a two-way ANOVA and more complicated designs.

Because this test is based on rank rather than variance, the test statistic is determined from:

H

N N

R

n

N

i

= ( ) + ∑ − + ( ) 12

1

3 1 1

2

[7–1]

where:

ni = number of observations in treatment i

N = total number of observations

Ri = sum of the ranks for each observation in treatment i

Observations are ranked from low (1) to high (N). The

Kruskal-Wallis nonparametric ANOVA for the N fertilizer data is demonstrated in example 7–4.

615.0705 Factorial

More complicated factorial design, split plot designs,

and Latin squares are rare in water quality studies, but

common in agronomic and soil investigations. An

introductory statistics text should be consulted before

planning one of these designs.

Example 7–4 Nonparametric ANOVA

Table 7–6 Annual NO3–N export (kg/ha) from plots

receiving different methods of N fertilizer

applications (ranks are in parentheses)

Control Spring Split Slow release

55 (2) 64 (8) 78 (16) 62 (6)

62 (5) 72 (13) 91 (19) 70 (12)

49 (1) 68 (11) 97 (20) 67 (10)

64 (7) 77 (15) 82 (17) 76 (14)

66 (9) 56 (4) 85 (18) 55 (3)

R (24) (51) (90) (45)

H

H

= ( ) ++++





 



 − + ( )

=

12

20 20 1

24

5

51

5

90

5

45

5

3 20 1

13 011

222 2

.

For the N fertilizer data described in previous

examples, determine the effects of the different

fertilizer treatments on NO3–N export using a

nonparametric approach (see table 7–6).

If the calculated H is greater than the table H

(appendix D, or χ2 for more than 5 groups) then

the null hypothesis is rejected. In this case the

table H is 5.78 at p = 0.05, and the null hypothesis

that the nitrate exports are the same for each

treatment is rejected.
Chapter 7

(450–VI–NWQH, September 2003) 7–9

Part 615

National Water Quality Handbook

Plot designs

615.0707 Multiple mean

comparisons

From ANOVA we may have determined that the means

are different; however, we do not know which of the

means are statistically different from one another.

Multiple comparison tests may be used to determine

which of the means are different (Zar 1984). Although

many such tests exist (e.g.; Duncan, LSD), the Tukey

test is recommended for most cases and will be described further in example 7–5. The multiple comparison using the rank sums from the Kruskal-Wallis

nonparametric ANOVA is described further in example

7–6.

Example 7–5 Tukey multiple comparison test

615.0708 References

Snedecor, G.W., and W.G. Cochran. 1980. Statistical

methods (7th ed.). The IA State Univ. Press,

Ames.

Sokal, R.R., and F.J. Rohlf. 1969. Introduction to biostatistics. W.H. Freeman and Co., San Francisco,

CA.

Steel, R.G.D., and J.H. Torrie. 1960. Principles and

procedures of statistics. McGraw-Hill Book Co.,

Inc., New York.

Zar, J.H. 1984. Biostatistical analysis. Prentice-Hall,

Inc., Englewood Cliffs, NJ.

For the N fertilizer data, it was determined that the

mean NO3–N exports were not equal. Using the

Tukey multiple comparison test, determine for

which groups the means are different.

First, the standard error is calculated from:

SE S

n =

2

where:

SE = standard error

S2 = variance (mean square error from the

ANOVA)

n = number of observations per group

For the example without blocking, the standard

error would be:

SE = = 58 325

5

3 415 . .

Second, the means from table 05–1 should be arranged in increasing order and coded with a name or

number, such as:

1234

59 66 67 87

The statistic q for each possible pair combination is

calculated from:

q

X X

SE α

β = − Α

If the calculated q is greater than the tabular q, the

null hypothesis that the means are equal is rejected. The order of comparisons affects the

conclusions. Therefore, the largest should be

compared with the smallest first, then the second

smallest and so on. The calculations are summarized in table 7–7.

The tabular q at rt–1 = 16 and k = 4 means degrees of

freedom and p = 0.05 is 4.05 (appendix E). Therefore, group 4 is different from groups 1, 2, and 3, but

no other groups are different. These results can be

displayed by drawing a line under the groups that

are not different, as shown above. More often the
Part 615

National Water Quality Handbook

Chapter 7

7–10 (450–VI–NWQH, September 2003)

Plot designs

means are listed in a table with letters following

them and a notation that the means followed by the

same letter are not different at p = 0.05, as follows:

Treatment NO3–N Export (kg/ha)

Control 59 a

Spring 67 a

Split 87 b

Slow release 66 a

The conclusion for this study would be that the

split application resulted in significantly higher

NO3–N export from the plots than all other treatments, including the control.

Using SAS®, the following statement could be

added below the Proc ANOVA statement. The

mean values will also be printed.

means tukey;

Table 7–7 Tukey's multiple comparison test of the N

fertilizer data

Comparison Difference q

4 vs 1 87 – 59 = 28 8.20

4 vs 2 87 – 66 = 21 6.15

4 vs 3 87 – 67 = 20 5.86

3 vs 1 67 – 59 = 8 2.34

3 vs 2 67 – 66 = 1 0.29

2 vs 1 66 – 59 = 7 2.05

Example 7–5 Tukey multiple comparison test—Continued

A multiple comparison can also be made for a

nonparametric ANOVA. The method is similar to

that described for Tukey's in example 7–5, but

uses the rank sums from the Kruskal-Wallis

nonparametric ANOVA (Zar 1984). The standard

error is determined from:

SE n nk nk = ( )( ) + = 1

12

13 23 .

where:

n = number of observations per k groups

(Zar 1984)

The rank sums from the table 7–6, rather than

the means, are used for arranging the data:

1234

24 45 51 90

The q statistic is determined as before. Table 7–8

displays nonparametric multiple comparison test

of the N fertilizer data. In this case only the split

treatment was higher than the control. There was

no difference among all other treatments.

Table 7–8 Nonparametric multiple comparison test of

the N fertilizer data

Comparison Difference q

4 vs 1 90 – 24 = 66 4.99

4 vs 2 90 – 45 = 45 3.40

4 vs 3 90 – 51 = 39 2.95

3 vs 1 51 – 24 = 27 2.04

3 vs 2 51 – 45 = 6 0.45

2 vs 1 45 – 24 = 21 1.59

Example 7–6 Multiple comparison using Kruskal-Wallas nonparametric ANOVA
(450–VI–NWQH, September 2003)

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Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 8 Single Watershed
(450–VI–NWQH, September 2003) 8–i

Chapter 8 Single Watershed

Contents: 615.0800 Introduction 8–1

615.0801 Unpaired comparison of means 8–1

615.0802 Nonparametric two-sample test 8–5

615.0803 Presentation of results 8–6

615.0804 References 8–6

Table Table 8–1 Mean daily total phosphorus concentrations in 8–2

watershed runoff from a period before and after

implementation of best manure management

Table 8–2 Test of normality for the total phosphorus data 8–3

Table 8–3 Summary of calculations for log10 transformed 8–3

phosphorus data

Table 8–4 Ranks of total phosphorus concentrations for the 8–5

before and after study of manure management

Figure Figure 8–1 Boxplots of phosphorus data 8–6

Examples Example 8–1 Single watershed analysis 8–2

Example 8–2 Nonparametric single watershed analysis 8–5
(450–VI–NWQH, September 2003) 8–1

Chapter 8 Single watershed

615.0800 Introduction

The single watershed design is used when a single

station is monitored both before and after a watershed

treatment occurs. As indicated in the National Water

Quality Handbook (NWQH), part 614, chapter 4, the

single watershed design is not recommended because

any difference observed is difficult to attribute to the

treatment rather than other influences that change

over time, such as climate. However, the appropriate

statistical approach when such a comparison is made

is the unpaired t-test of pre and post data. This test

actually determines the difference between the effects

(Snedecor and Cochran 1980).

Comparisons between groups can be either paired or

unpaired (independent). Paired comparisons occur

when two samples can be paired in some meaningful

way. For example, one pair could constitute an individual watershed measured before and after a treatment. However, in this case there is only one comparison and to make the test meaningful and valid, many

watersheds (degrees of freedom) must be compared. It

is generally not appropriate to pair observations, such

as weekly or monthly data, from a single watershed

across years. Because of climate variability, there is no

reason to believe that the water quality of the 13th

week or for July should be a valid pair across years.

Therefore, the unpaired comparison is more common

and is presented here.

615.0801 Unpaired comparison of means

The appropriate null hypothesis for the comparison of

means is:

HX X X X o : 12 1 2 −= = 0 or 

The appropriate alternative hypothesis would be:

HX X X X a : 12 1 2 −≠ ≠ 0 or 

The test of the significance of the difference between

the means is based on the t distribution where t is

defined as:

t

X X

Sd

= 1 2 − [8–1]

where:

X = the mean for either group 1 or 2

Sd = standard deviation of the difference between

the means, which is determined from:

S S

n n

n n d p = 21 2 ( ) +

1 2

[8–2]

for the case where n1 ≠ n2 and is determined from:

S

S

n d

p = 2

2

[8–3]

for the case n1 = n2.

Sp

2

 is the pooled sample variance determined from:

S

X

X

n

X

X

n

n n p

2

1

2 1

2

1

2

2 2

2

2

1 2 1 1 =

− ( ) 















+ − ( ) 















( ) − + −

∑ ∑ ∑ ∑

( )

[8–4]

where:

Sp = pooled standard deviation

Sp is calculated by pooling the individual standard

deviations as calculated from equation 2–6 (Steel and

Torrie 1960, Zar 1984). The t-test is appropriate when
Part 615

National Water Quality Handbook

Chapter 8

8–2 (450–VI–NWQH, September 2003)

Single watershed

the distributions are normally distributed and have

equal population variances. Example 8–1 illustrates

the analysis of a single watershed.

Example 8–1 Single watershed analysis

Table 8–1 presents a summary of total phosphorus

concentrations in watershed runoff for a before and

after study of manure applications. The before

period (X1) occurred during the period when manure was applied to the watershed during the winter

on ice and snow. The after period (X2) represents

samples that were taken during the period when

manure was applied during the spring and incorporated into the soil. Each value listed in the table is

the daily mean of eight 4-hour composite samples.

To determine whether the difference in phosphorus

concentrations is significant between the two

periods, the appropriate null hypothesis is:

HX X X X o : 12 1 2 −= = 0 or 

The appropriate alternative hypothesis would be:

HX X a : 1 2 >

The t-test assumes that the data are normally distributed and the groups have equal variances, so the

data should first be tested for these assumptions.

Table 8–1 Mean daily total phosphorus concentrations (mg/L) in watershed runoff from a

period before and after implementation of

best manure management

- - - - Total phosphorus - - - -

Before (X1) After (X2)

(mg/L) (mg/L)

6.330 0.185

2.166 0.049

0.642 0.040

0.754 0.087

0.728 0.142

0.478 0.060

0.464 0.187

0.444 0.068

0.375 0.043

0.120 0.039

0.086 0.404

0.064 0.110

0.099 0.085

0.054 0.082

0.063 0.138

0.197 1.617

0.088 0.798

0.089 0.104

0.110 0.341

0.105 0.055

0.081 0.295

0.090

0.211

0.151

0.158

0.047

0.029

0.027

0.065

0.152

0.087

0.041

0.544

0.296
Chapter 8

(450–VI–NWQH, September 2003) 8–3

Part 615

National Water Quality Handbook

Single watershed

Using a statistical package, such as SAS®, a test for

normality is made as described in chapter 4. Table

8–2 shows the test results for the total phosphorus

data.

Table 8–2 Test of normality for the total phosphorus

data

 Untransformed Log10

 transformed

 X1 X2 X1 X2

Mean 0.645 0.201 –0.631 –0.934

Median 0.120 0.097 –0.921 1.014

Skewness 3.840 3.690 0.998 0.764

Kurtosis 15.70 15.78 0.531 0.404

W:Normal 0.445 0.559 0.884 0.954

Prob < W <0.001 <0.001 0.015 0.204

Based on the nonsignificant Shapiro-Wilk W statistic, the data appear to be log-normally distributed.

Therefore, the log transformation is used prior to

the t-test. The next step is to calculate Sd, the standard deviation of the difference between means.

Since n1 does not equal n2, equation 8–2 is used to

calculate Sd. Table 8–3 provides a summary of

calculations needed to determine Sd.

Table 8–3 Summary of calculations for log10

transformed phosphorus data

 X1 X2

n 21 34

∑X –13.242 –31.764

∑X2 14.595 35.465

Log X –0.631 –0.934

X 0.234 0.116

Example 8–1 Single watershed analysis—Continued

First Sp is calculated from equation 8–4:

 

Sp

2

2 3

14 595 13 242

21

35 465 31 764

21 =

−  ( )















+ −

 ( ) −















. . . .

( ) − + − ( )

= + =

1 34 1

6 245 5 790

660

0 018235 . . .

Sd is calculated from equation 8–2:

Sd = ( ) +

( )( ) 0 018235 = 21 34

21 34 . . 0 037479

Student's t is calculated from equation 8–1:

t = − −( ) = 0 637 0 934

0 037479

8 085 . .

. .

From appendix A the table t-value is 2.006 for

df = (n1–1)+(n2–1) = 53 and p = 0.05. Therefore,

since the calculated t is greater than the table t, the

Ho is rejected. The mean is determined on the logtransformed values. Therefore, to transform the

mean back to original units, the antilog of the log

mean is taken by taking the value 10 and raising it

to the power of the log mean.

Based upon the t-test, this before and after study

determined that the mean phosphorus concentration was significantly reduced by 50 percent after

the implementation of the practice as compared to

before the practice. Confidence limits can be added

to this estimate of differences between means from:

X X tSX X 1 2 1 2− ± α − [8–5]

Where the standard error is calculated from:

S

S

n

S

n X X

p p

1 2

2

1

2

2

− = + [8–6]

or for log normal distributions when n is not large,

consult page 170 of Gilbert (1987).
Part 615

National Water Quality Handbook

Chapter 8

8–4 (450–VI–NWQH, September 2003)

Single watershed

For this example

SX X 1 2

0 0182

21

0 0182

34

0 037 − = += . . .

The confidence limit is:

0 234 0 116 2 004 0 037 0 118 0 074 . . .. . . − ± ( ) = ±

However, because of the limitations of this experimental design, it is possible that the differences are actually the result of some climate

difference from the first year to the second. The

design does not provide a way to correct for any

deterministic features in the data, such as cyclic

patterns or rainfall. For example, the change in

concentrations might also be caused by a dry

year following a wet year.

Example 8–1 Single watershed analysis—Continued The SAS® program for the t-test in example 8–1 would

be:

SAS PC Program

Data phos;

title 'TTest of Phos Data';

infile 'a:phos.dat';

input trt phos;

logphos = log10(phos);

Proc TTEST;

class trt;

run;
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(450–VI–NWQH, September 2003) 8–5

Part 615

National Water Quality Handbook

Single watershed

615.0802 Nonparametric

two-sample test

If data violate the assumptions of normal distributions

or equal variances, nonparametric or distribution-free

approaches may be used (Zar 1984). The MannWhitney test is the nonparametric equivalent to the ttest for two-samples. As previously described for other

nonparametric approaches, the ranks of the values are

used rather than the values themselves. Ranking is

done from highest to lowest, with the largest value in

both groups given a value of 1 and so on.

The Mann-Whitney U statistic is calculated from:

U nn

n n

= + R ( ) + 1 2 − 1 1

1

1

2 [8–7]

and

U nn U ′ = − 1 2 [8–8]

where:

n = number of samples in each group

R = sum of the ranks for that group (Zar 1984)

If either U or U ́ is equal to or greater than the table U,

the Ho is rejected at the appropriate α.

The data in table 8–1 are used in example 8–2, which is

a nonparametric approach for single watershed analysis.

Example 8–2 Nonparametric single watershed analysis

Table 8–4 provides the ranks for the data in table

8–1.

Table 8–4 Ranks of total phosphorus concentrations for the before (X1) and after (X2)

study of manure management

X1 X2 X2

1 20 32

2 48 17

7 52 23

5 36 21

6 24 49

9 45 54

10 19 55

11 41 42

13 50 22

26 53 35

37 12 51

43 27 8

31 38 15

47 39

44 25

18 3

34 4

33 30

28 14

29 46

40 16

n 21 34

R 474 1066

U

U

= ( )( ) +

( ) + − =

′ = ( )( ) − =

21 34 21 21 1

2

474 471

21 34 471 243

The table value for U is 450 (α=0.05) (Zar, 1984).

Since the calculated U is greater than the table U,

the Ho of equal concentrations is rejected. Using

either parametric approaches with a transformation or nonparametric approaches, the conclusion was that there was a significant difference

in the mean concentrations of total phosphorus

in runoff.
Part 615

National Water Quality Handbook

Chapter 8

8–6 (450–VI–NWQH, September 2003)

Single watershed

615.0803 Presentation of

results

The presentation of results from a before and after

study is generally a presentation of means. Box plots

(fig. 8–1) are also an appropriate presentation of the

data. The bottom and top of the box represent the 25th

and 75th percentiles, the center horizontal line is the

median, and the outer lines are the 10th and 90th

percentiles. In some cases time plots of the data can

be used; however, since the data are not paired in a

meaningful manner, the time plot could result in a

misleading interpretation.

615.0804 References

Gilbert, R.O. 1987. Statistical methods for environmental pollution monitoring. Van Nostrand Reinhold,

New York, NY.

Snedecor, G.W., and W.G. Cochran. 1980. Statistical

methods (7th ed.). The IA State Univ. Press,

Ames, Iowa.

Steel, R.G.D., and J.H. Torrie. 1960. Principles and

procedures of statistics. McGraw-Hill Book Co.,

Inc., New York, NY.

Zar, J.H. 1984. Biostatistical analysis. Prentice-Hall,

Inc., Englewood Cliffs, NJ.

Figure 8–1 Boxplots of phosphorus data

1.0

0.5

0.0

-0.5

-1.0

-1.5

Log total P

Logafter Logbefore
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 9 Above and Below

Watersheds
(450–VI–NWQH, September 2003) 9–i

Chapter 9 Above and Below Watersheds

Contents: 615.0900 Introduction 9–1

615.0901 Assumptions 9–1

615.0902 Paired comparison of means 9–2

615.0903 Nonparametric paired-sample test 9–4

615.0904 Presentation of results 9–5

615.0905 References 9–5

Tables Table 9–1 Mean daily total phosphorus concentrations in 9–3

watershed runoff above and below an area receiving

manure applications in the winter

Table 9–2 Test of normality for the difference in total phosphorus 9–3

data

Table 9–3 Summary calculation for determining the value of t 9–3

Figure Figure 9–1 Time plot of above-and-below phosphorus 9–5

concentration data

Examples Example 9–1 Above-and-below watershed analysis 9–2

Example 9–2 Nonparametric above-and-below watershed analysis 9–4
(450–VI–NWQH, September 2003) 9–1

Chapter 9 Above and Below Watersheds

615.0900 Introduction

The above-and-below design is often thought of as a

way to isolate the effect of a treatment. Theoretically,

if we sample the water before it flows into an area and

then again after it leaves an area, the difference in

water quality will be a result of the treatment in the

area. In some cases this may be true; however, the

difference may be caused by watershed differences as

well. An alternative is to conduct an above-and-below

study before and after the treatment. Such a study

becomes a paired watershed study as described in

chapter 10.

The above-and-below design is actually one watershed

physically nested within another. This design is applicable to streams as well as ground water systems. The

appropriate statistical approach is the paired t-test of

above-and-below data.

This chapter describes the assumptions used for the

above-and-below design, provides examples of how to

analyze the data using both parametric and nonparametric approaches, and gives examples of how to

present the results from the study.

615.0901 Assumptions

The t-test assumes that the data are normally distributed and the two groups being compared are of equal

variances (Snedecor and Cochran 1980, Steel and

Torrie 1960, Zar 1984). If the data fail these assumptions, a transformation or nonparametric approach

should be used. One of the conditions of the paired

t-test is that pairs actually exist. Thus if data are

collected at one station, but not the other, no pair

exists. Flow occurring at one station, but not at the

other still constitutes a pair since one of the values is a

zero and the other is above zero. However, when there

is no water to measure, a concentration value does not

exist and, therefore, a concentrated pair does not

exist.
Part 615

National Water Quality Handbook

Chapter 9

9–2 (450–VI–NWQH, September 2003)

Above and Below Watersheds

615.0902 Paired comparison of means

The paired comparison of means assumes that the

paired values are correlated in some way (Steel and

Torrie 1960). Therefore, when one value of the pair

was large, we would expect the other value to also be

large. The variance is then computed on the difference between paired values rather than on the individual observations as for the unpaired example.

