Printed on Recycled Paper

United States

Environmental Protection

Agency

Office of Water

4607

EPA 815-R-01-004

August 2001

Statistical Design and Sample

Selection for the Unregulated

Contaminant Monitoring

Regulation (1999)
UCMR Statistical Design August 2001
UCMR Statistical Design August 2001

i

Foreword

Under §1445(a)(2)(A) ofthe Safe Drinking Water Act (SDWA), as amended in 1996, the Environmental

Protection Agency (EPA) is required to establish criteria for a program to monitor for unregulated

contaminants and to publish a list of contaminants to bemonitored. In response to this requirement, EPA

published the Revisions to the UnregulatedContaminant MonitoringRegulation(UCMR) for public water

systems (PWSs) on September 17, 1999 (64 FR 50556), and in supplemental rules, including, the

Perchlorate and AcetochlorRule (March2, 2000 - 65FR11372), and the List 2 Rule (January11, 2001 -

66 FR 2273). EPA expects to publish other rules detailing updates and modifications to the UCMR

program, monitoring requirements, and analytical methods, as needed.

This document provides technical background information on the statistical process used to select the

nationally representative sample ofsmallPWSs(systems serving 10,000 or fewer people) forthe UCMR.

This document also explains the statisticalselectionprocessforlarge PWSs (systems serving greater than

10,000 people) selected to monitor for the Screening Survey component of the UCMR. Note that this

document does not explain all UCMR program requirements in detail. Where more detailed and

comprehensive informationis available through other EPA guidance documents, the reader will be referred

to these documents.
UCMR Statistical Design August 2001

ii
UCMR Statistical Design August 2001

iii

Acknowledgments

This document was prepared in support ofthe UnregulatedContaminant MonitoringRegulation (UCMR)

for EPA’s Office of Ground Water and Drinking Water. Charles Job served as EPA’s team leader for

development ofthe UCMR withJames Taft as Targeting and Analysis BranchChief. Rachel Sakata served

as Work Assignment Manager. The UCMR Work Group provided technical guidance throughout.

Andrew Schulman provided technical lead forfinalizingthe selection process. Also, Dennis Helsel of the

US Geological Survey, and Christopher Frebis provided valuable assistance. External expert reviewers

and many stakeholders provided valuable advice to improve the UCMRand this document. The Cadmus

Group, Inc., served as the prime contractor providing support for various components of this and other

UCMR support work. The major contributions of Kim Clemente, Maureen Devitt, Jonathan Koplos, and

Piyali Talukdar are gratefully acknowledged. George Hallberg served as Cadmus’ Project Manager.
UCMR Statistical Design August 2001

iv
UCMR Statistical Design August 2001

v

Contents

Section Page

Foreword .................................................................... i

Acknowledgments ............................................................ iii

Contents .....................................................................v

List of Tables and Figures ..................................................... vii

1. Introduction ............................................................1

1.1 Purpose and Background ............................................1

1.2 Overview of the UCMR Program .....................................2

2. Determining the UCMR Sampling Frame .....................................5

2.1 Background ......................................................5

2.2 Needs Survey Inventory Background ...................................5

2.3 Needs Survey Sample Frame Improvements .............................5

2.3.1 Community Water Systems ....................................5

2.3.2 Non-transient Non-community Water Systems .....................7

2.3.3 Tribal Water Systems .........................................7

2.3.4 System Classifications ........................................8

2.3.5 Additional Sampling Frame Improvements ........................8

3. Selecting the Statistical Population for Systems Serving 10,000 or Fewer People ......9

3.1 Determining the Population of Small PWS for Inclusion in the UCMR Sample . 9

3.2 Stratifying the Population ...........................................9

3.3 Tribal Water Systems as an Individual Stratum ......................... . 11

3.4 Consistency of State Plans ......................................... . 11

4. Selecting the Representative Sample for Systems Serving 10,000 or Fewer People .... 12

4.1 Objectives of the Sample ........................................... 12

4.1.1 Accuracy and Precision ...................................... 12

4.1.2 Stratification ............................................... 13

4.1.3 Representativeness .......................................... 14

4.1.4 Summary ................................................. 14

4.2 How the Samples Were Allocated .................................... 15

4.2.1 Allocation of Systems to States and Territories .................... 16

4.2.2 Calculation of Category Sampling Probabilities ................... 19

4.3 Statistical Implications ............................................. 22

4.3.1 Occurrence and Exposure Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.3.2 Margins of Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

5. Selecting Systems for the Initial Plan List and the Replacement List in Each State . . . . 24

6. Selecting Systems for the State Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
UCMR Statistical Design August 2001

vi

7. Index System Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

8. Assessment Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

9. Screening Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

10. Pre-Screen Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

11. References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

Appendices

Appendix A 

Statistical Theory and Optimal Choice of Probabilities

for Probability-Weighted Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1

Appendix B

Expected and Total Number of Systems Selected for Assessment Monitoring . . . . . . . B-1

Appendix C

Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-1

Appendix D

Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1
UCMR Statistical Design August 2001

vii

List of Tables and Figures

Tables

Number Title Page

Table 1. Systems Serving 10,000 or Fewer People . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Table 2. Distribution of Small Systems Required to Conduct Assessment 

Monitoring and Screening Survey in Each State/Tribe/Territory . . . . . . . . . . . . . . . . 16

Table 3. Sample Allocation Proportional to Population Served: Expected 

Number of Systems Drawn From Each Category, and Resulting 

Margins of Error for Exposure Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Table 4. Sample Allocation for Assessment Monitoring: Expected Number 

of Systems Drawn from Each Category, and Resulting Margins of 

Error for Exposure Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Table 5. National Representative Sample Distributed by System Size Category 

and Water Source Type as Selected for the Initial SMPs . . . . . . . . . . . . . . . . . . . . . . 21

Table 6. Comparison of 99% Normal and Wilson Score Confidence Intervals 

for Exposure Estimates in CWSs under Assessment Monitoring . . . . . . . . . . . . . . . 24

Table 7. Cumulative Probability of Selection by Stratum for Colorado . . . . . . . . . . . . . . . . . 25

Table 8. Distribution of Index Systems in the Representative Sample . . . . . . . . . . . . . . . . . . 27