The appropriate null hypothesis of the paired comparison of means is the same as for the unpaired comparison described in chapter 8:

HX X o : 1 2 − = 0

The appropriate alternative hypothesis would be:

HX X a : 1 2 − ≠ 0

The test of the significance of the difference between

the means is based on the t distribution (Steel and

Torrie 1960, Zar 1984) where t is defined as:

t d

sd

= [9–1]

where:

d = the mean of the differences between the paired

observations

Sd = standard deviation of the difference between

the means, which is determined from:

S

d

d

n

n n d

i

i

2

2

2

1 =

− ( )

( ) −

∑ ∑ [9–2]

where:

di = difference between the paired observation

n = number of observation pairs

Example 9–1 illustrates the statistical analysis using

the above-and-below process.

Table 9–1 presents a summary of total phosphorus

concentrations in watershed runoff above and

below an area that received winter manure applications on ice and snow. Each value listed in the table

is the daily means of eight 4-hour samples. The

below data are the same as those listed as before

data in table 8–1 in chapter 8. This example allows a

direct comparison of the single watershed analysis

to the above-and-below analysis since the data are

real observations from a watershed in Vermont.

Determine whether a significant difference in

phosphorus concentrations occurs between the

above and below stations. The appropriate null

hypothesis is:

HX X o : 1 2 − = 0

The appropriate alternative hypothesis would be:

HX X a : 1 2 − ≠ 0

Example 9–1 Above-and-below watershed analysis

Because the t-test assumes that the data are normally distributed and the groups have equal variances, the data should first be tested for these

assumptions.

Using a statistical package, such as SAS®, the data

should be examined for normality. As shown in

table 9–2, the data appear to be log-normally distributed. Therefore, the log transformation is used

before the t-test. To calculate Sd and t, the values in

table 9–3 are calculated.

From appendix A, the table t-value is 2.101 for df =

n–1 = 18 and p = 0.05. Therefore, since the calculated t is greater than the table t, the Ho is rejected.

The mean is determined on the log transformed

values. To transform the mean back to original

units, the antilog of the log mean is obtained by

taking the value 10 and raising it to the power of the

log mean. If a negative value had been obtained for

the difference, a constant would need to be added
Chapter 9

(450–VI–NWQH, September 2003) 9–3

Part 615

National Water Quality Handbook

Above and Below Watersheds

to all difference values before a log transformation

could be used because the log of a negative number

does not exist.

Based upon the t-test, this above-and-below study

determined that the phosphorus concentration was

significantly increased in runoff by 0.173 mg/L as a

result of the winter application of manure. However, because of the limitations of this experimental

design, it may be possible that the differences may

actually be the result of an inherent watershed

difference between the upstream and downstream

stations.

Table 9–1 Mean daily total phosphorus concentrations (mg/L) in watershed runoff above

and below an area receiving manure

applications in the winter

- - - - - - - - Total phosphorus (mg/L) - - - - - - - - -

Above Below Difference Rank

0.060 6.330 6.270 19

0.095 2.166 2.071 18

0.117 0.642 0.525 15

0.073 0.754 0.681 17

0.050 0.728 0.678 16

0.034 0.478 0.444 14

0.250 0.464 0.214 11

0.211 0.444 0.233 12

0.090 0.375 0.285 13

0.032 0.120 0.088 10

0.027 0.086 0.059 7

0.076 0.064 –0.012 1

0.058 0.099 0.041 2

0.012 0.054 0.042 3

0.011 0.063 0.052 5

0.056 0.088 0.032 1

0.029 0.089 0.060 8

0.040 0.110 0.070 9

0.049 0.105 0.056 6

0.036 0.081 0.045 4

Example 9–1 Above-and-below watershed analysis—Continued

Table 9–2 Test of normality for the difference in

total phosphorus data

Untransformed Log

transformed

d d

Mean 0.629 –0.7634

Median 0.088 –1.0555

Skewness 3.696 0.922

Kurtosis 14.442 0.158

W:Normal 0.449 0.888

Prob < W <0.001 0.029

Table 9–3 Summary calculation for determining the

value of t

log (d)

n 19

∑di –14.5048

∑di

2 18.6759

log X –0.763

X 0.173 (mean difference in mg/L)

Sd

2

2

18 6759 14 5048

19

19 19 1 = 0 0222

− ( ) −

( ) − =

. .

.

t = − = − 0 763

0 0222

34 369 .

. .
Part 615

National Water Quality Handbook

Chapter 9

9–4 (450–VI–NWQH, September 2003)

Above and Below Watersheds

The SAS® program for the t-test in example 9–1 would

be:

SAS PC Program

Data phos;

title 'TTest of Phos Data';

infile 'a:phos.dat';

input phos1 phos2;

diff=phos2-phos1;

logdiff = log10(diff);

Proc MEANS Mean Stderr T PRT;

Var diff;

run;

615.0903 Nonparametric

paired-sample test

If the data violate the assumptions of normal distributions or equal variances, nonparametric or distribution-free approaches may be used (Zar 1984) as was

used for the unpaired comparison of means in chapter

8. The Wilcoxon paired sample test is the nonparametric equivalent to the t-test for paired samples. As

previously described for other nonparametric approaches, the ranks of the differences between the

values are used rather than the differences themselves.

Ranking is done from lowest to highest with the smallest difference given a value of 1 and so on. The sign of

the difference is also carried with the rank. Ranks are

summed for both positive (T+) and negative (T–)

ranks. The T values are compared to a tabular T value;

if either value is less than or equal to the table T value,

the Ho of equal values is rejected.

The data in table 9–1 are used in example 9–2, which

illustrates the nonparametric approach to analysis of

the above-and-below design data.

Example 9–2 Nonparametric above-and-below watershed analysis

T+ = 19 + 18 + ... + 1 = 209

T– = 1

From appendix G, T at n = 20 df and p = 0.05 =

52. Since T– is less than the table T, the null

hypothesis of equal concentrations above and

below is rejected. Using either the log10 transformation or nonparametric approaches, the conclusion was that there was a significant difference in the mean total phosphorus concentrations in runoff at the below station as compared

to those at the above station.
Chapter 9

(450–VI–NWQH, September 2003) 9–5

Part 615

National Water Quality Handbook

Above and Below Watersheds

615.0904 Presentation of

results

The presentation of results from an above-and-below

study is usually a presentation of means. In this case

the mean total phosphorus concentration was increased from 0.052 to 0.234 mg/L or 4.5 times. Box

plots would be an informative graphic approach to

presenting the comparison between above and below

data.

In some cases time plots are useful in presenting the

results. For example 9–1, the time plot in figure 9–1

reveals that the below station was consistently higher

in phosphorus concentration than the above station.

The plot also reveals that the difference was greater

during the early part of the snowmelt season and

became progressively less as time went on.

Figure 9–1 Time plot of above-and-below phosphorus

concentration data

615.0905 References

Snedecor, G.W., and W.G. Cochran. 1980. Statistical

methods. 7th Ed. The IA State Univ. Press. Ames,

IA.

Steel, R.G.D., and J.H. Torrie. 1960. Principles and

procedures of statistics. McGraw-Hill Book Co.,

Inc., New York, NY.

Zar, J.H. 1984. Biostatistical analysis. Prentice-Hall,

Inc., Englewood Cliffs, NJ.

Above

Below

10

1

0.1

0.01

3/21 4/7 4/18 4/25 5/6

Total phosphorus (mg/L)

Date-mm/dd
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 10 Paired Watersheds
(450–VI–NWQH, September 2003) 10–i

Chapter 10 Paired Watersheds

Contents: 615.1000 Introduction 10–1

615.1001 Calibration 10–2

(a) Regression significance ............................................................................. 10–2

(b) Calibration duration ................................................................................... 10–3

(c) Residual errors ............................................................................................ 10–3

615.1002 Treatment 10–4

615.1003 Nonlinear/multiple regression 10–5

615.1004 Displaying results 10–5

615.1005 References 10–6

Tables Table 10–1 Schedule of BMP implementation 10–1

Table 10–2 Analysis of variance for linear regression 10–2

Table 10–3 Analysis of covariance for comparing regression lines 10–4

Table 10–4 Analysis of variance for regression of treatment 10–7

watershed runoff on control watershed runoff

Table 10–5 ANOVA for regression of treatment watershed runoff 10–8

on control watershed runoff for the treatment period

Table 10–6 ANCOVA for comparing calibration and treatment 10–8

regressions

Table 10–7 Mean values by period and watershed 10–9

Table 10–8 Example analysis of covariance for comparing 10–9

 regression lines
Part 615

National Water Quality Handbook

Chapter 10

10–ii (450–VI–NWQH, September 2003)

Paired Watersheds

Figures Figure 10–1 Calibration period regression 10–2

Figure 10–2 Treatment and calibration period regressions 10–9

Figure 10–3 Observed deviations from predicted discharge 10–9

Example Example 10–1 Paired watershed analysis 10–7
(450–VI–NWQH, September 2003) 10–1

Chapter 10 Paired watersheds

615.1000 Introduction

The purpose of this chapter is to describe data analysis

for the paired watershed design for conducting

nonpoint source (NPS) water quality studies. The

monitoring system design requires a minimum of two

watersheds—control and treatment—and two periods

of study—calibration and treatment (Green 1979,

Hewlett 1971, Hewlett and Pienaar 1973, Ponce 1980,

Reinhart 1967).

The control watershed accounts for year-to-year or

seasonal climate variations. The management practices within the control watershed remain the same

during the study. The treatment watershed has a

change in management at some point during the study.

During the calibration period, the two watersheds are

treated identically, and paired water quality data are

collected (table 10–1). Such paired data could be

annual means or totals, or for shorter studies (<5 yr),

the observations could be seasonal, monthly, weekly,

or event-based (Reinhart 1967). During the treatment

period, one watershed is treated with a best management practice (BMP) while the control watershed

remains in the original management (table 10–1). The

treated watershed should be selected randomly by

such means as a coin toss.

The reverse of this schedule is possible for certain

BMPs; the treatment period could precede the calibration period (Reinhart 1967). For example, the study

could begin with two watersheds in two different

treatments, such as BMP and no BMP. Later both

watersheds could be managed identically to calibrate

them. Since no calibration exists before the treatment

occurs, this reversed design is considered risky because you will not find out if the watersheds are properly calibrated until the end of the study.

The basis of the paired watershed approach is that

• The relationship between paired water quality

data for the two watersheds is quantifiable.

• This relationship is valid until a major change is

made in one of the watersheds (Hewlett 1971). At

that time, a new relationship will exist.

This basis does not require that the quality of runoff be

statistically the same for the two watersheds. It does

require that the relationship between paired observations of water quality remains the same over time

except for the influence of the BMP. Often, in fact, the

analysis of paired observations indicates that the

water quality is different between the paired watersheds. This difference further substantiates the need

to use a paired watershed approach. This is because

the technique does not assume that the two watersheds are the same; it does assume that the two watersheds respond in a predictable manner together.

Example 10–1 illustrates a paired watershed analysis.

Table 10–1 Schedule of BMP implementation

Period - - - - - - Watershed - - - - -

control treated

Calibration no BMP no BMP

Treatment no BMP BMP
Part 615

National Water Quality Handbook

Chapter 10

10–2 (450–VI–NWQH, September 2003)

Paired watersheds

615.1001 Calibration

The relationship between watersheds during the

calibration period is described by a simple linear

regression equation (fig. 10–1) between the paired

observations, taking the form:

treated=b b control e o i + ( ) + 1 [10–1]

where:

treated and control = flow, water quality concentration, or mass values for the appropriate watershed

bo and b1 = regression coefficients representing the

regression intercept and slope, respectively

e = residual error

Three important questions must be answered before

shifting from the calibration period to the treatment

period:

• Is there a significant relationship between the

paired watersheds for all parameters of interest?

• Has the calibration period continued for a sufficient length of time?

• Are the residual errors about the regression

smaller than the expected BMP effect?

In addition, the observations should cover the full

range of observations expected during treatment.

(a) Regression significance

The significance of the relationship between paired

observations is tested using analysis of variance

(ANOVA). The test assumes that the regression residuals are normally distributed, have equal variances

between treatments, and are independent.

Hand calculations to test for the significance of the

relationship are shown in Snedecor and Cochran

(1980, p. 157) and in table 10–2. The values for the

table are calculated from:

S =y

2 Y

Y

n

i

∑ ∑− ( ) 1

2

2

[10–2]

S =x

2 X

X

n

i

∑ ∑− ( ) 1

2

2

[10–3]

S =xy X Y

X Y

n i i

i i ∑ ∑ ∑ − ( )( ) [10–4]

S =2

yx

y

xy

x

S

S

S

n

2

2

2

2

− ( )

−

[10–5]

Figure 10–1 Calibration period regression

100

10-1

10-2

10-3

10-4

10-5

10-5 10-4 10-3 10-2 10-1 100

LogY=0.549+0.789(LogX)

r2=0.69

Control (West) field

storm runoff (cm)

Treatment (East) field

storm runoff (cm)

Calibration period

Table 10–2 Analysis of variance for linear regression

Source Degrees of Sum of Mean F

freedom squares squares

regression 1

S

S

xy

x

( )2

2

S

S

xy

x

( )2

2

S

S

S

xy

x

x

( ) 















2

2

2

residual n–2 S

S

S y

xy

x

2

2

2

( ) Syx

2

total n–1 Sy

2
Chapter 10

(450–VI–NWQH, September 2003) 10–3

Part 615

National Water Quality Handbook

Paired watersheds

Also, the regression coefficients and coefficient of

determination are determined from:

b

S

S

xy

x

1 2 = [10–6]

b Y bX o = − 1 [10–7]

r

S

S

S

xy

x

y

2

2

2

2 =

( )

[10–8]

To perform the calculations by hand, initially calculate:

Σ ΣΣ Σ Σ X Y XY X Y XY i i ii i i , , , , ,, 2 2

The mean squares (MS) are determined by dividing the

sum of squares by the degrees of freedom (df).

Using SAS®, the appropriate program is shown as:

SAS PC Program

data flow;

title 'Total Flow (cm)';

infile 'fname.dat';

input flow1 flow2;

logflow1=log10(flow1);

logflow2=log10(flow2);

Proc reg;

Model logflow2=logflow1

/P CLM;

run;

This program was used to generate table 10–4 in

example 10–1.

(b) Calibration duration

Methods for determining whether the length of the

calibration period has been sufficient have been described by Wilm (1949), Kovner and Evans (1954), and

Reinhart (1967). The ratio between the residual variance (mean squares, Syx

2 ) for the regression and the

smallest worthwhile difference (d) for the treatment

watershed is used to determine if a sufficient sample

has been taken to detect that difference, from (Kovner

and Evans 1954):

S

d

n n

n n F F

yx

n n

2

2

1 2

1 2

1

1 2 1 2

= +





 



 ( ) + −















 +

[10–9]

where:

Syx

2 = estimated residual variance about the

regression

d2 = square of the smallest worthwhile difference

n1 and n2 = numbers of observations in the calibration and treatment periods (n1 = n2 for

this calculation because n2 is not known

yet)

F = table value (p = 0.05) for the variance

ratio at 1 and n1 + n2 – 3df (appendix C)

The difference (d) is selected based on experience and

would vary with project expectations. If the left side of

the equation is greater than the right side, then the

number of samples taken was not sufficient to detect

the difference.

(c) Residual errors

The confidence bands for the regression equation

allow determining the level of change needed to have a

significant treatment effect. In other words, how far

away from the calibration regression must the treatment data be to be significantly different? Confidence

bands for the regression are determined from:

CI t S

n

X X

S yx

i

x

= ±( )( ) +

1 ( ) − 2

2 [10–10]

where:

CI = confidence interval

Syx = square root of Syx

2

n and Sx

2 = factors have been previously defined

t = Student's t

Xi = value at the point of comparison to

compare to the mean on the regression

line

Confidence limits can be generated in SAS® by adding

/ P CLM to the MODEL statement.
Part 615

National Water Quality Handbook

Chapter 10

10–4 (450–VI–NWQH, September 2003)

Paired watersheds

615.1002 Treatment

At the end of the treatment period the significance of

the effect of the BMP is determined using analysis of

covariance (ANCOVA). The analysis is actually a series

of steps determining:

• significance of the treatment regression equation

• significance of the overall regression that combines the calibration and treatment period data

• difference between the slopes of the calibration

and treatment regressions

• difference between the intercepts of the calibration and treatment regressions

The analysis can be computed by hand as shown in

table 10–3 (Snedecor and Cochran 1980, p. 386). The

summation's symbol (∑) in table 10–3 is used to signify

the addition of the column entries above it.

An example program using SAS® is shown below. This

program contains both a test of the treatment regression in the PROC REG statement and a test comparing

the regression lines in the PROC GLM statement.

SAS PC Program

Proc reg;

model logflow2=logflow1;

run;

Proc glm;

class period;

model logflow2=logflow1 period

logflow1 * period;

run;

Table 10–3 Analysis of covariance for comparing regression lines

Source df 2 Sx Sxy Sy

2 b1 df SS MS F

Within calibration n1–1 Eq 10–3 Eq 10–4 Eq 10–2 Eq 10–6 n1–2 S

S

S y

xy

x

2

2

2 = ( ) Eq 10–5

Within treatment n2–1 Eq 10–3 Eq 10–4 Eq 10–2 Eq 10–6 n2–2 S

S

S y

xy

x

2

2

2 = ( ) Eq 10–5

Pooled Error Σ Σ SS/df

_______ __ __ ______

Slopes n1+ n2–2 Σ Σ Σ Eq 10–6 n1+ n2–3 S

S

S y

xy

x

2

2

2 = ( ) Eq 10–5

Slope difference 1 Slope SS– MS/ 

Error SS Error MS

1 Combined SS- MS/

SlopeSS Slope MS

Intercepts n1+ n2–1 combined data n1+ n2-2 S

S

S y

xy

x

2

2

2 = ( )
Chapter 10

(450–VI–NWQH, September 2003) 10–5

Part 615

National Water Quality Handbook

Paired watersheds

615.1003 Nonlinear/

multiple regression

At times the effect of the treatment may be nonlinear.

Examples of nonlinear treatment effects include

different responses to storm size or gradual vegetation

changes. Swindel and Douglass (1984) described

approaches for testing nonlinear treatment effects

including quadratic approaches and fitting to a gamma

distribution. Multiple regression may also be used for

paired watershed studies (Hibbert 1969, Snyder 1962).

Regression through the origin can be used where zero

flow is expected to occur from both watersheds at

approximately the same time. This would occur for

adjacent, equally sized watersheds, but not for watersheds of different sizes.

615.1004 Displaying

results

The most common methods for displaying the results

include a bivariate plot of paired observations together

with the calibration and treatment regression equations (fig. 10–2). Another useful graph is a plot of

deviations (yobserved – ypredicted) as a function of time

during the treatment. The predicted values are obtained from the calibration regression equation.

Results should be provided of mean values for each

period and each watershed. The overall results caused

by the treatment can be expressed as the percent

change based on the mean predicted and observed

values.
Part 615

National Water Quality Handbook

Chapter 10

10–6 (450–VI–NWQH, September 2003)

Paired watersheds

615.1005 References

Green, R.H. 1979. Sampling design and statistical

methods for environmental biologists. John

Wiley and Sons, New York, NY.

Hewlett, J.D. 1971. Comments on the catchment experiment to determine vegetal effects on water

yield. Water Res. Bul. 7(2):376-381.

Hewlett, J.D., and L. Pienaar. 1973. Design and analysis

of the catchment experiment. In Proc. Symp., Use

of Small Watersheds, E.H. White (ed.), Univ. KY.

Hibbert, A.R. 1969. Water yield changes after converting a forested catchment to grass. Water

Resourc. Res. 5(3):634-640.

Kovner, J.L., and T.C. Evans. 1954. A method for

determining the minimum duration of watershed

experiments. Trans. AGU 35(4):608-612.

Ponce, S.L. 1980. Statistical methods commonly used

in water quality data analysis. WSDG Tech. Pap.

WSDG-TP-00001, USDA Forest Service, Fort

Collins, CO.

Reinhart, K.G. 1967. Watershed calibration methods.

In Proc. Intern. Symp. on Forest Hydrology, W.E.

Sopper and H.W. Lull. (eds.), Pergamon Press.

Oxford. pp. 715-723.

SAS Institute, Inc. 1986. SAS system for linear models.

Cary, NC

Snedecor, G.W., and W.G. Cochran. 1980. Statistical

methods (7th ed.). IA State Univ. Press, Ames.

Snyder, W.M. 1962. Some possibilities for multivariate

analysis in hydrologic studies. J. Geophysical

Res. 67(2):721-729.

Swindel, B.F., and J.E. Douglass. 1984. Describing and

testing nonlinear treatment effects in paired watershed experiments. Forest Science 30(2):305-313.

Wilm, H.G. 1949. How long should experimental watersheds be calibrated? Amer. Geophs. Union Trans,

Part II, 618-622.
Chapter 10

(450–VI–NWQH, September 2003) 10–7

Part 615

National Water Quality Handbook

Paired watersheds

Data from a study in Vermont is used to illustrate

the paired watershed approach. The purpose of the

study was to compare changes in field runoff as a

result of conversion of conventional tillage to

conservation tillage. Information included:

• West watershed was the control and was 1.46

hectares (ha) in area.

• East watershed was the treatment field and

was 1.10 ha.

• Conventional tillage was moldboard plow

whereas conservation tillage was a single disk

harrow.

• The calibration period was 1 year during

which 49 paired observations of storm runoff

were made.

• The treatment period was 3 years during

which 114 paired observations of runoff were

made.

The assumptions were tested for ANOVA. Data

were log-transformed to approach normality based

upon the Shapiro-Wilks (W) statistic. The equality

of variances between periods was tested using the

F-test. Residual plots were examined to check for

independence of errors. The statistical package

SAS® was used for all analyses (SAS 1986).

The regression coefficients of paired observations

are calculated by hand as follows:

X

Y

X Y

X

y

i

i

i i

i

i

∑

∑

∑

∑

∑

= −

= −

=

=

=

123 403

180 704

533 553

381 713

814

2

2

.

.

.

.

.847

2 518 10 0 003041

3 688 10 0 000205

X

Y

X

Y

=− = ( )

=− = ( )

. .

. .

cm

cm

Example 10–1 Paired watershed analysis

Therefore,

S

S

S

S

y

xy

x

yx

2

2

2

148 441

78 463

70 933

1 312

=

=

=

=

.

.

.

.

The resulting F statistic for this example would

indicate that the regression adequately explains a

significant amount (p<0.001) of the variation in

paired data.

For the example, Syx

2 was 1.312 (from table 10–4),

n1 = n2 was 49, and F was 3.94. A 10 percent change

from the mean was considered a worthwhile difference; therefore,

d X = ×= ×

=

0 10 0 10 0 003041

20 7

. . log .

.

cm

S

d

yx

2

2

The right side of equation 10–9 equals 6. Because

20.7 is greater than 6, the number of observations

was not sufficient to detect a 10 percent change in

discharge. Enough samples were taken to detect a

20 percent change in discharge:

S

d

2

2 = 5 2.

Table 10–4 Analysis of variance for regression of

treatment watershed runoff on control

watershed runoff

Source df MS F p

model 1 86.79 66.17 0.0001

error 47 1.31

total 48
Part 615

National Water Quality Handbook

Chapter 10

10–8 (450–VI–NWQH, September 2003)

Paired watersheds

To perform the calculations for determining analysis of covariance (ANCOVA) by hand, determine the

following for the example treatment data:

X

Y

X Y

X

Y

i

i

i i

i

i

∑

∑

∑

∑

∑

= −

= −

=

=

=

358 14

416 05

1 408 37

1 352 54

1 62

2

2

.

.

, .

, .

, 3 43

3 1416

3 650

114

.

.

.

X

Y

n

= −

= −

=

Therefore,

S

S

S

y

xy

x

2

2

135 00

101 32

227 43

=

=

=

.

.

.

The treatment period regression was found to be

significant based on the analysis of variance for

regression (table 10–5).

The analysis of covariance obtained in SAS® output

summarizes the significance of the overall model,

compares the two regression equations, the regression intercepts, and the slopes (table 10–6). The

ANCOVA indicates that the overall treatment and

calibration regressions were significantly different

and that the slopes and intercepts of the equations

also were different. The difference in slopes is

evident in figure 10–2. The slight differences in F

values between the hand calculation method and

the SAS® output are caused by rounding errors.

For the example, the plot of deviations indicates

that for most paired observations, the observed

value was less than that predicted by the calibration

regression equation (fig. 10–3).

In the example, a 64 percent reduction in mean

runoff was attributed to the treatment (table 10–7).

Example 10–1 Paired watershed analysis—Continued

The ANCOVA is completed for the example in table

10–8.

Since the slopes were found to be different, the

differences in intercepts do not have any real meaning and do not need to be calculated. That is, if

slopes are different, intercepts generally are different. However, the calculation for the test of intercepts is presented to show the method. The combined data are determined by summing the

Σ ΣΣ Σ X Y XY X i i ii i ,, , , 2 and ΣYi

2

 values for both the

calibration and treatment periods and calculating

new values for Sy

2 , Sxy, and Sx

2 . The calculation of F

for the intercept uses the slope MS in the denominator. The F for the slope test uses the error MS in the

denominator. A significant difference in intercepts,

but not slopes indicates an overall parallel shift in

the regression equation.

Table 10–5 ANOVA for regression of treatment

watershed runoff on control watershed

runoff for the treatment period

Source df MS F p

model 1 45.13 56.25 0.0001

error 112 0.80

total 113

Table 10–6 ANCOVA for comparing calibration and

treatment regressions

Source df MS F p

model 3 43.99 46.17 0.001

error 159 0.95

overall 1 103.09 108.18 0.0001

intercept 1 5.47 5.74 0.0178

slope 1 23.42 24.58 0.0001
Chapter 10

(450–VI–NWQH, September 2003) 10–9

Part 615

National Water Quality Handbook

Paired watersheds

Example 10–1 Paired watershed analysis—Continued

Table 10–8 Example analysis of covariance for comparing regression lines

Source df Sx

2 Sxy Sy2 b1 df SS MS F

Within calibration 48 70.933 78.463 148.441 1.106 47 61.650 1.3117

Within treatment 113 227.430 101.315 135.000 0.445 112 89.866 0.8024

Error 159 151.516 0.9529

Slopes 161 298.363 179.778 283.441 0.603 160 175.116 1.0945

Slope difference 1 23.600 23.600 24.77***

1 5.8453 5.8453 5.34*

Intercepts 162 311.671 178.762 283.492 161 180.961

*** indicates significance at p=0.001

* indicates significance at p=0.05

Table 10–7 Mean values by period and watershed

Runoff (cm) x 10–2

Calibration

Control 0.30

Treatment 1.63

Treatment

Control 0.08

Treatment 0.04

Predicted 0.11 –64%

Figure 10–3 Observed deviations from predicted

discharge

103

102

101

-101

0

-102

-103

Storm runoff (cm)

observed-predicted

J J A SO ND FMAM J J A FMAM J J A S SOND

1967 1968

Date

1969

Figure 10–2 Treatment and calibration period regressions

100

10-1

10-2

10-3

10-4

10-5

10-5 10-4 10-3 10-2 10-1 100

LogY=0.603+0.50(LogX)

r2=0.33

Control (West) field

storm runoff (cm)

Treatment (East) field

storm runoff (cm)

Calibration period

Treatment period
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 11 Multiple Watersheds
(450–VI–NWQH, September 2003) 11–i

Chapter 11 Multiple Watersheds

Contents: 615.1100 Introduction 11–1

615.1101 Assumptions 11–2

615.1102 Number of watersheds 11–2

615.1103 Comparison of groups 11–3

615.1104 Nonparametric approaches 11–5

615.1105 Presentation of results 11–6

615.1106 References 11–6

Tables Table 11–1 Phosphorus concentration of runoff from paved and 11–4

unpaved barnyards

Table 11–2 Univariate statistics for barnyard phosphorus 11–4

concentration data

Table 11–3 ANOVA for barnyard phosphorus concentration data 11–4

Table 11–4 Mean total phosphorus concentrations of runoff from 11–4

the paved and unpaved barnyards

Table 11–5 Wilcoxon rank-sum test for the barnyard phosphorus 11–5

data using JMP

Figures Figure 11–1 Boxplots of the paved and unpaved barnyard 11–5

phosphorus concentration data
Part 615

National Water Quality Handbook

Chapter 11

11–ii (450–VI–NWQH, September 2003)

Multiple Watersheds

Examples Example 11–1 Parametric multiple watershed analysis—chemical 11–3

Example 11–2 Nonparametric multiple watershed analysis using the 11–5

phosphorus barnyard data
(450–VI–NWQH, September 2003) 11–1

Chapter 11 Multiple Watersheds

615.1100 Introduction

The purpose of this chapter is to describe data analysis

for the multiple watershed approach for conducting

nonpoint source water quality studies. The multiple

watershed approach is a study involving more than

two watersheds in the design. Wicht (1967) described

this approach that was intended to overcome some of

the disadvantages of the paired watershed approach.

These disadvantages included:

• Inability to always find a stable control watershed

• Uncertainty in predicting the length of the calibration period

• Risk that meteorological conditions may change

at the same time as when treatment begins

• Progressive long-term response, such as during

major land use changes

In addition, extrapolation of the results from paired

watershed studies to broader areas or regions can be

questioned, and there is no true replicate in paired

watershed investigations.

For the multiple watershed approach, the treatments

are intended to be applied to a series of watersheds

that have comparable geology, topography, and initial

vegetative cover, and are subject to the same or related uncontrolled climate influences (Wicht 1967).

Striffler (1965) also described a multiwatershed

method that used multiple regression analysis to

assess the relationship between a dependent variable,

such as sediment yield, and several independent

variables, such as watershed area, soil or vegetative

types, and precipitation. Many watersheds selected

represent different levels for the independent variables. A major advantage of such an approach is that a

large range of watershed conditions is being sampled.

Sampled watersheds also can vary in size and other

characteristics, such as varying levels of a disturbance.

However, a different approach is more appropriate for

nonpoint source pollution studies. Watersheds that

have the treatment already in place could be selected

across a region of interest. The size of the region

would be dictated by the objectives of the study, but

could be as large as a state or perhaps limited to an

ecoregion or smaller unit. Once the watersheds were

selected, sampling of the appropriate water quality

variables would be conducted over a period of time.

Clausen and Brooks (1983a, b) used such an approach

when comparing the water quality associated with

different types of wetlands and when comparing

mined to unmined bogs.

This chapter describes the assumptions made in a

multiple watershed experiment, presents examples of

how to analyze the data from such designs using both

parametric and nonparametric approaches, and gives

examples of how to present the results from the study.
Part 615

National Water Quality Handbook

Chapter 11

11–2 (450–VI–NWQH, September 2003)

Multiple watersheds

615.1101 Assumptions

The primary statistical approach for comparing groups

of watersheds is the analysis of variance. Therefore,

the assumptions made are the same as those previously described for analysis of variance (ANOVA). The

major assumptions are:

• Water quality data are sampled randomly.

• Data come from a normal distribution.

• Variances are homogeneous across groups.

• Experimental errors are independently

distributed.

• Treatment effects are additive.

The approaches used to test these assumptions are

described in chapter 4. When using nonparametric

approaches, the assumption of normality is no longer

appropriate.

615.1102 Number of

watersheds

One of the first decisions to make when designing a

multiple watershed monitoring study is determining

the number of watersheds in each group to monitor.

Part 614, chapter 9, National Water Quality Handbook,

describes procedures for estimating the number of

sampling units for water quality monitoring. The basic

requirements are knowledge of the variance among

watersheds and a desired precision to achieve in the

study. Clausen and Brooks (1983a) found that 15

watersheds of each type were sufficient to determine

differences in the water quality of different peatland

types.
Chapter 11

(450–VI–NWQH, September 2003) 11–3

Part 615

National Water Quality Handbook

Multiple watersheds

615.1103 Comparison of

groups

The original analytical approach suggested was a

series of paired comparisons between different pairs

of watersheds using covariance analysis as for the

paired watershed technique (Wicht 1967). Both parametric and nonparametric approaches can be used to

compare the results from several groups. The methods

of analysis are quite similar to those used for plot

studies (part 615, chapter 7). Example 11–1 illustrates

parametric method of data analysis.

The multiple watershed approach was used to

assess the water quality effects associated with

paving dairy barnyards in Vermont. The objective of

the study was to determine the effect of paving on

runoff water quality within a 26,000-acre watershed.

Five paved and five unpaved barnyards were

sampled for runoff on an event basis nine times over

1 year. During each rainfall event, one or two grab

samples were collected from each barnyard.

Samples were analyzed for phosphorus (table 11–1),

nitrogen, and suspended solids; however, only the

total phosphorus concentration data are used in this

example. Missing concentration data occurred

during the study when either there was no runoff or

the sample was destroyed during the analysis process.

Using PROC UNIVARIATE in SAS® (SAS 1995) the

phosphorus concentration data were found to be log

normally distributed (table 11–2). A P-value <0.05

for the unlogged data (i.e., the data prior to log

transformation) indicated that the distribution may

be significantly different from a normal distribution

based on the Shapiro-Wilk W-statistic.

Example 11–1 Parametric multiple watershed analysis

PROC ANOVA was used to test the null hypothesis

that the mean phosphorus concentrations were the

same in runoff from the paved and unpaved barnyards. The resulting ANOVA (table 11–3) indicated

that there was a significant difference between

barnyard types, and the null hypothesis is rejected.

The log mean and antilog mean phosphorus concentrations for the barnyard data are reported in table

11–4. The antilog was obtained by taking 10 to the

power of the log value. These results indicate that

the paved barnyards in this watershed had runoff

phosphorus concentrations that were about two

times greater than that in runoff from the unpaved

barnyards.
Part 615

National Water Quality Handbook

Chapter 11

11–4 (450–VI–NWQH, September 2003)

Multiple watersheds

Table 11–1 Phosphorus concentration of runoff from

paved and unpaved barnyards

Date Paved Unpaved Date Paved Unpaved

- - - - mg/L - - - - - - - - mg/L - - - -

6/12 20.20 1.90 3/20 12.40 90.00

67.80 16.10 50.00 22.30

 3.40 4.90 13.30 ---

38.20 5.10 192.50 17.70

25.70 23.30 132.50 29.00

6/13 36.70 7.20 6/2 13.40 13.40

132.7 14.70 52.00 13.80

12.20 25.50 17.00 36.70

80.70 7.20 134.30 8.60

32.70 20.30 7.40 15.03

9/27 22.00 53.00 6/8 10.30 17.70

--- 18.20 105.50 27.60

19.80 40.85 47.30 18.80

59.20 23.30 68.80 6.40

--- 35.90 17.20 19.10

10/5 22.90 13.30 8/7 --- 19.00

54.15 19.00 63.35 26.00

38.30 44.40 93.02 ---

73.70 14.60 86.68 9.80

96.60 43.10 83.02 22.20

11/5 82.27 27.78

50.75 25.11

47.01 22.10

44.34 7.48

35.79 18.16

Table 11–2 Univariate statistics for barnyard phosphorus concentration data

Unlogged Log10

Skewness 2.04 –0.17

Kurtosis 4.68 –0.02

W-statistic 0.777 0.986

P-value <0.001 0.877

Table 11–3 ANOVA for barnyard phosphorus concentration data

Source of Degrees Sum of Mean F P > F

variation freedom squares squares

Between 1 2.627 2.627 21.53 <0.0001

Within 83 10.127 0.122

Total 84 12.754

Table 11–4 Mean total phosphorus concentrations of

runoff from the paved and unpaved

barnyards

Log mean Mean

- - - - - - mg/L - - - - - -

Paved 1.4099 25.70

Unpaved 1.0927 12.38

Example 11–1 Parametric multiple watershed analysis—Continued
Chapter 11

(450–VI–NWQH, September 2003) 11–5

Part 615

National Water Quality Handbook

Multiple watersheds

615.1104 Nonparametric

approaches

The nonparametric approaches described in chapters

7 to 9 are also appropriate for multiple watersheds

data analysis. For the comparison of two groups, the

Mann-Whitney or Wilcoxon rank-sum test may be

used. For the comparison of more than two groups,

the Kruskal-Wallis nonparametric analysis of variance

may be appropriate.

Example 11–2 uses the Wilcoxon rank-sum test for the

barnyard phosphorus data analyzed in example 11–1.

From the previous example it was determined that the

data were not normally distributed, which serves as

justification for performing nonparametric analysis.

For the data in example 11–1, test the null hypothesis that the median phosphorus concentrations are

the same for the paved and unpaved barnyards. The

alternative hypothesis would be that the median

concentrations are different.

Using JMP (SAS 1995), the box-and-whisker plots in

figure 11–1 were obtained. This boxplot shows the

median, the 25th and 75th quartiles framing the box,

and two lines indicating the 10th and 90th percentiles.

Output for the Wilcoxon rank-sums test is given in

table 11–5. This analysis indicates that the medians

are significantly different and the null hypothesis is

rejected. The median phosphorus concentration for

the paved barnyard runoff of 47.2 mg/L was 2.5

times greater than the median of 19.0 mg/L for the

unpaved barnyard. These results are similar to the

parametric results presented in example 11–1.

Example 11–2 Nonparametric multiple watershed analysis using the phosphorus barnyard data

Figure 11–1 Boxplots of the paved and unpaved

barnyard phosphorus concentration data

Table 11–5 Wilcoxon rank-sum test for the barnyard phosphorus data using JMP

Level Count Score Score Meanmean0

sum mean Std0

Paved 42 2273.5 54.1310 4.105

Unpaved 43 1381.5 32.1279 –4.105

2-sample test, normal approximation

S Z Prb>|Z|

2273.5 4.10501 0.0000

1-way test, chi-square approximation

ChiSquare DF Prob>ChiSq

16.8872 1 0.0000

200

150

100

50

0

Phosphorus (mg/L)

Paved

Barnyard type

Unpaved
Part 615

National Water Quality Handbook

Chapter 11

11–6 (450–VI–NWQH, September 2003)

Multiple watersheds

615.1105 Presentation of

results

The presentation of results depends in part on the

number of groups being compared. However, side-byside boxplots, as shown in figure 11–1, are a favored

method of presenting results because they display

graphically the data distributions. When viewing

boxplots, if the boxes do not overlap each other, the

groups are usually different.

615.1106 References

Clausen, J.C., and K.N. Brooks. 1983a. Quality of runoff

from Minnesota peatlands: I. a characterization.

Water Resourc. Bul. 19(5):763-767.

Clausen, J.C., and K.N. Brooks. 1983b. Quality of

runoff from Minnesota peatlands: II. a method for

assessing mining impacts. Water Resources Bul.

19(5):769-772.

SAS Institute, Inc. 1995. JMP statistics and graphics

guide. Ver. 3.1, SAS Institute, Inc. Cary, NC.

Striffler, W.D. 1965. The selection of experimental

watersheds and methods in disturbed forest

areas. Publ. No. 66, I.A.S.H. Symp. of Budapest,

pp. 464-473.

Wicht, C.L. 1967. The validity of conclusions from

South African multiple watershed experiments.