Table 9. Allocation of Systems for Screening Surveys by Size Category with 

the Associated Confidence Levels and Margins of Error . . . . . . . . . . . . . . . . . . . . . 30

Figures

Figure 1. UCMR (1999) Implementation Timeline ...................................4

Figure 2. Number and Probability of Small Systems Chosen for Assessment 

Monitoring and Screening Surveys for the UCMR Years 2001-2003 . . . . . . . . . . . 33
UCMR Statistical Design August 2001

viii
UCMR Statistical Design August 2001

1

1. Introduction

1.1 Purpose and Background

The requirement tomonitorunregulatedcontaminantswasestablished bythe 1986 Amendmentsto theSafe

Drinking Water Act (SDWA). Public water systems (PWSs) were required to report the monitoring

resultsfor up to 48 unregulated contaminantsto the States or primacyagencyunderseveralregulations (40

CFR 141.40(e), (j), and (n)(11) - (12)). Systems with less than 150 service connections were exempt,

provided those systems made their facilities available for the States to monitor. 

Under §1445(a)(2)(A) of the SDWA, as amended in1996, the Environmental Protection Agency (EPA)

was required to establish criteria for a program to monitor for unregulated contaminants and to publish a

list of contaminantsto be monitored. To fulfill the requirements of the SDWA, EPA published the Revisions

to the Unregulated Contaminant Monitoring Regulation (UCMR)for PWSs on September 17, 1999 (64

FR 50556). This regulation included programmatic changes to the UCMR and provided a list of

contaminants for which monitoring was required, or would be required in the future. The UCMR set up

a three-tiered monitoring approach for contaminants based on the availability of analytical methods and

insights oncontaminant properties and fate and transport. In response to public comments, and as relevant

analytical methods were refined and developed. EPA published the Perchlorate and Acetochlor Rule on

March 2, 2000 (65 FR 11372), and the List 2 Rule on January 11, 2001 (66 FR 2273). As EPA

continues to refine and develop additional methods and/or identify minor clarifications or modifications

needed for the successful implementation of the UCMR, the Agency will provide additional guidance

documents or fact sheets and will promulgate additional rules, as necessary. 

The UCMR program was developed in coordination with the Contaminant Candidate List(CCL) and the

NationalDrinkingWater Contaminant Occurrence Database (NCOD). The UCMR and the CCL operate

on a 5-year cycle to assess the impact of new and emerging contaminants on drinking water. The new

UCMR program is a cornerstone ofthe sound science approach to future drinking water regulation. The

data collected through the UCMR program will be stored in the NCOD to facilitate analysis or review of

contaminant occurrence, and willbe usedtosupport the development ofsubsequent CCLs, and to support

the Administrator’s determination of whether or not to regulate a contaminant in the interest of protecting

public health.

The SDWA provisions and EPA regulations described in this document contain legally binding

requirements. This document does not substitute for those provisions or regulations, nor is it a regulation

itself. It does notimposelegally-bindingrequirementsonEPA, States, or the regulated community, and may

not apply to a particular situation based uponthe circumstances. EPA and State decisionmakersretain the

discretion to adopt approaches on a case-by-case basis that differ fromthis guidance where appropriate.

Any decisions regarding a particular facility will be made based onthe applicable statutes and regulations.

Therefore, interested parties are free to raise questions and objections about the appropriateness of the

application of this guidance to a particular situation, and EPA will consider whether or not the

recommendations or interpretations inthe guidance are appropriate in that situation based on the law and

regulations. EPA may change this guidance in the future without notice or an opportunity for comment.

Mention of trade names or commercialproducts does not constitute endorsement or recommendation for

use.

The purpose of this document is to describe the statistical design and methods used to select the

representative sample of small PWSs (systems serving fewer than 10,000 people) that are required to
UCMR Statistical Design August 2001

2

conduct Assessment Monitoring and Screening Surveys. This document also describes the process used

to select large PWSs(systems servingmore than 10,000 people) for the Screening Survey component of

the UCMR. Portions of this document also describe how this process relates to individual State Monitoring

Plans (SMPs). Under the UCMR, the listed unregulated contaminants willbe monitored between 2001-

2005. All large PWSs are required to monitor for UCMR contaminants. Section 1445(a)(2) of SDWA

mandates that only a representative sample ofsmallPWSs maybe required to monitor under the UCMR.

The representative sample must be of adequate size and quality to obtain the necessary and valid

contaminant occurrence informationuponwhichto base regulatorydeterminations while minimizingburden

to the water system.

The objective of the statistical approach for the UCMR is to estimate contaminant exposure and

occurrence in a nationally representative sample of small systems which will enable extrapolations of

exposure and occurrence nationwide. For contaminant exposure assessments (the fraction ofpopulation

thatis exposed to a contaminant), the representative sample design wasfirstweighted bypopulationserved

byPWSs. However, information on contaminant occurrence is also necessary. The context of occurrence

(for example, the size of a water system or its water source) is a factor when evaluating potential future

regulatoryimplementation. Therefore, the representative sampling design incorporates a stratified sampling

approachand allocatessome samples among strata to enable evaluations of occurrence relative to system

size (based onpopulationserved), watersource type (surface water orgroundwater)and, to some degree,

geographic distribution. Although this statistical design is notstrictly optimalfor estimating either exposure

or occurrence, the design meets the data quality objective for overall exposure estimates (99% confidence

level with ±1% error tolerance, at 1% exposure), while providing more precise occurrence estimates for

categories of small systems.

1.2 Overview of the UCMR Program 

The first component of the UCMR is Assessment Monitoring which will be conducted by all of the

approximately 2,800 large community water systems (CWSs) and non-transient non-community water

systems (NTNCWSs)serving more than 10,000 persons (except those large systems that purchase all of

their water from another PWS), and by a statistically representative sample of 800 small CWSs and

NTNCWSs serving 10,000 or fewer persons (except those smallsystems that purchase all oftheir water

fromanother PWS). Assessment Monitoring will be conducted for the UCMR (1999) List 1 contaminants,

for which analytical methods have already been developed and refined. 

The second component ofthe UCMR includesthe Screening Surveys. Each of the two Screening Surveys

will be conducted at 120 large systems, and at 180 small systems randomly selected from the pool of

systems required to conduct Assessment Monitoring. Screening Survey monitoring will be conducted for

the List 2 contaminantsfor whichanalyticalmethods have beendeveloped,but mayneed furtherrefinement

before larger-scale monitoring is conducted.

The third component of the UCMR is Pre-Screen Testing which may be conducted at a combined total

of up to 200 large and small systems. States will be asked to nominate systems that are particularly

vulnerable to the Pre-Screen Testing contaminants. Pre-Screen Testingmaybe conducted forsome ofthe

UCMR (1999) List 3 contaminants for which analytical methods are in the initial stages of development.

EPA will provide further guidance on Pre-Screen Testing contaminants and analytical methods as

necessary. 
UCMR Statistical Design August 2001

3

EPA also selected 30 small systems to serve as Index Systems. These systems will conduct Assessment

Monitoring eachyear ofthe 5-year UCMR cycle to provide additionalprogrammatic informationand data

quality control. EPA contractors will collect data on temporal variations in contaminant occurrence, and

on the environmental and operating conditions of these 30 small systems. Detailed information from the

IndexSystems, together withthe monitoring data generatedthroughgeneralUCMR monitoring, will enable

EPA to develop future regulations that better reflect the environmental characteristics and operating

conditions of small PWSs.

General monitoring schedules are related to the type of monitoring (Assessment Monitoring, Screening

Survey, or Pre-Screen Testing) being conducted. Each participating system must conduct Assessment

Monitoring for the List 1 contaminantsfor a 12-monthperiod inthe first three years (2001 through 2003)

of the 5-year UCMR contaminant monitoring cycle (2001-2005), as per §141.40(a)(5). Randomly

selected large systems willsample forthe UCMR List 2 contaminants in 2002 (for chemicalcontaminants)

and 2003 (for the microbiological contaminant, Aeromonas), while smallsystems will sample in 2001and

2003, respectively. No time-frame has been established yet for Pre-Screen Testing forthe UCMR (1999)

List 3 contaminants.

Required monitoring locations are also related to the type of monitoring (see §141.40(a)(5)). Assessment

Monitoring samples must be collected at the entry point(s) to the distribution system unless otherwise

specified by the State or EPA. Samples for the first Screening Survey (for the List 2 chemicals) must

always be collected at the entry point(s) to the distribution system (source water samples are not

permitted). Samplesfor Aeromonas must be collected inthe distributionsystem. Sampling locations must

include one midpoint inthe distributionsystemwhere the disinfectant residualwill be expected to be typical

for the system (midpoint, or MD, as defined in the Rule), and two other points:one of maximum retention

time and one where the disinfectant residual will have typically declined (point of maximum residence, or

MR, and location of lowest disinfectant residual or LD, respectively, as defined in the Rule).

Discussions with States and other stakeholders indicated the need to select a representative sample of

systems across all States to ensure both confidence in the UCMR results and a comprehensive spatial

distribution. To ensure that the sample is representative of the nation and to reduce the burden on small

systems, EPA statistically selected a nationally representative sample of systems serving 10,000 or fewer

people for the UCMR. States are participating inthe UCMR through State Monitoring Plans (SMPs) as

established by Partnership Agreements (PAs) with EPA. Note, however, that a State was not required

to enter into a PA with EPA to participate in SMP development. Through the PAs and the SMPs, States

were givenanopportunityto participate inthe UCMR program, while sharing some of the responsibilities

withEPA. All steps involved with sample selection described throughout this document assume that a State

has entered into a PA with the appropriate EPA Regional Office, or has decided to review the SMP. 

As described laterinthis document, a list of the statistically-selected systems was provided byEPA to the

States. The list was comprised of a “primary list,” an “alternate list,” and a “supplemental alternate list” of

systems. These lists were provided to the Statesfortheir review and inclusionintheir SMPs. States could

either: (1) respond by accepting the primary list as their representative plans, or (2) propose an alternative

plan by selecting other system(s) from the replacement list(s), in cases where EPA’s initial plan identified

system(s) that no longer existed, because of merger or closure, or that switched to purchased water.

Figure 1 provides a summary of the UCMR three-tiered monitoring approach, and shows the

implementation timeline of UCMR activities.
UCMR Statistical Design August 2001

4

 2000 2001 2002 2003 2004 2005

Systems

notified of

requirements

by EPA/State

Perchlorate

Laboratory

Proficiency

Testing

List 2 Screening

Survey

(Chemicals)

180 randomly

selected small

systems must

monitor; subset of

systems doing

List 1 monitoring

during this year.

List 2 Screening

Survey

(Aeromonas)

Second set of 180

randomly selected

small systems must

monitor; subset of

systems doing

List 1 monitoring

during this year.

List 1 Assessment Monitoring - All Large Systems

must monitor for one year during this three-year period.

Data must be reported electronically to EPA.

List 2 Screening

Survey

(Chemicals)

120 randomly

selected large

systems must

monitor.

List 2 Screening

Survey

(Aeromonas)

Second set of

randomly selected

120 large systems

must monitor.

List 1 Assessment Monitoring - 800 Small Systems

(statistically selected) must monitor for one year during

this three-year period, as specified by the State and

EPA. Approximately one-third monitor each year. EPA

pays for the costs of testing.

Reporting - All Large and Small Systems Monitoring for List 1 and List 2 Contaminants

must report results to customers under the Consumer Confidence or Public Notification Rule.

Index Systems

30 Index Systems (selected from the 800 small systems) must monitor every year for List 1

contaminants during this five-year period, with additional support from EPA.

Large Systems (serving more than 10,000 people)

Small Systems (serving 10,000 or fewer people)

All Systems Conducting UCMR Monitoring

Figure 1. UCMR (1999) Implementation Timeline
UCMR Statistical Design August 2001

5

2. Determining the UCMR Sampling Frame

2.1 Background

A critical first step in selecting a nationally representative sample of small PWSs for the UCMR is

the selection of a sample frame, i.e., an appropriate inventory list of PWSs from which to select the

sample. This is particularly true in a stratified sample such as designed for the UCMR. Stratified

sampling studies are often subject to strata migration problems, which are caused by the inaccurate

strata classification of systems in the design and sample selection phase and which can complicate

and jeopardize the results of the strata-based sampling. Although the Safe Drinking Water

Information System (SDWIS) provides the raw inventory list, or “total population,” of PWSs from

which the statistical sample is drawn, SDWIS is not designed to be a sample frame. Many properties

of SDWIS, and, more importantly, some lingering problems of system classification in SDWIS, can

result in many inaccuracies for sample frame applications such as the sample selection procedures

necessary for the UCMR statistical sampling. 