In Forest Hydrology, W.E. Sopper and H.W. Lull

(eds.), Proc. Intern. Symp. on Forest Hydrol.,

Pergamon Press, Oxford.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 12 Trend Analysis
(450-VI-NWQH, September 2003) 12–i

Chapter 12 Trend Analysis

Contents: 615.1200 Introduction 12–1

615.1201 Missing data 12–1

615.1202 Time plots 12–2

615.1203 Least squares regression 12–2

615.1204 Comparison of annual means 12–5

615.1205 Cumulative distribution curves 12–5

615.1206 Q-Q plots 12–6

615.1207 Double mass analysis 12–6

615.1208 Paired regression analysis 12–7

615.1209 Nonparametric approaches 12–7

(a) Kendall tau .................................................................................................. 12–7

615.1210 Summary 12–9

615.1211 References 12–9

Tables Table 12–1 Univariate statistics for fecal coliform data 12–3

Table 12–2 Analysis of variance for regression of log fecal 12–4

coliform over time

Table 12–3 T-test of slope different from zero for fecal coliform 12–4

trend data

Table 12–4 Analysis of variance across years for fecal coliform data 12–4
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Table 12–5 Univariate statistics for fecal coliform data for 1984 12–6

and 1989

Table 12–6 Fecal streptococcus data for August from Jewett 12–8

Brook, St. Albans Bay Watershed, VT

Table 12–7 Summary of pluses and minuses for calculation of 12–8

Kendall's tau for the August fecal streptococcus

data for Jewett Brook, St. Albans Bay watershed, VT

Table 12–8 Summary of trend detection techniques 12–9

Figures Figure 12–1 Fecal Coliform bacteria in Jewett Brook in the 12–2

St. Albans Bay watershed, Vermont

Figure 12–2 Frequency histograms and box plots for fecal coliform 12–3

data from JMP

Figure 12–3 Regression of log fecal coliform data over time 12–4

Figure 12–4 Annual boxplots for fecal coliform data 12–4

Figure 12–5 Cumulative frequency curves for the fecal coliform data 12–5

Figure 12–6 Q-Q plot of log10 fecal coliform data for 1984 and 1989 12–6

Figure 12–7 Double-mass analysis of fecal coliform data 12–7

Examples Example 12–1 Determination of least squares regression of the 12–3

fecal coliform data over time for Jewett Brook

Example 12–2 Kendall's tau for August fecal streptococcus data 12–8
(450–VI–NWQH, September 2003) 12–1

Chapter 12 Trend Analysis

615.1200 Introduction

Several techniques have been applied to detect trends

in water quality data. A trend as used in this chapter is

intended to mean a persistent increase or decrease in

a hydrologic or water quality variable over time

(Erlebach 1978). Trend analysis methods range from

the simple to the complex. Different techniques can be

used to select different types of trends, such as monotonic and step trends. Monotonic trends are continuing increases or decreases over time (Helsel and

Hirsch 1992). Step trends are comparisons of two nonoverlapping periods of data, perhaps caused by some

intervention or time gap between the two periods.

Trends may also be persistent or not persistent, and

some trends may exhibit seasonality.

Some trend detection techniques require a continuous

time-series of data. Thus, interruptions in the temporal

data set must be eliminated for these detection techniques. Several methods are available for replacing

missing data.

The true first step in trend analysis is actually exploratory data analysis (EDA) as described in chapter 3.

Thus, the data should be examined using such techniques as stem-and-leaf diagrams and box-and-whisker

plots. Transformations, such as the log transformation,

of the data may be needed to bring out the trend as

well as to meet certain statistical assumptions. Finally,

some smoothing approaches may be useful in detecting trends.

In this chapter several techniques for trend detection

are presented along with examples. Both parametric

and nonparametric approaches are used. Generally,

more than one trend method should be used when

evaluating water quality data. The different techniques

show trends in different ways. The existence of a trend

does not mean causality. In fact, a major weakness of

relying on trend analysis for an experimental design is

that no causality can be inferred from a trend alone.

The trend must be explained by other data in conjunction with the trend data. Hipel and McLeod (1994)

present methods for testing causality between two

time series.

615.1201 Missing data

Several techniques are used for dealing with missing

data in a water quality data set. They include linear

interpolation, regression analysis, and seasonal adjustment modeling. Linear interpolation may be appropriate if only one or two adjacent data points are missing.

The missing data could be estimated by a linear interpolation between the known values before and after

the gap. Regressions between water quality observations at different stations or between a water quality

variable and flow may also be used to fill in missing

data (Dunne and Leopold 1978). The gap in the missing

data can be filled using the regression and the known

independent values.

In seasonal adjustment modeling, the data are broken

up into long-term, seasonal, and nonseasonal components (McLeod, et al. 1983). A missing data point is

calculated from an equation representing the summation of influences related to long-term (median), stable

seasonal (e.g., monthly), and irregular nonseasonal

components.
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Trend Analysis

615.1202 Time plots

Perhaps the first step in trend analysis is to plot the

data versus time. Figure 12–1 is a time plot of fecal

coliform bacteria counts obtained from Jewett Brook

in the St. Albans Bay watershed from 1981 to 1990.

The fecal coliform data suggest that there is a monotonic decrease in fecal coliform abundance over time.

The data also indicate that the variance of the data

about this trend is also decreasing. A log transformation could be used to decrease the differences in the

variance over time. The data may also show seasonality, but such variations are not obvious. Using just a

time plot, the rate of the decrease cannot be obtained.

615.1203 Least squares

regression

A parametric regression analysis can be used to test

the null hypothesis that the slope of the regression is 0

(i.e., no trend). This test requires the assumptions of

normality, constant variance, and independence of

errors. In example 12–1 the fecal coliform data previously described are tested using regression.

Figure 12–1 Fecal coliform bacteria in Jewett Brook in

the St. Albans Bay watershed, Vermont

5

4

3

2

1

0

12 6

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990

12 6 6 6 12 12 12 6 12 6 12 6 12 6 12 6

Fecal coliform bacteria (no./100 mL) X 100

Month
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Trend Analysis

Figure 12–2 contains frequency histograms and box

plots for the fecal coliform and log10 fecal coliform

data. The distribution and boxplots suggest that the

untransformed data are not normally distributed

and that the log10 transformed data are normally

distributed. The univariate statistics are shown in

table 12–1. Since the P-value for the untransformed

data is less than 0.05, the data are not normally

distributed. With a log10 transformation, the data

appear to be normally distributed and the log10

transformed will be used for further analysis. Tests

for normality are described in detail in chapter 4.

Figure 12–3 is a plot of the log10 transformed fecal

coliform data as a function of month including a

regression line.

The following linear regression equation was obtained using the statistical package JMP (SAS 1995):

Log fecal = 2.673 (month) – 0.0074

Example 12–1 Determination of least squares regression of the fecal coliform data over time for Jewett Brook

Table 12–1 Univariate statistics for fecal coliform

data

Untransformed Log10

transformed

Mean (No./100 mL) 458 2.285

Median (No./100 mL) 190 2.280

Shapiro-Wilk W 0.550 0.985

P<W 0.000 0.786

Figure 12–2 Frequency histograms and box plots for fecal coliform data from JMP

4,500

4,000

3,500

3,000

2,500

2,000

1,500

1,000

500

0

Fecal Fecal coliform bacteria (no./100 mL)

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

Log fecal Log 10 fecal coliform bacteria (no./100 mL)

The analysis of variance for the regression is shown

in table 12–2. The ANOVA indicates that the regression is significant. The Ho: slope = 0 is rejected.

Also, based on the t-statistic, the slope of the regression is significantly different from zero. The

results of the t-test are shown in table 12–3.

Using the slope of –0.0074, the fecal coliform bacteria are decreasing at a rate of 0.98 colonies per

month (antilog of –0.0074).
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Trend Analysis

Table 12–2 Analysis of variance for regression of log

fecal coliform over time

Source DF Sums of Mean F

squares squares

Model 1 4.750 4.750 16.378

Error 94 27.265 0.290

P>F 0.0001

Example 12–1 Determination of least squares regression of the fecal coliform data over time for Jewett Brook—Continued

Annual means were used for the fecal coliform data.

Boxplots for each year are shown in figure 12–4.

Generally, years might be expected to be different

when the boxes do not overlap each other, as for

1984 versus 1989. An analysis of variance indicates

that the means are different at p=0.05 (table 12–4).

To determine which means were different, annual

means were compared using the Tukey-Kramer

honestly significant difference (HSD) test (SAS

1995). Only the means for 1984 and 1989 were

different. In this example the comparison of annual

means does not show a definite trend, but rather a

high year early and a low year later. Additional

methods of trend analysis are recommended to

further analyze the data.

Table 12–3 T-test of slope different from zero for

fecal coliform trend data

Term Estimate Std error t ratio Prob>t

Intercept 2.673 0.111 24.18 0.0000

Month –0.0074 0.002 –4.05 0.0001

Table 12–4 Analysis of variance across years for fecal

coliform data

Source DF Sums of Mean F

squares squares

Model 9 6.626 0.762 2.494

Error 86 25.390 0.295

P>F 0.0139

Figure 12–4 Annual boxplots for fecal coliform data 1/

Figure 12–3 Regression of log fecal coliform data over

time

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0 20 30 40 50 60 10

Month

Log fecal

70 80 90 100 110

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

1982

1 Boxes with the same letter are not significantly different

 at p=0.05.

1984 1985 1986 1987 1988 1989

Year

1983 1990

Log fecal coliform

ab

ab

a

ab

ab

ab

b

ab

ab
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Trend Analysis

615.1204 Comparison of

annual means

A comparison of means may be used to infer trends.

Means across years, or some other unit of time such as

every 2 or 3 years, may be compared for the analysis.

The decision of what time unit to use is based partly

on the degrees of freedom for the time unit as well as

some scientific reasoning for dividing the time series.

It is important that the units of time be equal for the

analysis (UNESCO 1978).

615.1205 Cumulative

distribution curves

The comparison of cumulative distribution curves may

also be used to determine trends. Using the fecal

coliform data, cumulative distribution curves were

created for each year. By comparing the various

curves, such as the 1984 curve to the 1989 curve, the

decrease in fecal coliform bacteria is evident from

1984 to 1989 (fig. 12–5). These data could be tested

using the Kolmogorov-Smirnov Goodness of fit (Zar

1996). The differences between these two curves is

partly because of their individual means.

Figure 12–5 Cumulative frequency curves for the fecal

coliform data

0 0

1

1.0

2

2.5

3

3.5

0.5

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Cumulative frequency

Log fecal coliform

+

+ ++

+

+ ++ +

+

1984

1989
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Trend Analysis

615.1206 Q-Q plots

For a Q-Q plot, the percentile (quartile) of one data set

is plotted against another. For distributions that are

similar, the points should follow along a line defined

by Y = X (UNESCO 1978). The 1984 fecal coliform data

in table 12–5 are plotted against the 1989 data in figure

12–6. The 1984 quartiles are clearly higher than the

1989 quartiles, indicating a trend toward decreasing

fecal coliform in the stream.

615.1207 Double mass

analysis

Double-mass curves are plots of accumulated values

for a water quality station of interest as a function of

an average from a number of stations or a control or

reference station. This type of trend analysis requires

data from several different locations, preferably in

close proximity to each other.

Double mass analysis is commonly used to assess

changes in precipitation stations (Dunne and Leopold

1978). It is a visual tool that can be used to describe

changes in one station in reference to a control

station(s). A break in the slope of the line may indicate

a trend or intervention. A comparison of slopes can be

evaluated statistically (chapter 10) by analysis of

covariance as pointed out by Dingman (1994).

A double mass curve of the fecal coliform data is

shown in figure 12–7. In this case the cumulative

coliform counts from a watershed receiving animal

waste treatment (Sta a) are plotted as a function of the

average among several stations (Sta b+c+d) that did

not have watershed treatments. From this example the

double mass analysis indicates that fecal coliform

levels have fallen off gradually as compared to the

average at the other three stations. A series of plots

could be developed to check the other stations for

Figure 12–6 Q-Q plot of log10 fecal coliform data for 1984 trends (e.g., b vs. a+c+d, etc.) and 1989

3.2

3.0

2.8

2.6

2.4

2.2

2.0

1.8

1.6

1.4

1.2

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

1984 Quartiles

1989 Quartiles

Y=X

Table 12–5 Univariate statistics for fecal coliform data

for 1984 and 1989

Quartile Log10 fecal coliform

 (No./100mL)

 1984 1989

0% (min) 1.53 1.23

10% 1.73 1.24

25% 2.32 1.39

50% 2.66 1.72

75% 3.12 2.19

100% (max) 3.18 2.63
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Trend Analysis

Figure 12–7 Double-mass analysis of fecal coliform data

615.1208 Paired regression analysis

Paired regressions can be used to infer trends if the

data from two stations, one a control and one a treatment, are grouped into before and after time periods.

Such data analysis was described in detail in chapter

10. A significant change in the paired regressions

could signify a trend.

615.1209 Nonparametric

approaches

Several nonparametric approaches are used in trend

detection. The primary advantages of nonparametric

approaches are that there are no assumptions regarding the distribution, censored data, outlyers, and

missing data (Hirsch, et al. 1982). However, both

parametric and nonparametric approaches assume

that the data are not autocorrelated (i.e., that one

observation is not related to the next observation).

(a) Kendall's tau

Kendall's tau is a measure of correlation between a

water quality variable and time for monotonic trends

(Helsel and Hirsch 1992). Like most nonparametric

approaches the procedure is based on rank, rather

than the actual values. Although the calculation of tau

is on many statistical packages (chapter 13), in example 12–2 a hand calculation is performed.

When seasonality or flow effects are removed from the

trend, Spearman's rho test may be superior to the

Kendall test (Hipel and McLeod 1994)

1,750

1,500

1,250

1,000

750

500

250

0 200 400

Avg Sta b+c+d

Sta a

600 800
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Trend Analysis

Table 12–6 Fecal streptococcus data for August from

Jewett Brook, St. Albans Bay Watershed, VT

Date No./100 mL

8/82 200

8/83 4,000

8/84 430

8/85 390

8/86 370

8/87 237

8/88 790

8/89 60

8/90 140

The fecal streptococcus data from Jewett Brook

used in the previous example was used for this

example. To simplify the calculations, only the data

for August is used (table 12–6).

The null hypothesis is that there is no correlation

(trend) between bacteria level and time. The alternative hypothesis is that they are correlated.

Kendall's S is calculated from:

S = P – M [12–1]

where:

P = number of pluses or the number of times the

y's increase as the x's increase

M = number of minuses or the number of times

the y's decrease as the x's increase (Helsel

and Hirsch 1982)

Example 12–2 Kendall's tau for August fecal streptococcus data

To calculate the values, first compare 200/100 mL to

all other values. For example, since 4,000 is greater

than 200, a + is recorded, then 430 is greater than

200, a + is recorded, and so on. This can be summarized in a matrix format (table 12–7). Summing the

pluses and minuses yields 11 P's and 25 M's.

S = 11 – 25 = –14.

Tau is calculated from:

τ

τ

= ( ) −

= −

( ) − = −

S

n

n 1

2

14

9 9 1

2

0 389 .

From appendix H, for S = (x)=–14 and n=9, p = 2 x

0.090 = 0.180. Because the calculated tau is greater

than the table tau, the null hypothesis of no change

is rejected because tau is significantly different

from zero. The alternative hypothesis that there is a

significant trend is accepted.

For a data set with seasonality (for example,

months across years are different), the seasonal

Kendall test may be used (Hirsch et al. 1982). For

each season a separate S is calculated. They then

are summed across seasons.

A seasonal slope estimator (B) can be calculated as

the median of all the slopes between all possible

data pairs within the same season (Helsel and

Hirsch 1992). The individual slopes are calculated

using equation 12–3 (Hirsch, et al. 1982):

d

x x

j k ijk

ij ik = ( ) −

− [12–3]

where:

i = 1, 2, ..., 12 months

j = k+1, 2, ..., n years

k = 1, 2, ..., n–1 years

The slope estimator is determined in chapter 13 in

the WQStat II package.

[12–2]

Table 12–7 Summary of pluses and minuses for

calculation of Kendall's tau for the August

fecal streptococcus data for Jewett Brook,

St. Albans Bay watershed, VT

200 4,000 430 390 370 237 790 60 140

+––––+–+

+–––+––

+––+––

+–+––

+–––

+––

– –

–
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615.1210 Summary

Table 12–8 summarizes the trend methods described

in this chapter and whether they are suitable for missing data, censored data, or seasonality.

Table 12–8 Summary of trend detection techniques

Trend method Missing Censored Seasonality Comments

 data data

Time plot ok ok ok

Least squares ok no no

regression

Annual means ok no no

Cumulative ok no no

distribution

Q-Q plots ok no no

Double mass ok no no

analysis

Paired ok no ok

regressions

Nonparametric ok ok ok Distribuseasonal tion free

Kendall

615.1211 References

Dingman, S.L. 1994. Physical hydrology. Prentice Hall.

Englewood Cliffs, NJ.

Dunne, T., and L.B. Leopold. 1978. Water in environmental planning. W. H. Freeman and Co., San

Francisco, CA.

Erlebach, W.E. 1978. A systematic approach to monitoring trends in the quality of surface waters. In

Establishment of water quality monitoring programs, American Water Resources Association,

pp. 7-19.

Helsel, D.R., and R.M. Hirsch. 1992. Chapter 12. Trend

analysis. In Statistical methods in water resources, Studies in Environmental Science 49,

Elsevier, New York, NY.

Hipel, K.W., and A.I. McLeod. 1994. Time series modeling of water resources and environmental

systems. Elsevier Science BV. Amsterdam, The

Neatherlands.

Hirsch, R.M., J.R. Slack, and R.A. Smith. 1982. Techniques of trend analysis for monthly water

quality data. Water Resources Research

18(1):107-121.

McLeod, A.I., K.W. Hipel, and F. Comancho. 1983.

Trend assessment of water quality time series.

Water Resources Bulletin 19(4):537-547.

SAS Institute, Inc. 1995. Statistics and graphical guide.

Ver. 3.1, SAS Institute, Inc., Cary, NC.

UNESCO/WHO. 1978. Water quality surveys - a guide

for the collection and interpretation of water

quality data. IHD-WHO Working Group on Quality of Water, UNESCO/WHO, Geneva,

Switzerland.

Zar, J.H. 1996. Biostatistical analysis. Prentice Hall.

Upper Saddle River, NJ.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Chapter 13 Statistical Packages
(450–VI–NWQH, September 2003) 13–i

Chapter 13 Statistical Packages

Contents: 615.1300 Introduction 13–1

615.1301 Sample size and sampling frequency estimator 13–1

615.1302 Water quality statistical software 13–2

(a) WQStat II ..................................................................................................... 13–2

(b) DETECT ...................................................................................................... 13–6

(c) SDS ............................................................................................................... 13–9

(d) ESTREND .................................................................................................... 13–9

615.1303 General statistics 13–10

615.1304 References 13–12

Tables Table 13–1 WQStat II Mean / Skew values for the fecal 13–3

streptococcus data

Table 13–2 WQStat II seasonal box and whiskers for the fecal 13–4

streptococcus data

Table 13–3 WQStat II annual box and whiskers for the fecal 13–4

streptococcus data

Table 13–4 WQStat II autocorrela-tions for the fecal streptococcus 13–5

data

Table 13–5 WQStat II Kruskal-Wallis test for seasonality for the 13–5

fecal streptococcus data (test statistic = 11.62)

Table 13–6 WQStat II seasonal Kendal test for the fecal 13–5

streptococcus data (test statistic = –3.987)

Table 13–7 ANOVA table for equality of means for the fecal 13–8

streptococcus data
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Table 13–8 Autocorrelation coefficients for the fecal streptococcus 13–8

data

Table 13–9 DETECT Kendall's test for trend for the fecal 13–8

streptococcus data

Table 13–10 Summary of characteristics and capabilities of water 13–9

quality statistical packages

Table 13–11 Summary of cost (1997) and capabilities of statistical 13–10

software packages

Table 13–12 Summary of statistical methods included in software 13–11

packages

Figures Figure 13–1 Time series of fecal coliform data from DETECT 13–7

Figure 13–2 Double-mass curve for the fecal streptococcus data 13–8

Figure 13–3 CUSUM function for the fecal streptococcus data 13–8

Examples Example 13–1 WQStat II using the fecal streptococcus data 13–3

from the St. Albans Bay RCWP

Example 13–2 DETECT using the fecal streptococcus data 13–7

from the St. Albans Bay RCWP
(450–VI–NWQH, September 2003) 13–1

Chapter 13 Statistical Packages

615.1300 Introduction

Several statistical software packages were developed

specifically to aid in water quality data analysis. These

packages include WQStat II (Loftis 1989), DETECT

(Cluis 1989), SDS (Gaugush 1993), and ESTREND

(Shertz, et al. 1991). In addition, numerous statistical

software packages are available to assist in data

analysis of most any type data. This chapter describes

the packages available for water quality data analysis

so that their usefulness for your particular situation

can be determined. Statistical packages generally

available for personal computers are described as

well.

615.1301 Sample size

and sampling frequency

estimator

A sample size estimator has been developed by Region

6 of the United States Environmental Protection

Agency (USEPA). This Windows program is downloadable free of charge from:

www.epa.gov/Arkansas/6wq/ecopro/watershd/

monitrng/sampling/sampling.htm

This program estimates sample sizes for linear and

step trends, estimation of means and differences

between means. One major advantage of the software

is that it performs iterative procedures.
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Statistical Packages

615.1302 Water quality

statistical software

(a) WQStat Plus

WQStat II was developed at Colorado State University

(Loftis 1989, Ward, et al. 1990). The most recent version is WQStat Plus. The package is IBM-PC compatible and includes both data management and data

analysis capabilities. Although data for any frequency

of time series can be used in this program, WQStat

creates either a monthly or quarterly data file for

analysis. Data can be either manually entered, or the

program can read various files.

The following summary statistics are provided by

WQStat Plus as part of an exploratory data analysis

(EDA):

mean

median

standard deviation

number of data points

skewness and significance

kurtosis and significance

frequency histogram

correlogram (autocorrelation)

A time series plot also can be obtained as well as

indicators of seasonality:

seasonal box-and-whisker plot

annual box-and-whisker plot

Kruskal-Wallis test for seasonality

For trend detection the program determines:

Kendall tau

seasonal Kendall test

seasonal Kendall slope estimator

analysis of covariance

An analysis is also provided across groups using medians. This analysis allows comparison of sites or time

periods within a single site. The following nonparametric approaches are used:

Wilcoxon Signed Rank test

Mann-Whitney test

Kruskall-Wallis test

The package also provides an analysis of extreme

values, such as the proportion of values exceeding a

standard.

Example 26–1 gives an application of WQStat Plus

using the fecal streptococcus time series data for

Jewett Brook in the St. Albans Bay watershed in

Vermont, used in chapter 12.

WQStat Plus is available from Intelligent Decision

Technologies, 203 South Main Street, Longmont,

Colorado 80501, www.idt-ltd.com.
Chapter 13

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Example 13–1 WQStat using the fecal streptococcus data from the St. Albans Bay RCWP

Monthly mean fecal coliform values for Jewett

Brook for the period December 1981 through August

1990 were entered into WQStat using a Lotus 1-2-3

file. A plot of the time series is shown in figure 12–1

in chapter 12.

Following the WQStat main menu, the summary

statistics shown in table 13–1 were obtained.

The package produces a time plot and a seasonal

Box-and-Whisker Plot. The Box-and-Whisker data

indicate that seasons (months) are not greatly different (table 13–2).

An annual Box-and-Whisker Plot is provided. For the

fecal streptococcus data, the annual Box-and-Whisker Plot indicates that the median and quartiles

appear to decrease with time (table 13–3).

The program produces histograms and correlogram

plots. The autocorrelations output is presented in

table 13–4.

The autocorrelations shown in table 13–4 indicate

that no significant serial correlation exists within the

data. The highest autocorrelation was for the lag

9-month period, but it was not significant.

The Kruskal-Wallis test for seasonality using medians indicated that seasonality was not significant in

the fecal streptococcus data (table 13–5).

The Seasonal Kendall test for trend was used since

there were more than 5 years of data (table 13–6).

For this example, WQStat indicated that there was a

declining trend in fecal streptococcus in Jewett

Brook of 30 organisms per 100 mL per year, which is

significant.

Mean Skew values

(No / 100 mL)

Mean 458.010

Median 158.000

Standard deviation 783.943

Number of data points 96

Skew test for normality

(skew value = 3.400)

Confidence Test Significance

level

98% 3.400>0.579 significant

90% 3.400>0.397 significant

80% 3.400>0.306 significant

Kurtosis test for normality

(Kurtosis value = 15.11)

Confidence Test Significance

level

98% 15.11>4.42 significant

90% 15.11>3.79 significant

80% 15.11>3.53 significant

Table 13–1 WQStat Mean / Skew values for the fecal

streptococcus data
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Statistical Packages

Table 13–2 WQStat seasonal box and whiskers for the fecal streptococcus

data

Season Minimum Interquartile Median Interquartile Maximum

1/1-2/1 1.4E+01 1.3E+02 1.5E+02 5.3E+02 9.8E+02

2/1-3/1 7.9E+01 1.6E+02 2.1E+02 3.6E+02 1.5E+02

3/1-4/1 3.4E+01 5.5E+01 1.5E+02 6.9E+02 2.7E+03

4/1-5/1 2.5E+01 4.8E+01 6.5E+01 3.4E+02 4.8E+02

5/1-6/1 1.6E+01 2.1E+01 1.3E+02 2.9E+02 7.1E+02

6/1-7/1 8.4E+01 9.9E+01 1.5E+02 2.1E+02 1.5E+03

7/1-8/1 1.7E+01 1.8E+02 2.8E+02 7.6E+02 3.7E+03

8/1-9/1 1.4E+02 2.4E+02 4.0E+02 7.9E+02 4.0E+03

9/1-10/1 2.0E+01 6.9E+01 2.2E+02 4.8E+02 7.6E+02

10/1-11/1 4.0E+00 1.0E+02 2.1E+02 3.5E+02 8.0E+02

11/1-12/1 5.1E+01 1.7E+02 2.4E+02 4.2E+02 4.3E+03

12/1-1/1 2.6E+01 7.6E+01 1.5E+02 1.5E+03 2.1E+03

Table 13–3 WQStat annual box and whiskers for the fecal streptococcus data

Season Minimum Interquartile Median Interquartile Maximum

1981 9.6E+02 9.6E+02 9.6E+02 9.6E+02 9.6E+02

1982 9.8E+01 1.3E+02 2.2E+02 6.1E+02 4.3E+03

1983 7.6E+01 1.5E+02 2.9E+02 7.1E+02 4.0E+03

1984 3.4E+01 1.8E+02 4.6E+02 1.2E+03 1.5E+03

1985 1.7E+01 9.2E+01 2.0E+02 7.8E+02 2.1E+03

1986 2.1E+01 5.8E+01 1.6E+02 4.9E+02 3.7E+03

1987 1.4E+01 3.1E+01 1.9E+02 2.3E+02 1.0E+03

1988 4.0E+00 6.5E+01 1.5E+02 3.9E+02 7.9E+02

1989 1.7E+01 2.6E+01 5.3E+01 1.5E+02 4.3E+02

1990 2.5E+01 3.4E+01 1.3E+02 2.8E+02 3.6E+02

Example 13–1 WQStat using the fecal streptococcus data from the St. Albans Bay RCWP—Continued
Chapter 13

(450–VI–NWQH, September 2003) 13–5

Part 615

National Water Quality Handbook

Statistical Packages

Table 13–5 WQStat Kruskal-Wallis test for seasonality

for the fecal streptococcus data

(test statistic = 11.62)

Confidence Test Significance

level

95% 11.62<19.68 not significant

90% 11.62<17.28 not significant

75% 11.62<13.70 not significant

Table 13–6 WQStat seasonal Kendall test for the fecal

streptococcus data (test statistic = –3.987)

Confidence Test Significance

level

95% -3.987<-1.960 significant

90% -3.987<-1.645 significant

80% -3.987<-1.282 significant

Seasonal Kendall slope estimate:

Slope = –30.00000 units/year

Example 13–1 WQStat using the fecal streptococcus data from the St. Albans Bay RCWP—Continued

Table 13–4 WQStat autocorrelations for the fecal

streptococcus data

Rho 1 : –0.0232

Rho 2 : –0.0996

Rho 3 : 0.1379

Rho 4 : 0.0825

Rho 5 : –0.0045

Rho 6 : 0.0403

Rho 7 : 0.0529

Rho 8 : –0.0347

Rho 9 : 0.1988

Rho10 : 0.0816

Rho 11 : 0.0048

Rho 12 : 0.0235

Rho 13 : –0.0651

Rho 14 : –0.0469

Rho 15 : 0.0434

Rho 16 : –0.0051

Rho 17 : –0.0099

Rho 18 : –0.0379

Rho 19 : 0.1106

Rho 20 : 0.0232

Rho 21 : 0.0004

Rho 22 : 0.0219

Rho 23 : –0.0296

Rho 24 : –0.0175

Boundary value = 0.2041
Part 615

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Chapter 13

13–6 (450–VI–NWQH, September 2003)

Statistical Packages

(b) DETECT

The program DETECT was developed in Quebec,

Canada, to utilize nonparametric approaches to detect

trends in water quality data (Cluis 1989). This package

is IBM-PC compatible and is somewhat directed toward Canada's national water quality data collection

program (NAQUADAT). A typical input file contains

the date (YY MM DD), the concentration, and the

discharge (optional). Mass loading information may be

input as well. The input file must be in columns with a

row in a strict FORTRAN format:

(12X, I2, 1X, I2, 1X, I2, 16X, F12.6, F12.6)

This format is designed to read as: 12 spaces, YY, one

space, MM, one space, DD, 16 spaces, concentration in

12 spaces with 6 following decimal, and discharge in

12 spaces with 6 following decimal (optional). Concentration data should be in milligrams per liter and

discharge in cubic meters per second.

Graphic analysis includes a time plot, double-mass

curves, and the CUSUM function. Double-mass curves

show the accumulated sum of the concentration or

discharge as a function of accumulated time (days

from first observation). The CUSUM function, or

cumulative sum, is the summation of the deviations of

the observations from the mean plotted as a function

of time.

CUSUM X X j X t j

j

t

( ) = − ( ) =

∑1

[13–1]

where:

t = time (Cluis 1989, Hipel and McLeod 1994)

DETECT allows elimination of high and low outliers.

Among the tests in DETECT is one for seasonality

based on ANOVA. Missing values may be replaced

using three different options:

• Temporal interpolation

• Seasonal mean

• Concentration-discharge relationship

Persistence in the trend is examined using autocorrelation coefficients. The appropriate test for trend

recommended in the user's manual is suggested based

on:

• Type of trend–monotonic or stepwise

• Persistence–Markovian or none

• Seasonality

The following trend tests are available:

Lettenmaier/Spearman (Lettenmaier 1976)

Hirsch and Slack (Hirsch and Slack 1984)

Spearman/Kendal (Helsel and Hirsch 1992)

Kendall seasonality (Helsel and Hirsch 1992)

Lettenmaier/Mann-Whitney (Lettenmaier 1976)

Mann-Whitney (Lettenmaier 1976)

Example 13–2 shows an application of DETECT using

the fecal streptococcus time series data for Jewett

Brook in the St. Albans Bay watershed in Vermont,

used in chapter 12.
Chapter 13

(450–VI–NWQH, September 2003) 13–7

Part 615

National Water Quality Handbook

Statistical Packages

Monthly mean fecal coliform values for Jewett

Brook for the period December 1981 through August 1990 were prepared for entry into DETECT by

editing a file in a DOS editor to put it in the proper

format. A plot of the time series generated by DETECT is shown in figure 13–1.

The outliers were not eliminated from the data set

for this example. As indicated in the manual, nonparametric tests yield stable results even with

outliers present.

The double mass curve generated by DETECT is

shown in figure 13–2. This plot shows the accumulated sum of fecal coliform abundance as a function

of the accumulated time in months. The plot contains several lines. A general mean line is drawn

from the origin to the upper right hand corner of the

graph. The individual points are shown as X's. The

general mean slope can be compared to groups of

points in the double-mass curve. Slope of a group of

points less than the general mean line indicates that

the mean of these points would be less than the

general mean. The lines above and below the mean

line are termed rails and are two standard deviations from the mean line based on deviations from

only its side of the line. Rails located far from the

Example 13–2 DETECT using the fecal streptococcus data from the St. Albans Bay RCWP

Figure 13–1 Time series of fecal coliform data from DETECT

mean line indicate large variability in the data. If no

trend is present, points on the double-mass curve

are located on both sides of the mean line randomly. This in not the case in this example, indicating a trend is most likely present.

The CUSUM function is shown in figure 13–3. This

plots the summation of the deviations from the

general mean line in the previous figure.

Departures on one side of the line at Y=0 indicate a

likely trend, as in this case. If the curve is parabolic,

a monotonic linear trend is suggested. If the curve

includes discontinuous lines, a stepwise trend is

suggested. In this case a monotonic trend is suspected. The analysis of variance in table 13–7 tests

whether monthly means are different as a test of

seasonality.

The ANOVA in table 13–7 indicates no difference

among months. Also, a Bartlett's test of the equality

of variances is performed, which indicates in this

case that the variances may not be equal across

groups. Some data was missing in the fecal streptococcus data set, and the interpolation option was

selected to fill missing data.

5

4

3

2

1

1982 1984 1986 1988 1990

Fecal coliform bacteria (no./100 mL)X100

Month-Year
Part 615

National Water Quality Handbook

Chapter 13

13–8 (450–VI–NWQH, September 2003)

Statistical Packages

Figure 13–2 Double-mass curve for the fecal streptococcus data

Autocorrelation correlation coefficients were used

for an analysis of persistence (table 13–8). The

autocorrelation coefficient is significant if the value

is at least two times the standard deviation. In this

case there was no significant persistence since no

autocorrelations were significant. If the lag 1 r was

significant and the lag 2 r was not, this would be

termed Markovian persistence.

Using the decision tree in the program, the data

displayed a monotonic trend without persistence or

seasonality. Therefore, the Kendall test was used

for analysis of the trend. Table 13–9 shows the

results from Kendall's test as displayed by DETECT.

5

4

3

2

1

1982 1984 1986

Month-Year

1988 1990 ΣFecal streptococcus bacteria (no./100 mL)X100

15

10

5

0

1982

Month-Year

1990 Σ(Xi

-X)Fecal streptococcus bacteria

(no./100 mL)X100

Figure 13–3 CUSUM function for the fecal streptococcus data

Table 13–7 ANOVA table for equality of means for the

fecal streptococcus data

Source df MS F

Month 11 0.61241E-06 0.995

Error 84 0.61568E-06

Total 95 0.61530E-06

Equality of means accepted

No seasonality

Equality of variances is rejected!

Table 13–8 Autocorrelation coefficients for the fecal

streptococcus data

- - -- - - - - - - - - - - - - - Lag - - - - - - - - - - - - - - -

1234

coeff. 0.16 –0.02 0.10 0.12

std. dev 0.10 0.10 0.10 0.10

Table 13–9 DETECT Kendall's test for trend for the

fecal streptococcus data

statistic –1375.63

test value –3.86

signif. level 0.00

Comment: Decreasing monotonic trend detected.

Example 13–2 DETECT using the fecal streptococcus data from the St. Albans Bay RCWP—Continued
Chapter 13

(450–VI–NWQH, September 2003) 13–9

Part 615

National Water Quality Handbook

Statistical Packages

(c) SDS

The Sampling Design Software (SDS) was developed

by the U.S. Army Corps of Engineers. This software is

used to determine sample sizes, variance components,

optimization of stratified samples among strata, and

clustering of groups to increase efficiency of sampling

(Gaugush 1993).

The sample size determination can be based on multivariable sampling using either simple random or

stratified sampling. The decision analysis is based on

the mean, coefficient of variation, precision level,

acceptable error, and the costs of sampling. The program displays the sample sizes and costs for each

variable at different precision and error levels.

The variance component program determines the

contribution to the variability in a water quality variable from different factors, such as station, date, and

depth. The analysis attempts to determine which

factors are most important in sampling and, therefore,

which factors should dominate the design. For example, if most of the variance was explained by date,

the station and depth subsampling could be reduced.

The number of samples applied to different strata can

be optimized using error analysis in the program. The

percent variance for each strata is compared to the

percent of the number of samples and a percent optimum number of samples. Generally, more samples are

allocated to strata with the higher variability.

Cluster analysis can be used to identify redundancy in

the sampling program. For example, if a number of

water quality stations are producing the same type of

information, one or more could be dropped.

(d) ESTREND

ESTREND (Shertz, et al. 1991) is used by the U.S.

Geological Survey for nonparametric trend analysis at

its various water quality stations. The program is

written for UNIX and has been commonly used on

PrimeTM computers.

Table 13–10 summarizes the characteristics and capabilities of the various water quality statistical packages.

Table 13–10 Summary of characteristics and capabilities of water quality statistical packages

WQStat II DETECT SDS

Data manager

Data type monthly, seasonal monthly summary

ASCII import X X X

Lotus 1-2-3 import X

Manual entry X

Missing data X

Data analyses

EDA X

Trends X X

Group comparisons X

Extreme values X

Autocorrelation X

Sample sizes X

Graphics

 time plot X X

 double-mass X

 CUSUM X
Part 615

National Water Quality Handbook

Chapter 13

13–10 (450–VI–NWQH, September 2003)

Statistical Packages

615.1303 General statistics

Many statistical packages are commercially available

that will perform the statistical analyses described in

NWQH Part 615. Table 13–11 provides a summary of

some of the capabilities and features of these packages, and table 13–12 summarizes the statistical methods included in each package.

Table 13–11 Summary of cost (2001) and capabilities of general statistical software packages

Statistical package Cost Win/ Mac Graphics Documentation Comments

 ($)

Analyse-it 125 W X on-line Plug-in for MS Excel, www.analyse-it.com

(note British spelling)

DataDesk £399 1/ W/M X manual www.longman.net/datadesk-activstats

Instat 79 W/M X www.graphpad.com

JMP 895 W/M X manual www.jmpdiscovery.com

Quick Statistica 495 W www.statsoft.com

SAS W X manual Primarily for mainframe computers,

www.sas.com

SPSS 858 2/ W/M www.spss.com

Statistica 1095 W www.statsoft.com

Statistix 495 W www.statistix.com

SYSTAT 1299 W www.spss.com

WINKS Basic 99 W X manual www.texasoft.com/homepage

1/ Price in British Pounds.

2/ GSA Schedule.
Chapter 13

(450–VI–NWQH, September 2003) 13–11

Part 615

National Water Quality Handbook

Statistical Packages

Table 13–12 Summary of statistical methods included in software packages (O = blank)

Package Descriptive/ Boxplot Test of Regression/ t-test ANOVA Multiple ANCOVA Nonparametric

univariate normality correlation comparisons

Analyse-it X X X X X X O O X

DataDesk X X X X X X X X X

Instat X O X X X X X O X

JMP X X X X X X X X X

Quick Statistica X X X X X X O X X

SAS X X X X X X X X X

SPSS X X X X X X X X X

Statistica X X X X X X X X X

Statistix X X X X X X O X O

SYSTAT X X X X X X O X X

WINKS X X X X X X X X X
Part 615

National Water Quality Handbook

Chapter 13

13–12 (450–VI–NWQH, September 2003)

Statistical Packages

615.1304 References

Cluis, D. 1989. Detection of trend and norm violation.

User's manual—DETECT and EXCEED, Ver. 2,

INRS-Eau, Quebec, Canada.

Gaugush, R.F. 1993. Sample design software user's

manual. Instructions report W-93-1, Vicksburg,

MS, U.S. Army Engineer Waterways Experiment

Station.

Helsel, D.R., and R.M. Hirsch. 1992. Trend analysis,

chapter 12. In Statistical Methods in Water

Resources, Studies in Environmental Science 49,

Elsevier, New York, NY.

Hipel, K.W., and A.I. McLeod. 1994. Time series modeling of water resources and environmental

systems. Elsevier Science. The Neatherlands.

Hirsch, R.M., and J.R. Slack. 1984. A nonparametric

trend test for seasonal data with serial dependence. Water Resources Research 20(6):727-732.

Lettenmaier, D.P. 1976. Detection of trend in water

quality data from records with dependent observations. Water Resources Research

12(5):1037-1046.

Loftis, J.C. 1989. User's manual—WQStat II. A water

quality statistics program, CO State Univ.

Shertz, T.L., R.B. Alexander, and D.J. Ohe. 1991. Computer program estimate trend (ESTREND). Water

Resources Investigations WRI 91-4040.