EPA utilized the inventory list provided by the 1999 Drinking Water Infrastructure Needs Survey

(Needs Survey) to select small systems for Assessment Monitoring and Screening Survey

monitoring, and to select large systems for Screening Survey monitoring. EPA then improved upon

the SDWIS inventory and created a more suitable inventory list for a sample frame. The sample

frame improvements and sample selection considerations used to improve the 1999 Needs Survey

inventory information for use as the UCMR sampling frame are described in the following sections

of this document. 

2.2 Needs Survey Inventory Background

The Needs Survey is conducted every four years to assess infrastructure needs of the Nation’s

drinking water systems. The Needs Survey data, along with other relevant information, is also used

to allocate State Drinking Water Revolving Fund (DWSRF) monies. The Needs Survey requires that

inventory information is as accurate as possible so that PWS needs are accurately estimated. A

process was established to develop a reliable and accurate database from which to draw the Needs

Survey samples. The Needs Survey inventory is based on inventory information on all PWSs

included in SDWIS as of March 1998. The steps used to ensure that inventory data (system status,

population served, number of service connections, source of water, contact name and address, etc.)

are correct are described in detail below.

2.3 Needs Survey Sample Frame Improvements

2.3.1 Community Water Systems

Inventory data are confirmed before being used by the Needs Survey. The Needs Survey uses the

confirmed data in specific size categories (large and medium CWSs serving greater than 50,000

people, and 3,301 to 50,000 people, respectively) to select systems that will complete questionnaires

describing current and future system infrastructure needs. Inventory data are also confirmed before

small CWSs serving less than 3,300 people and non-profit non-community water systems are

selected for site visits. 

Problematic data were first identified and addressed based on the experience of the 1995 Needs

Survey. This step included reviewing and cleaning up odd, repeated values (such as repeated “99s"

for the population-served value). EPA then provided the confirmed inventory data to the States
UCMR Statistical Design August 2001

6

(including the Virgin Islands and Puerto Rico) for review and asked the States to provide any

necessary changes. 

EPA also worked with the States to identify the total “consecutive” population served (including the

population of retail buyers) by many prominent large systems, and to group systems into size and

type categories that more accurately reflect actual populations served by a particular water system.

For instance, the reported population served by the Metropolitan Water District of Southern

California (MWD) was adjusted to account for the fact that the system actually serves a much larger

population than the SDWIS inventory suggests. Based on the SDWIS inventory, the MWD is

categorized as a small system serving less than 3,300 people. Adjusting the population to account

for the approximately 16 million consumers actually served by the system, the system is then

reclassified as a large system, which accurately reflects how this system is regulated under the

SDWA. This example highlights the types of changes incorporated into the adjusted sample frame

through identification of the consecutive population served. 

On site inventory verifications were conducted for States where: (1) the 1995 inventory verification

discrepancy rate was greater than 1 percent; or (2) the number of CWSs in a State in SDWIS as of

March 1998 was at least 3 percent greater than in the sampling frame used for the 1995 Needs

Survey. On site inventory verifications were also conducted for States that contributed to at least

0.8 percent of total national need in the 1995 Needs Survey, and if EPA determined that SDWIS

inventory may not accurately reflect a State’s inventory. Inventory verifications were conducted in

Arizona, Arkansas, California, Colorado, New York, North Carolina, Ohio, Oklahoma, and

Tennessee. SDWIS-Fed inventory information for Virginia was replaced with SDWIS-State

inventory information, since SDWIS-Fed was known to be an inaccurate source of current inventory.

The process of State corrections includes a variety of inventory review procedures and data

verifications as described below:

C A stratified random sample of systems was used to select systems within each State that

would then be subject to inventory verification. The systems were stratified by service size

category and water source (surface or ground water), and a representative sample was

selected for each State to represent a 95 percent confidence level with a relative error of 10

percent. The sample was selected based on the expected proportion of systems with

discrepancies, from experience with data verifications conducted by EPA between 1991 and

1997. CWSs serving 25 to 1,000 people were expected to have a discrepancy rate of 7.5

percent, while CWSs serving 1,001 to 40,000 people were expected to have a discrepancy

rate of 5 percent. 

C A two-staged cluster sampling approach was used to select systems in New York, since data

in this State are managed by numerous district offices. The first stage selected enough

offices to include systems of all strata in the sample. The second stage was a random sample

of systems within the district offices. 

C Sanitary survey information, bacteriological results, or other chemical records in State files

and/or databases were reviewed on site to ensure that inventory data were accurate. If

inventory information was different between SDWIS and the State files and/or database, a

discrepancy was issued. Each State so identified was then given an opportunity to provide

monitoring results or other documentation of a system’s characteristics, and, in some cases,

documentation of a system’s actual existence. Systems that were inactive were removed

from the Needs Survey sampling frame, while other systems were re-categorized if

necessary. For instance, SDWIS may have a system categorized as a surface water system,

while State records indicate that the system purchases surface water. It is this type of miscategorization that is routinely corrected in the Needs Survey sample frame. 
UCMR Statistical Design August 2001

7

C Based on results of the inventory verification, the total inventory for each State was further

refined. The inventory verification results were extrapolated to all systems in each State to

estimate the number of active systems in each size and type category (stratum). The

determined proportion of inactive systems in the inventory verification sample was applied

to the number of total systems in the sample frame. Then systems were assigned to each

stratum based on the proportion of active systems that moved from one stratum to another.

For instance, if 5 percent of systems in the inventory verification sample were inactive, then

it was assumed that 5 percent of the total number of systems in the State were inactive. This

was then applied to the revised active frame, reflecting the final inventory of active systems

in a State. 