Ward, R.C., J.C. Loftis, and G.B. McBride. 1990. Design

of water quality monitoring systems. Van

Nostrand Reinhold, New York.
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Appendixes
(450–VI–NWQH, September 2003)

Appendixes

Contents: Appendix A Distribution of t A–1

Appendix B Skewness A–3

Appendix C Values of F A–4

Appendix D Kruskal-Wallis H A–10

Appendix E Tukey's q A–13

Appendix F Mann-Whitney U distribution A–15

Appendix G Wilcoxon T distribution A–16

Appendix H Quantities for Kendall's Tau A–17

Appendix I Conversion factors A–18
Part 615

National Water Quality Handbook

Appendixes

(450–VI–NWQH, September 2003) Appendixes–1

Appendix A Distribution of t (two-tailed) 1/

Degrees of - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - Probability of a Larger Value, Sign Ignored - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - -

Freedom 0.500 0.400 0.20 0.10 0.050 0.025 0.010 0.005 0.001

1 1.000 1.376 3.078 6.314 12.706 25.452 63.657

2 0.816 1.061 1.886 2.920 4.303 6.205 9.925 14.089 31.598

3 .765 0.978 1.638 2.353 3.182 4.176 5.841 7.453 12.941

4 .741 .941 1.533 2.132 2.776 3.495 4.604 5.598 8.610

5 .727 .920 1.476 2.015 2.571 3.163 4.032 4.773 6.859

6 .718 .906 1.440 1.943 2.447 2.969 3.707 4.317 5.959

7 .711 .896 1.415 1.895 2.365 2.841 3.499 4.029 5.405

8 .706 .889 1.397 1.860 2.306 2.752 3.355 3.832 5.041

9 .703 .883 1.383 1.833 2.262 2.685 3.250 3.690 4.781

10 .700 .879 1.372 1.812 2.228 2.634 3.169 3.581 4.587

11 .697 .876 1.363 1.796 2.201 2.593 3.106 3.497 4.437

12 .695 .873 1.356 1.782 2.179 2.560 3.055 3.428 4.318

13 .694 .870 1.350 1.771 2.160 2.533 3.012 3.372 4.221

14 .692 .868 1.345 1.761 2.145 2.510 2.977 3.326 4.140

15 .691 .866 1.341 1.753 2.131 2.490 2.947 3.286 4.073

16 .690 .865 1.337 1.746 2.120 2.473 2.921 3.252 4.015

17 .689 .863 1.333 1.740 2.110 2.458 2.898 3.222 3.965

18 .688 .862 1.330 1.734 2.101 2.445 2.878 3.197 3.922

19 .688 .861 1.328 1.729 2.093 2.433 2.861 3.174 3.883

20 .687 .860 1.325 1.725 2.086 2.423 2.845 3.153 3.850

21 .686 .859 1.323 1.721 2.080 2.414 2.831 3.135 3.819

22 .686 .858 1.321 1.717 2.074 2.406 2.819 3.119 3.792

23 .685 .858 1.319 1.714 2.069 2.398 2.807 3.104 3.767

24 .685 .857 1.318 1.711 2.064 2.391 2.797 3.090 3.745

25 .684 .856 1.316 1.708 2.060 2.385 2.787 3.078 3.725

26 .684 .856 1.315 1.706 2.056 2.379 2.779 3.067 3.707

27 .684 .855 1.314 1.703 2.052 2.373 2.771 3.056 3.690

28 .683 .855 1.313 1.701 2.048 2.368 2.763 3.047 3.674

29 .683 .854 1.311 1.699 2.045 2.364 2.756 3,.038 3.659

30 .683 .854 1.310 1.697 2.042 2.360 2.750 3.030 3.646

35 .682 .852 1.306 1.690 2.030 2.342 2.724 2.996 3.591

40 .681 .851 1.303 1.684 2.021 2.329 2.704 2.971 3.551

45 .680 .850 1.301 1.680 2.014 2.319 2.690 2.952 3.520

50 .680 .849 1.299 1.676 2.008 2.310 2.678 2.937 3.496

55 .679 .849 1.297 1.673 2.004 2.304 2.669 2.925 3.476

60 .679 .848 1.296 1.671 2.000 2.299 2.660 2.915 3.460

70 .678 .847 1.294 1.667 1.994 2.290 2.648 2.899 3.435

80 .678 .847 1.293 1.665 1.989 2.284 2.638 2.887 3.416

90 .678 .846 1.291 1.662 1.986 2.279 2.631 2.878 3.402

100 .677 .846 1.290 1.661 1.982 2.276 2.625 2.871 3.390

120 .677 .845 1.289 1.658 1.980 2.270 2.617 2.860 3.373

∞ .6745 .8416 1.2816 1.6448 1.9600 2.2414 2.5758 2.8070 3.2905

1/ Snedecor, G.W., and W.G. Cochran. 1980. Statistical methods, 7th ed. Iowa State Univ. Press, Ames. (No part of this appendix may be

reproduced, stored in a retrieval system, or transmitted in any form or by any means—electronic, mechanical, photocopying, recording, or

otherwise—without the prior written permission of the publisher.)
Part 615

National Water Quality Handbook

Appendixes

Appendixes–2 (450–VI–NWQH, September 2003)
Part 615

National Water Quality Handbook

Appendixes

(450–VI–NWQH, September 2003) Appendixes–3

Appendix B Table for testing skewness (one-tailed) 1/

Size of - - Percentage points - - Standard

sample deviation

n 5% 1%

25 0.711 1.061 0.4354

30 .661 .982 .4052

35 .621 .921 .3804

40 .587 .869 .3596

45 .558 .825 .3418

50 .533 .787 .3264

60 .492 .723 .3009

70 .459 .673 .2806

80 .432 .631 .2638

90 .409 .596 .2498

100 .389 .567 .2377

125 .350 .508 .2139

150 .321 .464 .1961

175 .298 .430 .1820

200 .280 .403 .1706

250 .251 .360 .1531

300 .230 .329 .1400

350 .213 .305 .1298

400 .200 .285 .1216

450 .188 .269 .1147

500 0.179 0.255 0.1089

1/ Snedecor, G.W., and W.G. Cochran. 1980. Statistical methods, 7th

ed. Iowa State Univ. Press, Ames. (No part of this appendix may

be reproduced, stored in a retrieval system, or transmitted in any

form or by any means—electronic, mechanical, photocopying,

recording, or otherwise—without the prior written permission of

the publisher.)
Part 615

National Water Quality Handbook

Appendixes

Appendixes–4 (450–VI–NWQH, September 2003)

Appendix C Values of F 1/

Denom- Probability - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Numerator df - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

inator of a larger

df F 1 2 34567 8 9

1 0.050 161.40 199.50 215.70 224.60 230.20 234.00 236.80 238.90 240.50

0.010 4052.00 4999.50 5403.00 5625.00 5764.00 5859.00 5928.00 5982.00 6022.00

2 0.050 18.51 19.00 19.16 19.25 19.30 19.33 9.35 19.37 19.38

0.010 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39

3 0.050 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81

0.010 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35

4 0.050 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00

0.010 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66

5 0.050 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77

0.010 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16

6 0.050 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10

0.010 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98

7 0.050 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68

0.010 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72

8 0.050 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39

0.010 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91

9 0.050 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18

0.010 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35

10 0.050 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02

0.010 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94

11 0.050 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90

0.010 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63

12 0.050 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80

0.010 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39

13 0.050 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71

0.010 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19

14 0.050 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65

0.010 8.88 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03

See footnote at end of table.
Part 615

National Water Quality Handbook

Appendixes

(450–VI–NWQH, September 2003) Appendixes–5

Appendix C Values of F 1/ —Continued

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Numerator df - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

10 12 15 20 24 30 40 60 120 ∞ P

241.90 243.90 245.90 248.00 249.10 250.10 251.10 252.20 253.30 254.30 0.050

6056.00 6106.00 6157.00 6209.00 6235.00 6261.00 6287.00 6313.00 6339.00 6366.00 0.010

19.40 19.41 19.43 19.45 19.45 19.46 19.47 19.48 19.49 19.50 0.050

99.40 99.42 99.43 99.45 99.46 99.47 99.47 99.48 99.49 99.50 0.010

8.79 8.74 8.70 8.66 8.64 8.62 8.59 8.57 8.55 8.53 0.050

27.23 27.05 26.87 26.69 26.60 26.50 26.41 26.32 26.22 26.13 0.010

5.96 5.91 5.86 5.80 5.77 5.75 5.72 5.69 5.66 5.63 0.050

14.55 14.37 14.20 14.02 13.93 13.84 13.75 13.63 13.56 13.46 0.010

4.74 4.68 4.62 4.56 4.53 4.50 4.46 4.43 4.40 4.36 0.050

10.05 9.89 9.72 9.55 9.47 9.38 9.29 9.20 9.11 9.02 0.010

4.06 4.00 3.94 3.87 3.84 3.81 3.77 3.74 3.70 3.67 0.050

7.87 7.72 7.56 7.40 7.31 7.23 7.14 7.06 6.97 6.88 0.010

3.64 3.57 3.51 3.44 3.41 3.38 3.34 3.30 3.27 3.23 0.050

6.62 6.47 6.31 6.16 6.07 5.99 5.91 5.82 5.74 5.65 0.010

3.35 3.28 3.22 3.15 3.12 3.08 3.04 3.01 2.97 2.93 0.050

5.81 5.67 5.52 5.36 5.28 5.20 5.12 5.03 4.95 4.86 0.010

3.14 3.07 3.01 2.94 2.90 2.86 2.83 2.79 2.75 2.71 0.050

5.26 5.11 4.96 4.81 4.73 4.65 4.57 4.48 4.40 4.31 0.010

2.98 2.91 2.85 2.77 2.74 2.70 2.66 2.62 2.58 2.54 0.050

4.85 4.71 4.56 4.41 4.33 4.25 4.17 4.08 4.00 3.91 0.010

2.85 2.79 2.72 2.65 2.61 2.57 2.53 2.49 2.45 2.40 0.050

4.54 4.40 4.25 4.10 4.02 3.94 3.86 3.78 3.69 3.60 0.010

2.75 2.69 2.62 2.54 2.51 2.47 2.43 2.38 2.34 2.30 0.050

4.30 4.16 4.01 3.86 3.78 3.70 3.62 3.54 3.45 3.36 0.010

2.67 2.60 2.53 2.46 2.42 2.38 2.34 2.30 2.25 2.21 0.050

4.10 3.96 3.82 3.66 3.59 3.51 3.43 3.34 3.25 3.17 0.010

2.54 2.53 2.46 2.39 2.35 2.31 2.27 2.22 2.18 2.13 0.050

3.94 3.80 3.66 3.51 3.43 3.35 3.27 3.18 3.09 3.00 0.010
Part 615

National Water Quality Handbook

Appendixes

Appendixes–6 (450–VI–NWQH, September 2003)

Appendix C Values of F 1/ —Continued

Denom- Probability - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Numerator df - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

inator of a larger

df F 1 2 34567 8 9

15 0.050 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59

0.010 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89

16 0.050 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54

0.010 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78

17 0.050 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49

0.010 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68

18 0.050 4.41 3.35 3.16 2.93 2.77 2.66 2.58 2.51 2.46

0.010 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60

19 0.050 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42

0.010 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52

20 0.050 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39

0.010 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46

21 0.050 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37

0.010 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40

22 0.050 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34

0.010 7.95 5.72 4.62 4.31 3.99 3.76 3.59 3.45 3.35

23 0.050 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32

0.010 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30

24 0.050 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30

0.010 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26

25 0.050 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28

0.010 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22

26 0.050 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27

0.010 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18

27 0.050 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25

0.010 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15

28 0.050 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24

0.010 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12

See footnote at end of table.
Part 615

National Water Quality Handbook

Appendixes

(450–VI–NWQH, September 2003) Appendixes–7

Appendix C Values of F 1/ —Continued

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Numerator df - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

10 12 15 20 24 30 40 60 120 ∞ P

2.54 2.48 2.40 2.33 2.29 2.25 2.20 2.16 2.11 2.07 0.050

3.80 3.67 3.52 3.37 3.29 3.21 3.13 3.05 2.96 2.87 0.010

2.49 2.42 2.35 2.28 2.24 2.19 2.15 2.11 2.06 2.01 0.050

3.69 3.55 3.41 3.26 3.18 3.10 3.02 2.93 2.84 2.75 0.010

2.45 2.38 2.31 2.23 2.19 2.15 2.10 2.06 2.01 1.96 0.050

3.59 3.46 3.31 3.16 3.08 3.00 2.92 2.83 2.75 2.65 0.010

2.41 2.34 2.27 2.19 2.15 2.11 2.06 2.02 1.97 1.92 0.050

3.51 3.37 3.23 3.08 3.00 2.92 2.84 2.75 2.66 2.57 0.010

2.38 2.31 2.23 2.16 2.11 2.07 2.03 1.98 1.93 1.88 0.050

3.43 3.30 3.15 3.00 2.92 2.84 2.76 2.67 2.58 2.49 0.010

2.35 2.28 2.20 2.12 2.08 2.04 1.99 1.95 1.90 1.84 0.050

3.37 3.23 3.09 2.94 2.86 2.78 2.69 2.61 2.52 2.42 0.010

2.32 2.25 2.18 2.10 2.05 2.01 1.96 1.92 1.87 1.81 0.030

3.31 3.17 3.03 2.88 2.80 2.72 2.64 2.55 2.46 2.36 0.010

2.30 2.23 2.15 2.07 2.03 1.98 1.94 1.89 1.84 1.78 0.050

3.26 3.12 2.98 2.83 2.75 2.67 2.58 2.50 2.40 2.31 0.010

2.27 2.20 2.13 2.05 2.01 1.96 1.91 1.86 1.81 1.76 0.050

3.21 3.07 2.93 2.78 2.70 2.62 2.54 2.45 2.35 2.26 0.010

2.25 2.18 2.11 2.03 1.98 1.94 1.89 1.84 1.79 1.73 0.050

3.17 3.03 2.89 2.74 2.66 2.58 2.49 2.40 2.31 2.21 0.010

2.24 2.16 2.09 2.01 1.96 1.92 1.87 1.82 1.77 1.71 0.050

3.13 2.99 2.85 2.70 2.62 2.54 2.45 2.36 2.27 2.17 0.010

2.22 2.15 2.07 1.99 1.95 1.90 1.85 1.80 1.75 1.69 0.050

3.09 2.96 2.81 2.66 2.58 2.50 2.42 2.33 2.23 2.13 0.010

2.20 2.13 2.06 1.97 1.93 1.88 1.84 1.79 1.73 1.67 0.050

3.06 2.93 2.78 2.63 2.55 2.47 2.38 2.29 2.20 2.10 0.010

2.19 2.12 2.04 1.96 1.91 1.87 1.82 1.77 1.71 1.65 0.050

3.03 2.90 2.75 2.60 2.52 2.44 2.35 2.26 2.17 2.06 0.010
Part 615

National Water Quality Handbook

Appendixes

Appendixes–8 (450–VI–NWQH, September 2003)

Appendix C Values of F 1/ —Continued

Denom- Probability - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Numerator df - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

inator of a larger

df F 1 2 34567 8 9

29 .050 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22

.010 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09

30 .050 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21

.010 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07

40 .050 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12

.010 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89

60 .050 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04

.010 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72

120 .050 3.92 3.07 2.68 2.45 2.29 2.17 2.09 2.02 1.96

.010 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56

× .050 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94 1.88

.010 6.63 4.61 3.78 3.32 3.02 2.80 2.64 2.51 2.41

1/ Steel, R.G.D., and J.H. Torrie. 1960. Principles and procedures of statistics. McGraw-Hill, Inc., New York, NY. (Reproduced with permission

of the McCraw-Hill Companies.)
Part 615

National Water Quality Handbook

Appendixes

(450–VI–NWQH, September 2003) Appendixes–9

Appendix C Values of F 1/ —Continued

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Numerator df - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

10 12 15 20 24 30 40 60 120 ∞ P

2.18 2.10 2.03 1.94 1.90 1.85 1.81 1.75 1.70 1.64 .050

3.00 2.87 2.73 2.57 2.49 2.41 2.33 2.23 2.14 2.03 .010

2.16 2.09 2.01 1.93 1.89 1.84 1.79 1.74 1.68 1.62 .050

2.98 2.84 2.70 2.55 2.47 2.39 2.30 2.2l 2.11 2.01 .010

2.08 2.00 1.92 1.84 1.79 1.74 1.69 1.64 1.58 1.51 .050

2.80 2.66 2.52 2.37 2.29 2.20 2.11 2.02 1.92 1.80 .010

1.99 1.92 1.84 1.75 1.70 1.65 1.59 1.53 1.47 1.39 .050

2.63 2.50 2.35 2.20 2.12 2.03 1.94 1.84 1.73 1.60 .010

1.91 1.83 1.75 1.66 1.61 1.55 1.50 1.43 1.35 1.25 .050

2.47 2.34 2.19 2.03 1.95 1.86 1.76 1.66 1.53 1.38 .030

1.83 1.75 1.67 1.57 1.52 1.46 1.39 1.32 1.22 1.00 .050

2.32 2.18 2.04 1.88 1.79 1.70 1.59 1.47 1.32 1.00 .010
Part 615

National Water Quality Handbook

Appendixes

Appendixes–10 (450–VI–NWQH, September 2003)

Appendix D Critical Values of the Kruskal-Wallis H Distribution 1/

n1 n2 n3 ∝ = 0.10 0.05 0.02 0.01 0.005 0.002 0.001

2 2 2 4.571

3 2 1 4.286

3 2 2 4.500 4.714

3 3 1 4.571 5.143

3 3 2 4.556 5.361 6.250

3 3 3 4.622 5.600 6.489 (7.200) 7.200

4 2 1 4.500

4 2 2 4.458 5.333 6.000

4 3 1 4.056 5.208

4 3 2 4.511 5.444 6.144 6.444 7.000

4 3 3 4.709 5.791 6.564 6.745 7.318 8.018

4 4 1 4.167 4.967 (6.667) 6.667

4 4 2 4.555 5.455 6.600 7.036 7.282 7.855

4 4 3 4.545 5.598 6.712 7.144 7.598 8.227 8.909

4 4 4 4.654 5.692 6.962 7.654 8.000 8.654 9.269

5 2 1 4.200 5.000

5 2 2 4.373 5.160 6.000 6.533

5 3 1 4.018 4.960 6.044

5 3 2 4.651 5.251 6.124 6.909 7.182

5 3 3 4.533 5.648 6.533 7.079 7.636 8.048 8.727

5 4 1 3.987 4.985 6.431 6.955 7.364

5 4 2 4.541 5.273 6.505 7.205 7.573 8.114 8.591

5 4 3 4.549 5.656 6.676 7.445 7.927 8.481 8.795

5 4 4 4.619 5.657 6.953 7.760 8.189 8.868 9.168

5 5 1 4.109 5.127 6.145 7.309 8.182

5 5 2 4.623 5.338 6.446 7.338 8.131 6.446 7.338

5 5 3 4.545 5.705 6.866 7.578 8.316 8.809 9.521

5 5 4 4.523 5.666 7.000 7.823 8.523 9.163 9.606

5 5 5 4.940 5.780 7.220 8.000 8.780 9.620 9.920

6 1 1 - - - - -

5 2 1 4.200 4.822

6 2 2 4.545 5.345 6.182 6.982

5 3 1 3.909 4.855 6.236

5 3 2 4.682 5.348 6.227 6.970 7.515 8.182

6 3 3 4.538 5.615 6.590 7.410 7.872 8.628 9.346

See footnote at end of table.
Part 615

National Water Quality Handbook

Appendixes

(450–VI–NWQH, September 2003) Appendixes–11

Appendix D Critical Values of the Kruskal-Wallis H Distribution 1/ —Continued

n1 n2 n3 ∝ = 0.10 0.05 0.02 0.01 0.005 0.002 0.001

6 4 1 4.038 4.947 6.174 7.106 7.614

6 4 2 4.494 5.340 6.571 7.340 7.846 8.494 8.827

5 4 3 4.604 5.610 6.725 7.500 8.033 8.918 9.170

5 4 4 4.595 5.681 6.900 7.795 8.381 9.167 9.861

6 5 1 4.128 4.990 6.138 7.182 8.077 8.515

6 5 2 4.596 5.338 6.585 7.376 8.196 8.967 9.189

5 5 3 4.535 5.602 6.829 7.590 8.314 9.150 9.669

5 5 4 4.522 5.661 7.018 7.936 8.643 9.458 9.960

6 5 5 4.547 5.729 7.110 8.028 8.859 9.771 10.27I

5 6 1 4.000 4.945 6.286 7.121 8.165 9.077 9.692

6 6 2 4.438 5.410 6.667 7.467 8.210 9.219 9.752

6 6 3 4.558 5.625 6.900 7.725 8.458 9.458 10.150

5 6 4 4.548 5.724 7.107 8.000 8.754 9.662 10.342

5 5 5 4.542 5.765 7.152 8.124 8.967 9.948 10.524

6 6 6 4.643 5.801 7.240 8.222 9.170 10.187 10.889

7 7 7 4.594 5.819 7.332 8.378 9.373 10.516 11.310

8 8 8 4.595 5.805 7.355 8.465 9.495 10.805 11.705

2 2 1 1 - - - - -

2221 5.357 5.679

2222 5.667 6.167 (6.667) 6.667

3 1 1 1 - - - - -

3211 5.143

3221 5.556 5.833 6.500

3222 5.544 6.333 6.978 7.133 7.533

3311 5.333 6.333

3321 5.689 6.244 6.689 7.200 7.400

3322 5.745 6.527 7.182 7.636 7.873 8.018 8.455

3331 5.655 6.600 7.109 7.400 8.055 8.345

3332 5.879 6.727 7.636 8.105 8.379 8.803 9.030

3333 6.026 7.000 7.872 8.538 8.897 9.462 9.513

4 1 1 1 - - - - -

4211 5.250 5.833

4221 5.533 6.133 6.667 7.000

4222 5.755 6.545 7.091 7.391 7.964 8.291

4311 5.067 6.178 6.711 7.067

See footnote at end of table.
Part 615

National Water Quality Handbook

Appendixes

Appendixes–12 (450–VI–NWQH, September 2003)