The Needs Survey sample frame was further refined during the course of the data collection period.

System status as of January 1, 1999 was used to determine inclusion and placement within the

sample frame. Additional systems were added to the sampling frame based on information provided

by the State of Virginia in the last quarter of 1999. 

2.3.2 Non-transient Non-community Water Systems

Limited verification was conducted on the non-profit non-community water systems (NCWSs). A

random sample of 100 systems was selected from the total number of non-profit NCWSs across the

US to determine how many systems would be selected in each State for a site visit. This random

sample was used only to estimate the number of systems in each State where EPA would conduct

a site visit. The actual sample of non-profit NCWSs were then randomly selected from the counties

in each State where EPA already had plans to conduct site visits at small CWSs. The sample of nonprofit NCWSs was not selected based on strata, and only non-profit NCWSs were selected for review

for the Needs Survey (since they are the only NCWSs that are eligible to receive DWSRF monies).

The sample of non-profit NCWSs does not include transient non-community water systems. The

sample size of 100 systems provides a confidence level of 95 percent and a margin of error of 30

percent. 

Thus, for UCMR use, inventory data for NTNCWSs has undergone the least confirmation and

correction. Each State participating in the UCMR through PAs with EPA reviewed the systems

selected by the UCMR process for the SMP

2.3.3 Tribal Water Systems

The sample frame for Tribal systems and Alaska Native water systems was based on input from the

Indian Health Service (IHS) Sanitary Deficiency System (SDS), Tribes, and EPA regions. There are

approximately 940 systems nationwide that are owned and operated by Tribes and Alaska Natives.

Some of the Tribal systems are regulated by the States, and many State-owned and operated systems

serve a large population of American Indians. Since the Needs Survey considers all State-owned and

operated systems, EPA worked with the Tribes, Alaska Natives, the IHS, and the States to determine

how to classify each Tribal system. Each Tribe notified the appropriate EPA region if they believed

that the State-owned or operated system should be considered in the Tribal system sample frame,

rather than in the State sample frame. Inventory information for Tribal systems and Alaska Native

systems were taken from SDWIS, then corrected, and updated by both the appropriate EPA Region

and the IHS. The corrected data were then compiled and comprises the sample frame for the Needs

Survey.

For the UCMR, the Alaska Native systems were grouped with the remainder of the Alaska CWSs

and NTNCWSs. These systems were not grouped with the Tribal water systems. All State-owned
UCMR Statistical Design August 2001

8

and operated water systems that serve a large proportion of American Indians were not treated as

Tribal water systems. The State-owned and operated water systems were treated as State systems

in the UCMR sampling frame. 

2.3.4 System Classifications

Another potentially problematic issue is the source water classification of systems used in SDWIS.

Compliance and monitoring requirements under the SDWA are more stringent for surface water

systems than for ground water systems based on historic occurrence data and vulnerability

considerations. Generally, surface water systems are more vulnerable to releases, spills, and other

potential sources of contamination than ground water systems. Also, water systems can depend on

a single water source type, but can have a mix of sources. Therefore, to ensure that the level and

type of compliance and monitoring requirements are appropriate to the type(s) of source water used

by a water system, EPA created a hierarchy of system source water classifications. The hierarchy

(or sequence from lowest to highest regulatory regime) is: purchased ground water, ground water,

purchased ground water under the direct influence of surface water, ground water under the direct

influence of surface water, purchased surface water, and surface water. This hierarchy helps

establish the appropriate regulatory oversight relative to source water type to provide the highest

degree of human health protection possible. A water system with mixed sources is regulated

according to the water source type used that ranks highest in the regulatory hierarchy. 

This hierarchy of compliance and monitoring classification scheme is designed to implement the

most protective regulatory approach, but it may also pose a problem for the national representative

sample. If a system uses ground water and also purchases surface water, the system will be listed

in SDWIS as a purchased surface water system since purchased surface water ranks higher on the

hierarchy. However, the UCMR sample selection criteria excludes purchased water systems;

therefore, this system would not be selected for inclusion in the national representative sample. The

number of purchased water systems is small compared to the total number of PWSs, and this

exclusion of purchased water systems will not significantly affect the UCMR sample. States and

PWSs adjusted their monitoring schedules to accommodate the above problems relative to the source

of the actual entry points to the distribution system (EPTDS). Using the single SDWIS classification

for each system resulted in some inaccuracies which could not be avoided. These inaccuracies were

corrected where needed by the States or EPA when the SMPS were reviewed. 

2.3.5 Additional Sampling Frame Improvements

The resulting Needs Survey inventory list may not exactly reflect the information in SDWIS in the

fall of 1999 or 2000 since it is likely that a few systems will have changed status in the intervening

time. To minimize the effect of system status changes, EPA verified the status, water source,

population served, and system type for small CWSs in 19 States and three territories where there

were three or fewer PWSs within each stratum (system size category by water source type). Eleven

systems in five States were determined to be inactive. Four systems in four different States purchase

their water, and were removed from the system list. One system changed from a CWS to a

NTNCWS, and seven systems in four States changed their source water type from surface water to

ground water. The population of 12 systems changed, and three systems were moved into a different

service size category. The status of these systems was verified before sample selection to ensure that

the sample of systems selected from these categories was truly representative of the number of

systems in existence.

Each State, as noted earlier, has already received an additional opportunity to correct the inventory

system data and the strata assignments when they reviewed and approved the systems selected for
UCMR Statistical Design August 2001

1 As noted earlier, the inventory sampling frame is based on the 1999 Needs Survey. The original data

were taken from SDWIS in March 1998.

9

their SMPs. Each State (and EPA itself, in the cases where a State did not wish to participate) had

an opportunity to improve the sample by removing systems from the sampling pool that were

inactive, and replace them with active systems from the alternate/replacement list(s) provided to

them. States or EPA were also permitted to remove systems from their SMPs for reasons other than

those listed above, as long as the reasons were clearly explained in consultation with EPA. All

changes were included in the final SMPs sent back to States or EPA so that systems could be notified

of their requirements under the UCMR. States and EPA Regions will continue to update UCMR

inventory information as changes occur.