Appendix D Critical Valuesof the Kruskal-Wallis H Distribution 1/ —Continued

n1 n2 n3 a = 0.10 0.05 0.02 0.01 0.005 0.002 0.001

4321 5.591 6.309 7.018 7.455 7.773 8.182

4322 5.750 6.621 7.530 7.871 8.273 8.689 8.909

4331 5.589 6.545 7.485 7.758 8.212 8.697 9.182

4332 5.872 6.795 7.763 8.333 8.718 9.167 8.455

4333 6.016 6.984 7.995 8.659 9.253 9.709 10.016

4411 5.182 5.945 7.091 7.909 7.909

4421 5.568 6.386 7.364 7.886 8.341 8.591 8.909

4422 5.808 6.731 7.750 8.346 8.692 9.269 9.462

4431 5.692 6.635 7.660 8.231 8.583 9.038 9.327

4432 5.901 6.874 7.951 8.621 9.165 9.615 9.945

4433 6.019 7.038 8.181 8.876 9.495 10.105 10.467

4441 5.564 6.725 7.879 8.588 9.000 9.478 9.758

4442 5.914 6.957 8.157 8.871 9.486 10.043 10.429

4443 6.042 7.142 8.350 9.075 9.742 10.542 10.929

4444 6.088 7.235 8.515 9.287 9.971 10.809 11.338

2 1 1 1 1 - - - - -

2211 1 5.785

2221 1 6.250 6.750

2222 1 6.600 7.133 (7.533) 7.533

2222 2 6.982 7.418 8.073 8.291 (8.727) 8.727

3 1 1 1 1 - - - - -

3211 1 6.139 6.583

3221 1 6.511 6.800 7.400 7.600

3222 1 6.709 7.309 7.836 8.127 8.327 8.618

3222 2 6.955 7.682 8.303 8.682 8.985 9.273 9.364

3311 1 6.311 7.111 7.467

3321 1 6.600 7.200 7.892 8.073 8.345

3322 1 6.788 7.591 8.258 8.576 8.924 9.167 9.303

3322 2 7.026 7.910 8.667 9.115 9.474 9.769 10.026

3331 1 6.788 7.576 8.242 8.424 8.848 (9.455) 9.455

3332 1 6.910 7.769 8.590 9.051 9.410 9.769 9.974

3332 2 7.121 8.044 9.011 9.505 9.890 10.330 10.637

3333 1 7.077 8.000 8.879 9.451 9.846 10.286 10.549

3333 2 7.210 8.200 9.267 9.876 10.333 10.838 11.171

3333 3 7.333 8.333 9.467 10.200 10.733 10.267 11.667

1/ Zar, J.H. 1996. Biostatistical analysis. 3rd ed., Prentice Hall, Upper Saddle River, NJ 07458.
Part 615

National Water Quality Handbook

Appendixes

(450–VI–NWQH, September 2003) Appendixes–13

Appendix E Upper Percentage Points of the Studentized Range, 

q

x x

s a

x

=

−

max min

1/

Error - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - p = number of treatment means - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - -df

α 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

5 .05 3.64 4.60 5.22 5.67 6.03 6.33 6.58 6.80 6.99 7.17 7.32 7.47 7.60 7.72 7.83 7.93 8.03 8.12 8.21

.01 5.70 6.97 7.80 8.42 8.91 9.32 9.67 9.97 10.24 10.48 10.70 10.89 11.08 11.24 11.40 11.55 11.68 11.81 11.93

6 .05 3.46 4.34 4.90 5.31 5.63 5.89 6.12 6.32 6.49 6.65 6.79 6.92 7.03 7.14 7.24 7.34 7.43 7.51 7.59

.01 5.24 6.33 7.03 7.56 7.97 8.32 8.61 8.87 9.10 9.30 9.49 9.65 9.81 9.95 10.08 10.21 10.32 10.43 10.54

7 .05 3.34 4.16 4.68 5.06 5.36 5.61 5.82 6.00 6.16 6.30 6.43 6.55 6.66 6.76 6.85 6.94 7.02 7.09 7.17

.01 4.95 5.92 6.54 7.01 7.37 7.68 7.94 8.17 8.37 8.55 8.71 8.86 9.00 9.12 9.24 9.35 9.46 9.55 9.65

8 .05 3.26 4.04 4.53 4.89 5.17 5.40 5.60 5.77 5.92 6.05 6.18 6.29 6.39 6.48 6.57 6.65 6.73 6.80 6.87

.01 4.74 5.63 6.20 6.63 6.96 7.24 7.47 7.68 7.87 8.03 8.18 8.31 8.44 8.55 8.66 8.76 8.85 8.94 9.03

9 .05 3.20 3.95 4.42 4.76 5.02 5.24 5.43 5.60 5.74 5.87 5.98 6.09 6.19 6.28 6.36 6.44 6.51 6.58 6.64

.01 4.60 5.43 5.96 6.35 6.66 6.91 7.13 7.32 7.49 7.65 7.78 7.91 8.03 8.13 8.23 8.32 8.41 8.49 8.57

10 .05 3.15 3.88 4.33 4.65 4.91 5.12 5.30 5.46 5.60 5.72 5.83 5.93 6.03 6.11 6.20 6.27 6.34 6.40 6.47

.01 4.48 5.27 5.77 6.14 6.43 6.67 6.87 7.05 7.21 7.36 7.48 7.60 7.71 7.81 7.91 7.99 8.07 8.15 8.22

11 .05 3.11 3.82 4.26 4.57 4.82 5.03 5.20 5.35 5.49 5.61 5.71 5.81 5.90 5.99 6.06 6.14 6.20 6.26 6.33

.01 4.39 5.14 5.62 5.97 6.25 6.48 6.67 6.84 6.99 7.13 7.25 7.36 7.46 7.56 7.65 7.73 7.81 7.88 7.95

12 .05 3.08 3.77 4.20 4.51 4.75 4.95 5.12 5.27 5.40 5.51 5.62 5.71 5.80 5.88 5.95 6.03 6.09 6.15 6.21

.01 4.32 5.04 5.50 5.84 6.10 6.32 6.51 6.67 6.81 6.94 7.06 7.17 7.26 7.36 7.44 7.52 7.59 7.66 7.73

13 .05 3.06 3.73 4.15 4.45 4.69 4.88 5.05 5.19 5.32 5.43 5.53 5.63 5.71 5.79 5.86 5.93 6.00 6.05 6.11

.01 4.26 4.96 5.40 5.73 5.98 6.19 6.37 6.53 6.67 6.79 6.90 7.01 7.10 7.19 7.27 7.34 7.42 7.48 7.55

14 .05 3.03 3.70 4.11 4.41 4.64 4.83 4.99 5.13 5.25 5.36 5.46 5.55 5.64 5.72 5.79 5.85 5.92 5.97 6.03

.01 4.21 4.89 5.32 5.63 5.88 6.08 6.26 6.41 6.54 6.66 6.77 6.87 6.96 7.05 7.12 7.20 7.27 7.33 7.39

15 .05 3.01 3.67 4.08 4.37 4.60 4.78 4.94 5.08 5.20 5.31 5.40 5.49 5.58 5.65 5.72 5.79 5.85 5.90 5.96

.01 4.17 4.83 5.25 5.56 5.80 5.99 6.16 6.31 6.44 6.55 6.66 6.76 6.84 6.93 7.00 7.07 7.14 7.20 7.26

16 .05 3.00 3.65 4.05 4.33 4.56 4.74 4.90 5.03 5.15 5.26 5.35 5.44 5.52 5.59 5.66 5.72 5.79 5.84 5.90

.01 4.13 4.78 5.19 5.49 5.72 5.92 6.08 6.22 6.35 6.46 6.56 6.66 6.74 6.82 6.90 6.97 7.03 7.09 7.15

17 .05 2.98 3.63 4.02 4.30 4.52 4.71 4.86 4.99 5.11 5.21 5.31 5.39 5.47 5.55 5.61 5.68 5.74 5.79 5.84

.01 4.10 4.74 5.14 5.43 5.66 5.85 6.01 6.15 6.27 6.38 6.48 6.57 6.66 6.73 6.80 6.87 6.94 7.00 7.05

18 .05 2.97 3.61 4.00 4.28 4.49 4.67 4.82 4.96 5.07 5.17 5.27 5.35 5.43 5.50 5.57 5.63 5.69 5.74 5.79

.01 4.07 4.70 5.09 5.38 5.60 5.79 5.94 6.08 6.20 6.31 6.41 6.50 6.58 6.65 6.72 6.79 6.85 6.91 6.96

19 .05 2.96 3.59 3.98 4.25 4.47 4.65 4.79 4.92 5.04 5.14 5.23 5.32 5.39 5.46 5.53 5.59 5.65 5.70 5.75

.01 4.05 4.67 5.05 5.33 5.55 5.73 5.89 6.02 6.14 6.25 6.34 6.43 6.51 6.58 6.65 6.72 6.78 6.84 6.89

20 .05 2.95 3.58 3.96 4.23 4.45 4.62 4.77 4.90 5.01 5.11 5.20 5.28 5.36 5.43 5.49 5.55 5.61 5.66 5.71

.01 4.02 4.64 5.02 5.29 5.51 5.69 5.84 5.97 6.09 6.19 6.29 6.37 6.45 6.52 6.59 6.65 6.71 6.76 6.82

24 .05 2.92 3.53 3.90 4.17 4.37 4.54 4.68 4.81 4.92 5.01 5.10 5.18 5.25 5.32 5.38 5.44 5.50 5.54 5.59

.01 3.96 4.54 4.91 5.17 5.37 5.54 5.69 5.81 5.92 6.02 6.11 6.19 6.26 6.33 6.39 6.45 6.51 6.56 6.61
Part 615

National Water Quality Handbook

Appendixes

Appendixes–14 (450–VI–NWQH, September 2003) Appendix E Upper Percentage Points of the Studentized Range, 

q

x x

s a

x

=

−

max min

1/ — Continued

Error - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - p = number of treatment means - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - -df

α 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

30 .05 2.89 3.49 3.84 4.10 4.30 4.46 4.60 4.72 4.83 4.92 5.00 5.08 5.15 5.21 5.27 5.33 5.38 5.43 5.48

.01 3.89 4.45 4.80 5.05 5.24 5.40 5.54 5.65 5.76 5.85 5.93 6.01 6.08 6.14 6.20 6.26 6.31 6.36 6.41

40 .05 2.86 3.44 3.79 4.04 4.23 4.39 4.52 4.63 4.74 4.82 4.91 4.98 5.05 5.11 5.16 5.22 5.27 5.31 5.36

.01 3.82 4.37 4.70 4.93 5.11 5.27 5.39 5.50 5.60 5.69 5.77 5.84 5.90 5.96 6.02 6.07 6.12 6.17 6.21

60 .05 2.83 3.40 3.74 3.98 4.16 4.31 4.44 4.55 4.65 4.73 4.81 4.88 4.94 5.00 5.06 5.11 5.16 5.20 5.24

.01 3.76 4.28 4.60 4.82 4.99 5.13 5.25 5.36 5.45 5.53 5.60 5.67 5.73 5.79 5.84 5.89 5.93 5.98 6.02

120 .05 2.80 3.36 3.69 3.92 4.10 4.24 4.36 4.48 4.56 4.64 4.72 4.78 4.84 4.90 4.95 5.00 5.05 5.09 5.13

.01 3.70 4.20 4.50 4.71 4.87 5.01 5.12 5.21 5.30 5.38 5.44 5.51 5.56 5.61 5.66 5.71 5.75 5.79 5.83

× .05 2.77 3.31 3.63 3.86 4.03 4.17 4.29 4.39 4.47 4.55 4.62 4.68 4.74 4.80 4.85 4.89 4.93 4.97 5.01

.01 3.64 4.12 4.40 4.60 4.76 4.88 4.99 5.08 5.16 5.23 5.29 5.35 5.40 5.45 5.49 5.54 5.57 5.6l 5.65

1/ Steel, R.G.D., and J.H. Torrie. 1960. Principles and procedures of statistics. McGraw-Hill, Inc., New York, NY. (Reproduced with permission of the McCraw-Hill Companies.)
Part 615

National Water Quality Handbook

Appendixes

(450–VI–NWQH, September 2003) Appendixes–15

Appendix F Wilcoxon two-sample rank test (Mann-Whitney test) 1/

n2 = P - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - n1 = smaller n - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

larger n 2 3 4 5 6 7 8 9 10 11 12 13 14 15

4 .05 10

.01 ---

5 .05 6 11 17

.01 --- --- 15

6 .05 7 12 18 26

.01 --- 10 16 23

7 .05 7 13 20 27 36

.01 --- 10 17 24 32

8 .05 3 8 14 21 29 38 49

.01 --- --- 11 17 25 34 43

9 .05 3 8 15 22 31 40 51 63

.01 --- 6 11 18 26 35 45 56

10 .05 3 9 15 23 32 42 53 65 78

.01 --- 6 12 19 27 37 47 58 71

11 .05 4 9 16 24 34 44 55 68 81 96

.01 --- 6 12 20 28 38 49 61 74 87

12 .05 4 10 17 26 35 46 58 71 85 99 115

.01 --- 7 13 21 30 40 51 63 76 90 106

13 .05 4 10 18 27 37 48 60 73 88 103 119 137

.01 --- 7 14 22 31 41 53 65 79 93 109 125

14 .05 4 11 19 28 38 50 63 76 91 106 123 141 160

.01 --- 7 14 22 32 43 54 67 81 96 112 129 147

15 .05 4 11 20 29 40 52 65 79 94 110 127 145 164 185

.01 --- 8 15 23 33 44 56 70 84 99 115 133 151 171

16 .05 4 12 21 31 42 54 67 82 97 114 131 150 169

.01 --- 8 15 24 34 46 58 72 86 102 119 137 155

17 .05 5 12 21 32 43 56 70 84 100 117 135 154

.01 --- 8 16 25 36 47 60 74 89 105 122 140

18 .05 5 13 22 33 45 58 72 87 103 121 139

.01 --- 8 16 26 37 49 62 76 92 108 125

19 .05 5 13 23 34 46 60 74 90 107 124

.01 3 9 17 27 38 50 64 78 94 111

20 .05 5 14 24 35 48 62 77 93 110

.01 3 9 18 28 39 52 66 81 97

21 .05 6 14 25 37 50 64 79 95

.01 3 9 18 29 40 53 68 83

22 .05 6 15 26 38 51 66 82

.01 3 10 19 29 42 55 70

23 .05 6 15 27 39 53 68

.01 3 10 19 30 43 57

24 .05 6 16 28 40 55

.01 3 10 20 31 44

25 .05 6 16 28 42

.01 3 11 20 32

26 .05 7 17 29

.01 3 11 21

27 .05 7 17

.01 4 11

28 .05 7

.01 4

1/ Steel, R.G.D., and J.H. Torrie. 1960. Principles and procedures of statistics. McGraw-Hill, Inc., New York, NY. (Reproduced with permission

of the McCraw-Hill Companies.)
Part 615

National Water Quality Handbook

Appendixes

Appendixes–16 (450–VI–NWQH, September 2003)

Appendix G Wilcoxon's signed rank test (tabulated

values of T are such that smaller values,

regardless of sign, occur by chance with

stated probability) 1/

Pairs - - Probability - -

n .05 .02 .01

6 0——

7 2 0—

8 420

9 632

10 8 5 3

11 11 7 5

12 14 10 7

13 17 13 10

14 21 16 13

15 25 20 16

16 30 24 20

17 35 28 23

18 40 33 28

19 46 38 32

20 52 43 38

21 59 49 43

22 66 56 49

23 73 62 55

24 81 69 61

25 89 77 68

1/ Steel, R.G.D., and J.H. Torrie. 1960. Principles and procedures of

statistics. McGraw-Hill, Inc., New York, NY. (Reproduced with

permission of the McCraw-Hill Companies.)
Part 615

National Water Quality Handbook

Appendixes

(450–VI–NWQH, September 2003) Appendixes–17

Appendix H Quantiles (p-values) for Kendall's tau correlation coefficient (p = Prob[S ≥ x] = Prob [S≤ –x]) 1/

 - - - - - - - - - - Number of data pairs = n - - - - - - - - - - - - - - - Number of data pairs = n - - - -

x 4 5 8 9 x 6 7 10

0 0.625 0.592 0.548 0.540 1 0.500 0.500 0.500

2 0.375 0.408 0.452 0.460 3 0.360 0.386 0.431

4 0.167 0.242 0.360 0.381 5 0.235 0.281 0.364

6 0.042 0.117 0.274 0.306 7 0.136 0.191 0.300

8 0.042 0.199 0.238 9 0.068 0.119 0.242

10 0.0083 0.138 0.179 11 0.028 0.068 0.190

12 0.089 0.130 13 0.0083 0.035 0.146

14 0.054 0.090 15 0.0014 0.015 0.108

16 0.031 0.060 17 0.0054 0.078

18 0.016 0.038 19 0.0014 0.054

20 0.0071 0.022 21 0.0002 0.036

22 0.0028 0.012 23 0.023

24 0.0009 0.0063 25 0.014

26 0.0002 0.0029 27 0.0083

28 <0.0001 0.0012 29 0.0046

30 0.0004 31 0.0023

32 0.0001 33 0.0011

35 0.0005

37 0.0002

1/ Helsel, D.R., and R.M. Hirsch. 1992. Chapter 12, Trend analysis. In Statistical methods in water resources, Studies in Environmental Science

49, Elsevier, New York, NY.
Part 615

National Water Quality Handbook

Appendixes

Appendixes–18 (450–VI–NWQH, September 2003)

Appendix I Conversion Factors

Length

From: To: Multiply by:

foot inch 12

foot meter .3048

inch centimeter 2.54

kilometer mile 0.621

meter yard 1.094

mile kilometer 1.6093

yard inch 36

Area

From: To: Multiply by:

acre ft2 43,560

acre hectare 0.405

ft2 m2 0.0929

hectare acre 2.471

hectare m2 104

mile2 kilometer2 2.59

Volume

From: To: Multiply by:

ft3 liter 28.317

ft3 gallon 7.481

gallon liter 3.785

m3 ft3 35.314

m3 liter 1,000

Discharge

From: To: Multiply by:

ft3/s gpm 448.83

ft3/s m3/s .0283

m3/s liter/s 1,000

m3/s gpm 15,850

Mass

From: To: Multiply by:

pound kilogram 0.4536

ton pound 2,000

tonnes pound 2,205

pound/ac kg/ha 1.1208

ft3 - water pound 62.4

Temperature

o o

o o

F C

C F

= ( ) +

= ( ) −

9

5

32

5

9

32

Concentration

From: To: Multiply by:

mg/L ppm 1.0

ppm ppb 1,000

mg/L mg/kg 1.0

ug/L mg/m3 1.0

g/m3 mg/L 1.0

lb/ac kg/ha 1.120851

% solution mg/L 1 x 104

Metric

To convert SI prefixes

From: To: Multiply by:

Suffix mega (M) 1 x 106

Suffix kilo (k) 1,000

Suffix hecto (c) 100

Suffix deca 10

Suffix Suffix 1

Suffix deci .1

Suffix centi .01

Suffix milli .001

Suffix micro .000001
(450–VI–NWQH, September 2003)

United States

Department of

Agriculture

Natural

Resources

Conservation

Service

Part 615

National Water Quality Handbook

Index
(450–VI–NWQH, September 2003) Index–1

A

Above-and-below watershed 6–5,

9–2 to 9–4

Analysis of covariance 1–2, 1–3,

10–4, 10–8, 10–9, 12–6, 13–2

ANOVA (Analysis of variance)