3. Selecting the Statistical Population for Systems Serving 10,000 or Fewer People

3.1 Determining the Population of Small PWS for Inclusion in the UCMR Sample

The total population of small PWSs is comprised of CWSs, NTNCWSs and transient noncommunity water systems (TNCWSs). Two categories of PWSs were excluded from the population

for selecting the sample. PWSs that purchase their entire water supply from another PWS are

generally exempt from the regulation, since monitoring at these systems could result in double

counting of systems using the same source. Additionally, TNCWSs were excluded from the UCMR,

since projecting contaminant exposure from monitoring results is difficult and inconclusive due to

the transient nature of the population that use these sources of drinking water.

EPA estimates that there are approximately 66,808 non-purchased CWSs and NTNCWSs, based on

the 1999 Needs Survey inventory.1

 Table 1 illustrates the total number of non-purchased CWSs and

NTNCWSs in each service size category (serving 25 to 500, 501 to 3,300, 3,301 to 10,000, 10,001

to 50,000, and greater than 50,000 people) by source water type (ground or surface water), from the

UCMR sampling frame. 

3.2 Stratifying the Population

In developing the representative sample, EPA considered factors such as (1) geographic location, (2)

population served, and (3) water source. The sample was stratified by population served, allocating

samples proportionately to each State by system size, and then by water source type. NTNCWSs

were selected as a separate category since these systems may be a significant source of water

consumed by residents of a community.

Sources of water may not be evenly distributed across any given State. Cities transfer water across

watershed boundaries, or move water from one State to another. To account for the proportion of

the population served by a specific water source, EPA defined "geographic location" as the location

of the water source and stratified the sample further by source of water supply. For example, if 10

percent of the population in a State obtains their water from surface water supplied PWSs that serve

less than 500 individuals, then approximately 10 percent of the sampled systems in that State should

come from the PWSs in this size and source category. The distribution of systems across the State,

then, is accommodated by the population-weighted statistical sample selection. As explained further

in Section 4, the sample is not strictly population-weighted. The sample size for each State and each

stratum were optimized to ensure that UCMR sampling results have a high level of confidence and

a low margin of error. Therefore, the sample was stratified by system type (CWSs and NTNCWSs)
UCMR Statistical Design August 2001

10

Table 1. Systems Serving 10,000 or Fewer People

Population

Served

Total Population Served Nationally Number of Non-p

Size

Category

CWSs NTNCWSs Total CWSs N

Ground

Water

Surface

Water

Ground

Water

Surface

Water

Ground

Water

Surface

Water

Grou

Wat

25 - 500 4,321,261 248,417 2,292,697 68,088 6,930,463 28,149 1,403 16,5

501 - 3,300 12,894,496 2,542,195 2,493,942 179,371 18,110,004 9,551 1,586 2,60

3,301 -

10,000

13,415,514 6,269,284 282,405 57,643 20,024,846 2,349 1,027 55 

Subtotal 30,631,271 9,059,896 5,069,044 305,102 45,065,313 40,049 4,016 19,2

10,0001-

50,000

25,909,335 23,033,999 108,027 0 49,051,361 1,217 993 7 

Over 50,000 30,478,607 139,106,597 0 0 169,585,204 240 482 0 

Total 87,019,213 171,200,492 5,177,071 305,102 263,701,878 41,506 5,491 19,2

The population and water system information used in this table is from the 1999 Needs Survey inventory database. The information in tderive the sample distribution and statistical calculations found in other tables in this document.
UCMR Statistical Design August 2001

11

and by source water type within each small system size category (categories 1 through 3) in each

State.

3.3 Tribal Water Systems as an Individual Stratum

Small PWSs that are located on Tribal lands in each of the 10 EPA Regions were grouped into a

single category for the representative sample; this Tribal category is equivalent to a State for the

statistical selection process. Tribal systems had the same probability of being selected as other water

systems in the stratified random selection process that weighs systems by water source and size class

by population served. Using this discrete stratum ensures that some Tribal systems were selected

as part of the national representative sample. The systems selected comprise the “SMP” for Tribal

water systems. 

3.4 Consistency of State Plans

EPA selected the representative sample from the population of CWSs and NTNCWSs nationally,

then allocated the sample to individual States, weighted approximately for the proportion of the

population served by each service size category and water source type. Based on a stratified random

selection process applied to CWSs and NTNCWSs, the sample size was weighted by population

served (to enable exposure assessments from Assessment Monitoring results) and water source type

(to enable comparisons between surface or ground water) while allocated proportionately amongst

States (to ensure geographic coverage) within service size category (categories 1 through 3). EPA

also randomly selected two alternate/replacement systems for each PWS selected for the national

representative sample. EPA selected a supplemental alternate/replacement list, in cases where the

primary system, and both alternates were determined to be inactive. All of these systems appear in

the initial SMPs sent to States.

States could have include the EPA-selected systems on the initial plan list in their SMP. If, however,

the State review determined that a system on the initial plan list had closed or merged, the system

could be removed from the SMP List. To remove a system from the SMP List and replace it with

another system, the State should have notified EPA of the reasons for removal. Valid reasons for

removal included system closure, system merger, or a determination that a system operates

exclusively with purchased water. To identify a replacement system for the system removed, States

selected the first water system (from the appropriate category) from the existing replacement list for

the PWS removed. (See Section 5 for a more detailed discussion of initial plan and replacement list

selection procedures.) More detailed directions on modifying the initial SMP and using the lists of

alternate/replacement systems are included in the instructions of each SMP.

Once the list of systems was finalized, States informed the EPA Regional Office of the States’ choice

of plans (including the details of any modified plans). The EPA Regional Office worked with the

State to develop an acceptable modified plan. This approach ensures a nationally consistent system

selection process and enables acceptable SMP development with minimal State burden. 

If the EPA Regional Office did not receive the notice of a final SMP within 60 days, EPA assumed

that systems on the initial plan represented the final SMP. The plan also specifies the timing of the

monitoring. 
UCMR Statistical Design August 2001

12

4. Selecting the Representative Sample for Systems Serving 10,000 or Fewer People

4.1 Objectives of the Sample

The representative sample of small PWSs must allow EPA to collect high quality data about

contaminant occurrence. Such data must allow precise estimates of national occurrence (the fraction

of systems in which a contaminant occurs) and exposure (the fraction of people exposed to a

contaminant). The data must also provide enough information within smaller categories of systems

(e.g., small, medium, or large systems) to inform the development of possible regulatory alternatives.