1–2 to 1–4, 4–1, 4–4, 4–7,

5–1, 5–2, 6–5, 7–1 to 7–10,

10–2, 10–7, 10–8, 11–2 to

11–5, 12–3, 12–4, 13–6 to

13–8, 13–11

one-way ANOVA 4–4

Association 5–1, 5–2, 12–9

Assumption 1–1, 6–1

additivity 4–1, 4–4, 4–7

independence 1–1, 1–3, 3–7,

4–1, 4–4, 4–5, 4–7, 10–7, 12–2

normality 1–3, 4–1, 4–2, 4–3,

4–7, 7–8, 8–3, 9–2, 9–3, 10–7,

11–2, 12–2, 12–3, 13–3, 13–11

randomness 1–1, 4–1, 4–7

Autocorrelation 1–2, 1–3, 4–4, 

4–7, 13–2, 13–3, 13–5, 13–8,

13–9

B

Box-and-whisker plot 3–2, 3–3,

3–5, 3–6, 11–5, 12–1, 13–2,

13–3

Boxplot 3–3, 4–2, 11–5, 11–6,

12–3, 12–4, 13–11

C

Calibration 5–4, 10–1, 10–2, 10–3,

10–4, 10–5, 10–6, 10–7, 10–8,

10–9, 11–1

Causality 5–1, 5–4, 5–5, 5–6, 12–1

Coefficient of determination 1–2,

1–3, 10–3

Coefficient of skewness 1–2, 1–3,

2–9

Coefficient of variation 1–2, 1–3,

2–8, 2–9, 2–10, 13–9

Comparison of mean 8–1, 9–2,

9–4, 12–5

Computer 3–6, 3–8

Computer package 1–1

Confidence intervals 1–2, 1–3,

3–3, 10–3

Consistency 5–1, 5–2

Cumulative distribution 2–7, 12–5

D

Data analysis 3–1, 3–8

DETECT 13–1, 13–6 to 13–9,

13–12

Double mass analysis 12–6

E

EDA 1–1, 3–1, 12–1, 13–2, 13–9

Error 8–3

standard error 1–2, 1–3, 2–8,

2–10, 7–9, 7–10, 8–3

type I 4–3, 4–4, 6–1, 6–2, 6–6

type II 6–1, 6–2, 6–6

Experimental design 5–1, 5–5,

5–6, 8–4, 9–3, 12–1

Exploratory data analysis 1–1,

1–4, 3–1, 3–8, 13–2

F

F ratio 1–2, 1–3, 4–3, 4–7, 6–7,

7–5

Frequency(ies) 2–1, 2–3 to 2–5,

2–7, 3–2, 3–4, 4–2, 12–3,

12–5, 13–1, 13–2

G

Goodness of fit 4–2, 4–3, 12–5

H

Homogeneity of variance 1–1,

1–3, 4–1, 4–3

Hypothesis 4–3, 4–4, 6–1, 6–2,

6–3, 6–4, 6–5, 6–6, 6–7, 7–4,

7–5, 7–8, 7–9, 8–1, 8–2, 9–2,

9–4, 11–3, 11–5, 12–2, 12–8

one-sample 6–3

two-sample 6–3

paired-sample 6–4, 9–4

I

Independence 1–1, 1–3, 3–7, 4–1,

4–4, 4–5, 4–7, 10–7, 12–2

K

Kendall's tau 1–2, 1–3, 12–7,

12–8, 13–2, A–19

Kruskal-Wallis 1–2, 1–3, 7–8,

7–9, 7–10, 11–5, 13–2, 13–3,

13–5, A–11, A–12, A–13

Kurtosis 1–2, 1–3, 2–9, 2–10, 

4–2, 4–3, 8–3, 9–3, 11–4,

13–2, 13–3

M

Mann-Whitney U 1–2, 1–3, 8–5,

11–5, 13–2, 13–6

Mean 1–2, 1–3, 2–1, 2–2, 2–6 to

2–9, 2–11, 3–2 to 3–7, 4–1 to

4–4, 4–6, 5–1, 5–3, 5–5, 6–1 to

6–7, 7–1, 7–2, 7–4 to 7–7, 7–9,

7–10, 8–1 to 8–3, 8–6, 9–2 to

9–5, 10–3, 10–5, 11–3, 11–4,

11–5, 12–1, 12–3, 12–4, 13–1

to 13–3, 13–6 to 13–9

Mean comparison 7–5, 7–9

Median 1–2, 1–3, 2–6, 2–7, 3–2,

3–3, 3–5 to 3–7, 4–2, 4–3, 8–3,

9–3, 11–5, 12–1, 12–3, 12–8,

13–2 to 13–4

Missing value 4–5, 4–6, 13–6

Mode 1–2, 1–3, 2–6, 2–7

Multiple comparison 1–2, 1–3,

6–5, 7–9, 7–10

Multiple watershed 11–1 to 11–6

N

Nonparametric 1–2, 1–3, 4–3,

4–4, 6–6, 7–1, 7–3, 7–8 to

7–10, 8–5, 8–6, 9–1, 9–4, 11–1

to 11–3, 11–5, 12–1, 12–7,

12–9, 13–2, 13–6, 13–7, 13–9,

13–11, 13–12

Normal distribution 2–7 to 2–10,

3–5, 4–1 to 4–3, 7–3, 8–3, 

8–5, 9–4, 11–2, 11–3

Index
Part 615

National Water Quality Handbook

Index

Index–2 (450–VI–NWQH, September 2003)

Normality 1–3, 4–1 to 4–3, 4–7,

7–8, 8–3, 9–2, 9–3, 10–7,

11–2, 12–2, 12–3, 13–3, 13–11

O

Observation 1–3, 2–1 to 2–3, 2–6

to 2–8, 2–11, 3–2, 3–8, 4–1,

4–4, 4–6, 6–4, 7–1 to 7–4, 7–8

to 7–10, 8–1, 9–2, 10–1 to

10–3, 10–5, 10–7, 10–8,

12–1, 12–7, 13–6, 13–12

One-sample t-test 1–3

Outliers 2–3, 3–3, 4–1, 4–6,

13–6, 13–7

P

Paired comparison 6–4, 8–1, 9–2,

9–4, 11–3

Paired watershed 5–4, 9–1, 10–1,

10–2, 10–5 to 10–9, 11–1, 11–3

Plot 3–1 to 3–7

Plot design 7–1, 7–3, 7–8

Population 2–1, 2–2, 2–8, 4–2 to

4–4, 5–1, 5–2, 5–5, 6–1 to

6–3, 6–5, 6–6, 8–2

Q

Q-Q plot 12–6, 12–9

R

Random sample 2–2

Randomness 1–1, 4–1, 4–7

Regression 1–2, 1–3, 3–7, 4–5,

4–7, 5–1, 5–2, 5–6, 10–2 to

10–5, 10–7 to 10–9, 11–1, 12–1

to 12–4, 12–7, 12–9, 13–11

Replications 4–7, 5–1, 7–1 to 7–3,

7–6

Residual plot 4–1, 4–5, 4–7, 10–7

Residuals 4–4, 4–5, 10–2, 10–3,

10–7

Responsiveness 5–1, 5–4

Runoff 3–7

S

Sample 1–2, 1–3, 2–1 to 2–3, 2–8,

2–9, 2–11, 3–6, 4–1, 4–3 to

4–7, 6–1 to 6–7, 7–1, 7–2, 8–1,

8–2, 8–5, 9–1, 9–2, 9–4, 10–3,

10–7, 11–1 to 11–3, 11–5,

13–1, 13–9, 13–12

Sample size 2–3, 2–9, 3–6, 4–3 to

4–6, 6–1, 6–6, 13–1, 13–9

Shapiro-Wilk W-statistic 1–2, 1–3,

4–3, 10–7, 11–3, 12–3

Single watershed 8–1 to 8–6, 9–2

Skewness 1–2, 1–3, 2–9, 2–10,

3–5, 4–2, 4–3, 8–3,9–3, 11–4,

13–2, A–3

Smoothing 3–1, 3–7, 3–8, 12–1

Standard deviation 1–2, 1–3, 2–7

to 2–10, 3–4, 3–5, 6–2, 7–2,

8–1, 8–3, 9–2, 13–2, 13–3,

13–7, 13–8

Standard error 1–2, 1–3, 2–8,

2–10, 7–9, 7–10, 8–3

Statistical significance 6–1, 6–6

Statistics, purpose of 1–1, 1–2,

1–3, 2–1

Stem-and-leaf diagram 3–1, 3–2,

3–5, 12–1

T

T-test 1–2, 1–3, 4–3, 4–4, 6–3 to

6–5, 8–1 to 8–3, 8–5, 9–1 to

9–4, 12–3, 12–4, 13–11

Time plot 3–6, 3–7, 8–6, 9–5, 

12–2, 12–9, 13–3, 13–6, 13–9

Transformation 3–1, 3–4 to 3–7,

4–2 to 4–4, 7–3, 8–3, 8–6, 9–1

to 9–4, 11–3, 12–1 to 12–3

Treatment period 5–4, 10–1 to

10–4, 10–7, 10–8

Trend analysis 4–4, 4–5, 6–4,

12–1, 12–2, 12–4, 12–6, 12–9,

13–9, 13–12, A–19

Tukey's multiple comparison 1–2,

1–3, 7–10

Two-sample hypothesis 6–3

Two-sample t-test 1–3

Type I error 4–3, 4–4, 6–1,

6–2, 6–6

Type II error 6–1, 6–2, 6–6

V

Variance 1–1 to 1–3, 2–8, 2–10,

2–11, 3–4, 3–5, 4–1, 4–3 to

4–5, 4–7, 5–1, 5–2, 6–5, 7–1,

7–3, 7–8, 7–9, 8–1, 9–1 to

9–4, 10–2 to 10–4, 11–2, 11–3,

11–5, 12–2 to 12–4, 12–6, 13–2,

13–7 to 13–9

W

Watersheds

above-and-below 6–5, 9–2 to

9–4

multiple 11–1 to 11–6

paired 5–4, 9–1, 10–1, 10–2,

10–5 to 10–9, 11–1, 11–3

single 8–1 to 8–6, 9–2

Wilcoxon 9–4,

Wilcoxon paired sample 1–2, 1–3, 

9–4, 11–5, 13–2, A–15, A–16

WQStat II 12–8, 13–1, 13–2, 13–9,

13–12
United States

Department of

Agriculture

Natural

Resource

Conservation

Service

National Water Quality Handbook

Part 616

Part 616
United States

Department of

Agriculture

Natural

Resource

Conservation

Service

National Water Quality Handbook

Part 617

Examples/Case Studies

Part 617 Examples/Case Studies
United States

Department of

Agriculture

Natural

Resource

Conservation

Service

National Water Quality Handbook

Part 618

Part 618
United States

Department of

Agriculture

Natural

Resource

Conservation

Service

National Water Quality Handbook

Glossary

Part 619

Part 619 Glossary
United States

Department of

Agriculture

Natural

Resources

Conservation

Service

National Water Quality Handbook

Part 619 Glossary
(450-VI-NWQH, September 2003) Glossary—1

Glossary

Aerobic The presence of oxygen.

Alternate hypothesis Any hypothesis alternative to the one under a test.

Anaerobic The absence of oxygen.

Analysis of variance An analysis of the total variation displayed by a set of observations, measured by the sums of squares of deviations from the mean. The variation is

usually separated into components associated with sources of interest.

Aquifer A geologic formation containing water, usually able to yield appreciable

water.

Baseflow A part of stream discharge not attributed to direct runoff from precipitation

or snowmelt and usually contributed by subsurface flow.

Baseline Initial or background water quality conditions. Also a surveyed line.

Bedload Sediment, not in suspension, moving along the streambed by rolling or

bouncing.

Benthos The assemblage of organisms living on or at the bottom of a body of water.

Best Management Practice A practice or combination of practices found to be the most effective,

practicable (including economic and institutional considerations) means of

preventing or reducing the amount of pollution generated by nonpoint

sources to a level compatible with water quality goals.

Blurring An exploratory data analysis technique of smoothing by replacing data

points with short vertical lines of appropriate length beginning with the

median of the residuals.

Calibration The beginning period of time for a paired watershed design somewhat

synonymous with a baseline period.

Catchment The area providing runoff to a lake, stream, or well (drainage area, drainage

basin, watershed).

Coefficient of determination The square of the correlation coefficient. Decimal fraction of percent of

variance explained.

Coefficient of variation The standard deviation of a distribution divided by the mean.

Coliform bacteria A group of bacteria predominantly found in the intestines of animals, but

also occasionally found elsewhere.

Composite sample A combination of individual samples taken at selected intervals or volumes

to minimize variability.

Concentration The amount of a substance dissolved or suspended in a unit volume of

water.
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Conductance The measure of the conducting ability of a solution that is equal to the

reciprocal of the resistance.

Confidence level The measure of probability (α) of the truth of a statement.

Confidence limits The values of an upper and lower t of a confidence interval. The interval has

a probability (α) that the value will lie between the upper and lower limits.

Confined aquifer An aquifer that is surrounded by formations of less permeable or impermeable material that is isolated from the atmosphere. (Artesian aquifer)

Conservation practice A specific treatment, such as a structural or vegetative measure, or management technique, commonly used to meet specific needs in planning and

implementating conservation for which standards and specifications have

been developed. Conservation practices are listed in the Field Office Technical Guide (FOTG), section IV, which is based on the National Handbook

of Conservation Practices (NHDP).

Contamination An introduction of a substance into water in a sufficient concentration to

make the water unfit for its intended use.

Continuous data Data for which all values in some range are possible, such as height and

weight.

Control In a study, a standard for comparison against which other treatments are

compared, but is either untreated or receives a standard treatment. Also, a

stable cross section in a stream that controls flow upstream.

Critical area An area within a watershed determined to be an important source of a

pollutant.

Current meter A devise for measuring the velocity of flowing water.

Discharge The rate or volume of water flowing at a specific cross section within a

specified time.

Discharge rating curve A curve showing the relationship between the stage at a cross section and

the discharge at that cross section.

Discrete data Data for which the possible values are fixed, such as counts.

Dispersion The mixing of the concentration of a substance in the water with another

body of water due to the flow of water.

Dissolved oxygen The oxygen dissolved in water, expressed in milligrams per liter or percentage saturation.

Drainage basin See catchment.

Drainage density The density of natural drainage channels in a given area, expressed as

length per unit area.
Glossary National Water Quality Handbook

(450–VI–NWQH, September 2003) Glossary—3

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Effluent stream A stream that receives water from saturated ground water.

Epilimnion The upper waters of a thermally stratified lake.

Equipotential line A contour line that connects points of equal head for the water table or

equipotential surface.

Error The difference between an occurring value and its true or expected value.

Eye smoothing Drawing s smooth curve through points of data on a graph.

Field A small agricultural unit implying a management area.

Filter strip A conservation practice that is a strip of vegetated land established

downslope of a nonpoint source of pollution with the purpose of reducing

the pollutant.

Flow line A line indicating the direction of ground water flow toward the point of

discharge. Flow lines are perpendicular to equipotential lines and together

they form a flow net.

Flume An open conduit for flow.

Frequency distribution A listing of the way the frequencies of members of a population are distributed according to the values of the variable. The distribution is usually

shown in a table.

Gage A device for determining the water level.

Grab sample A single sample taken at a certain time and place.

Ground water Subsurface water in the saturated zone below the water table.

Hydrograph A graph showing discharge as a function of time for a given location on a

stream.

Hypolimnion The bottom waters of a thermally stratified lake.

Hypothesis A hypothesis concerning the parameters or form of the probability distribution for a designated population.

Intermittent stream A stream or portion that flows only in direct response to precipitation.

Interval scale A measurement with a constant interval size, but no true zero, such as

temperature (arbitrary zero) and time.

Kurtosis The extent to which a unimodal frequency curve is peaked.

Least squares regression Estimation of regression parameters by minimizing a quadratic form.
Glossary National Water Quality Handbook

Glossary—4 (450–VI–NWQH, September 2003)

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Limnocorral A device used in lakes that isolates the water column from surrounding

water.

Load The quantity of material entering a receiving body of water.

Lysimeter A device used to measure the water quantity or quality draining through the

soil.

Macroinvertebrate A large animal without a backbone that can be observed without the aid of

magnification.

Macrophyton A large plant that can be observed without the aid of magnification.

Mean The arithmetic average of the values for a variate.

Median That value of the variate which divides the total frequency into two halves.

Mesocosm A medium-sized experimental unit with boundaries.

Metalimnion The middle layer of a thermally stratified lake.

Mode The value of the variate that has the greatest number of members of the

population.

Model A description of a system; often mathematical.

Nonparametric statistics Better termed distribution-free statistics. Testing a hypothesis that does not

depend on the form of the underlying distribution.

Nonpoint source A diffuse location with no particular point of origin.

Null hypothesis A hypothesis under test that determines the probability of the Type I error.

Also a hypothesis under a test of no difference.

Objective A statement describing what is to be accomplished that contains an infinitive verb and an object.

Observation Data that are collected or analyzed.

Ordinal scale Data that consist of an ordering or ranking of measurements, such as A is

bigger than B.

Parametric statistics A statistical test that assumes the distribution type is known.

Perennial stream A stream that flows continuously all seasons of a year and during both wet

and dry years.

Periphyton Small or microscopic aquatic plants attached to submerged objects.

Phytoplankton Small or microscopic aquatic plants.
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Piezometer An instrument for measuring pressure head in the soil.

Plankton Small or microscopic aquatic organisms that are floating, or weakly motile

and generally considered to be at the mercy of the currents.

Plot A small experimental unit with boundaries.

Pollutant An undesirable substance in water, soil, or air at sufficient concentrations

to impair the intended use of the resource.

Pollution A condition caused by the presence of harmful or objectionable substances

in water.

Population A collection of individuals.

Random sample A sample collected from a population where every sample has an equal

probability of being selected.

Rating A relation between stage and discharge of a stream.

Ratio scale Measurements having a constant interval size and a true zero point, such as

lengths, weights, volumes, and rates.

Reconnaissance survey A survey to obtain a general view of water quality; may imply samples

collected at approximately the same time (synoptic survey).

Regression A statistical method to investigate relationships between two components.

Replication The execution of an experiment more than once.

Resource management system A combination of conservation practices and resource management, for the

treatment of all identified resource concerns for soil, water, air, plants, and

animals, that meets or exceeds the quality criteria in the Field Office

Technical Guide (FOTG) for resource sustainability.

Responsiveness In establishing cause-and-effect, the evidence that the dependent variable is

related to the independent variable.

Runoff That portion of precipitation or irrigation found in surface channels and

streams.

Runoff coefficient The ratio of the depth of runoff from a watershed to the depth of precipitation.

Sample A part of all the possible measurements in some larger group, such as the

population.

Sampler A device used to obtain an aliquot of water.

Significance The probability of committing a Type I error (α). Biological significance

refers to an underlying assumption about relationships.
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Skewness A measure of asymmetry in a frequency distribution.

Smoothing The process of removing fluctuations in a series of data.

Specific conductance The ability of water to conduct electricity across a specific length at a

specified temperature.

Stage The elevation of the water surface above some datum.

Stage-discharge relation The relationship between stream stage and discharge at a gaging station.

Standard deviation A measure of dispersion of a frequency distribution that is the square root

of the variance.

Statistic A summary value calculated from a sample of observations.

Statistical error See Error.

Statistics The science of collecting, analyzing, and interpreting data.

Steady-state Conditions that are averaging constant over time.

Stilling well A chamber with small inlets connected to a water body used for measuring

the water level.

Streamflow Water flowing in a stream channel. (Stream discharge)

Surface runoff The portion of runoff that reaches a stream by traveling over the surface of

the land. (Overland flow)

Suspended solids Solids in suspension in water.

Synoptic survey See reconnaissance survey.

Tensiometer An instrument filled with water with a porous cup used for measuring the

soil water potential.

Turbidity A condition in water caused by suspended matter that causes the scattering

and absorption of light.

Unconfined aquifer An aquifer where the water table is exposed to the atmosphere. (Water

table aquifer)

Vadose zone Zone of soil between the surface and the water table that is not saturated.

Variance The mean of the squares of the deviations from the mean.

Velocity meter A meter used to measure stream velocity.

Water quality The physical, chemical, and biological properties of water with respect to

its suitability for an intended use.
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Water quality management The management of the physical, chemical, and biological characteristics of

water.

Water quality monitoring The collection of information on the characteristics of water.

Water quality standards A rule established by an agency or units of government; often numerical.

Water table The upper surface of the saturated zone in a soil that is at atmospheric

pressure.

Water-level recorder A device used for recording the water elevation over time.

Watershed The area contributing water to a stream, lake, or well.

Weir A device used in a stream with a damming crest and an opening of some

known geometric shape, such as a V-notch.

Zooplankton Small or microscopic aquatic animals.