The sample must also be representative of the population of small PWSs. Each of these data quality

objectives are described in more detail in the following section.

4.1.1 Accuracy and Precision

The representative sample of small PWSs must be selected so that the data collected yield accurate

and precise estimates of national contaminant occurrence and exposure.

Accurate or unbiased estimates are correct on average over the long term, or over many samples.

For instance, if the sampling plan were to be carried out many times, the average of the occurrence

or exposure estimates derived from all of the samples would be close to the true occurrence or

exposure fraction of the population. The first data quality objective is that the sample estimates be

unbiased.

Precise estimates have small variability. All estimators are variable: even if an estimator is unbiased

over many samples, the estimate computed from any particular sample will be different from the true

population value. The second data quality objective is to limit the amount of this variability.

Precision may be measured in terms of a margin of error and its associated confidence level. For

estimates of exposure fractions, EPA will allow a margin of error of ± 1% with 99% confidence,

when the estimated exposure fraction is 1%. That is, if the estimated exposure fraction is 1%, EPA

must be able to state with 99% confidence that the true exposure fraction is between 0% and 2%.

The meaning of “99% confidence” is that if the sampling plan were to be repeated many times, the

true exposure fraction would fall within the margin of error around the estimate in 99% of all cases.

EPA specified these stringent statistical parameters to ensure high quality data and dependable

monitoring results. In general, many similar random surveys with continuous variables use a lower

level of confidence (95%) and/or a larger allowable error (plus or minus 5%). However, use of a

larger error is unacceptable for the UCMR. Examination and analysis of current occurrence data

show that many contaminants which are currently regulated, or being considered for regulation,

occur in 1% or less of systems on a national basis. However, for many contaminants, a 1%

occurrence nationally reflects a substantially larger occurrence regionally. Even a small percentage

of systems with detections of a contaminant can translate into exposure of a significant population.

By accepting a greater margin of error, and the resultant smaller sample size, such small national

occurrence might be missed entirely.

There are also other uncertainties and sources of variation in such a sample program. For example,

all contaminants have censored distributions (i.e., “less than the detection level” analytical results)

and there are many factors that affect variability and vulnerability of ground water systems. The

statistical sampling theory used to derive levels of accuracy and precision may not account for all

of these sources of variation. Hence, the high confidence level, low allowable error, and consequent

larger sample size should help ensure adequate data to meet the objectives of the UCMR program.
UCMR Statistical Design August 2001

13

The data quality objective of a 1% margin of error with 99% confidence level holds for CWSs. EPA

is allowing a 2.5% margin of error with a 95% confidence level for NTNCWS since these systems

serve fewer people than CWSs. Therefore, less information is required about NTNCWSs to compute

national exposure estimates. Although more information about contaminant exposure in NTNCWSs

would be desirable, with only 800 systems available for Assessment Monitoring, trade-offs are

required in placing sampling effort where it will yield the most information about exposure. Note

that previous EPA contaminant occurrence research has not identified any significant difference in

the quality of drinking water between CWSs and NTNCWSs (see EPA document A Review of

Contaminant Occurrence in Public Water Systems, EPA 816-R-99-006, November 1999). 

The precision of an estimate is determined in part by the size of the sample used to derive it. Other

things being equal, a larger sample allows a more precise estimate. A rough idea of the sample size

needed to achieve the stated goals for margin of error and confidence may be obtained from the

formula:

(1)

in which n is the sample size; p is the true or estimated exposure fraction, or 0.01 in our case; d is

the desired margin of error, or 0.01; and z is the critical value of the normal distribution at the desired

confidence level. For a 99% confidence level, a table of the normal distribution gives z = 2.58.

Inserting the given values of p, d, and z into equation (1) gives n = (2.58)2

(.01)(.99)/(.01)2 . 659.

Therefore, approximately 659 CWSs are needed to achieve the UCMR’s stated data quality

objectives. Similarly for NTNCWSs, a 2.5% margin of error with 95% confidence gives p = 0.01,

d = 0.025, z = 1.96, and therefore n = 61 NTNCWSs are required to meet UCMR data quality

objectives.

The underlying assumptions of the approximation used to derive equation (1) are: (1) that the

sample is a simple random sample from the population of systems; (2) that the sample is large

enough for a normal approximation to hold; and (3) that in each system the presence of a

contaminant can be determined with certainty. However, these assumptions are more or less untrue

for the UCMR sample, so the estimate of 659 systems is only a rough guideline. Under the more

complicated stratified sampling plan described in Section 4.2, the 800 systems allocated to

Assessment Monitoring are more than enough to meet the objectives of accuracy and precision.

4.1.2 Stratification

EPA must be able to evaluate contaminant occurrence not only nationally, but within categories (or

“strata”) of systems, including source water type (ground or surface), size (3 categories), and system

type (CWS or NTNCWS). Many statutes and regulations are implemented differently for systems

of different size, or for different source water categories. Combining the representative (small

system) sample with the results from all large systems provides increased power in the total sample,

but EPA must also be able to evaluate occurrence, and possible regulatory options, related to the

small systems themselves. The SDWA and many current rules focus on burden reduction for small

systems when feasible.

EPA has not placed a specific limit on the precision that can be achieved within each category of

water systems. In general, the level of precision that can be achieved within any category is less than

for all systems taken together, because fewer samples are taken within a single category. Therefore,

instead of requiring a set level of precision for each category, EPA has taken the approach of

minimizing the highest amount of variability of the estimates within any of the categories, while
UCMR Statistical Design August 2001

14

maintaining the objectives of accuracy and precision of the overall estimates, as described above.

This approach is described further in Section 4.2.

4.1.3 Representativeness

A representative sample should be representative. This implies some sort of fairness in selecting

systems and thereby a fairness in imposing the burden of required sampling. Some properties of a

fair and representative sample are: systems are selected at random; all systems have a chance of

being selected; the characteristics of the sample will be close on average to that of the population,

such as system sizes and types; and systems from all subgroups of interest (e.g., Minnesota, or Size

1 surface water NTNCWS) are present in the sample.

In a representative sample, every system should have a chance of being selected, but not all systems

will necessarily have the same chance. Whether that is true depends on what the sample is intended

to represent. To accurately estimate contaminant occurrence (percent of systems) in PWSs, the

sample should be selected based on systems, so it makes sense to assign an equal probability of

selection to each system. To represent exposure, the sample should be selected based on people

exposed to a contaminant. In this case it makes sense to assign sampling probabilities in proportion

to the population served, so that the systems that serve the most people are most likely to be selected.

Clearly these two types of representativeness conflict and cannot both be optimized in the UCMR

sample. Since EPA needs to represent both contaminant occurrence and exposure for the UCMR,

EPA devised a sampling plan to reflect both the number of systems and the population served by

those systems while maintaining balance between the two objectives. 

Although occurrence is important, EPA is interested first in estimating contaminant exposure. If this

were the only criterion, then EPA would allocate systems to States in proportion to the population

served. Then systems that serve the most people would be sampled most often. This populationweighted allocation can be shown to lead to the most accurate and precise estimates of overall or

national exposure. But a problem with this approach is that it assigns small numbers of systems, or

even zero systems, to the smallest States and territories. For example, Guam serves 0.015% of the

population served by PWSs in the U.S., so a population-weighted allocation would assign 0.015%

of 800 systems to Guam. That is 0.1 systems, or rounded off, zero systems assigned to Guam.

Similarly, American Samoa and the Mariana Islands would each receive zero systems, and Rhode

Island would receive one system. Such a sample would not be fully representative of the population

of CWSs in the U.S.

EPA believes that to be fully representative of the nation, a sample of water systems must include

at least 2 systems from each State and Territory in the U.S. Therefore, EPA has imposed the

additional constraint that its representative sample must contain at least 2 systems from each State

and Territory in the U.S. (The exception is Guam, which has only one PWS in the Needs Survey

inventory; so exactly one system was selected to sample in Guam.)

4.1.4 Summary

To summarize, a sample of small PWS must provide data that meet the following data quality

objectives:

C provide national exposure estimates that are unbiased, and have a margin of error of ±

1% with 99% confidence for CWSs, or a margin of error of ± 2.5% with 95% confidence

for NTNCWSs, when the estimated exposure fraction is 1%;
UCMR Statistical Design August 2001

15

C minimize the maximum variability of exposure estimates within categories of system size

and source water type; and

C sample at least 2 systems from each State and Territory.

The next section describes the sampling plan that EPA designed to satisfy these objectives.

4.2 How the Samples Were Allocated

EPA is using a representative sample of 800 small systems for Assessment Monitoring. The sample

size was selected for various statistical and budgetary considerations. A sample of 800 systems is

more than the approximately 720 systems (659 CWSs and 61 NTNCWSs; see section 4.1.1, above)

needed to meet the first data quality objective, and allows at least two PWSs to be selected in each

State.

To meet the data quality objectives described above, the crucial step is to allocate the sampling effort

in the right amounts among strata (categories) of system size, source water type, and State or

Territory. With 3 size categories, 2 source water types, 2 system types, and 56 States and Territories,

there are 3×2×2×56 = 672 strata in which to allocate the 800 systems for Assessment Monitoring.

EPA used the following three-step procedure to allocate the 800 systems:

1. The systems were allocated among the 56 States and Territories. The allocation was

roughly in proportion to population, but with at least 2 systems allocated to each State

or Territory.

2. Within each State or Territory, a probability was selected for each of the 12 categories

of system size, source water type, and system type.

3. Within each State or Territory, a category was selected at random for each allocated

system, using the probabilities computed in step 2. Within the selected category, a PWS

was selected at random, with probability proportional to its population served among all

PWSs in the category.

In this way, each of the 800 systems was assigned first to a State, then to a category within that State,

then to a particular PWS within the category.

The rest of this section describes how the State allocations and category probabilities were selected

in Steps 1 and 2 above, in order to achieve the UCMR’s stated data quality objectives. The random

assignment of PWSs to categories in Step 3 is described in Section 5. The description in this section

is meant to convey the idea of the procedure and the assumptions used to derive it, but it is not a

complete technical description. A complete description and justification of the procedure is provided

in Appendix A.
UCMR Statistical Design August 2001

16

4.2.1 Allocation of Systems to States and Territories

To obtain the most precise national exposure estimates, the optimal allocation of systems to each

State should be in proportion to the State’s population served. For example, Table 2 below shows

that Texas has about 8.9% of the population served by small systems, so Texas should receive 8.9%

of the 800 systems, or 71.4 systems. This population-weighted allocation has two drawbacks. First,

the allocation is only theoretical, since each State receives a fractional number of systems. Second,

under this scheme some small States receive fewer than two systems. For example, Rhode Island

would receive 1.1 systems, and American Samoa would receive 0.1 systems. To get around this

problem, the population-weighted allocation was modified as follows:

Table 2. Distribution of Small Systems Required to Conduct Assessment Monitoring and

Screening Survey in Each State/Tribe/Territory

State/Tribes/

Territories

Population Served by

Small Systems

(10,000 or less people)1

(Pn)

Number of Small Systems

Conducting Assessment

Monitoring,2

(An)

Number of Small Systems

Conducting Screening

Surveys,3

(Sn)

Tribes4 394,267 7 2

Alabama 826,868 15 4

Alaska 207,650 4 3

American Samoa 6,278 2 2

Arizona 654,139 12 3

Arkansas 736,435 13 8

California 2,706,432 48 24

Colorado 545,759 10 6

Connecticut 348,727 6 2

Delaware 128,494 2 1

Florida 1,810,083 32 11

Georgia 1,254,642 22 12

Guam 5,504 1 0

Hawaii 159,339 3 2

Idaho 436,697 8 2

Illinois 1,599,786 28 8

Indiana 1,108,704 20 8

Iowa 940,771 16 10

Kansas 675,059 12 6

Kentucky 505,977 9 4

Louisiana 1,552,807 27 14

Maine 323,762 6 3

Mariana Islands 12,769 2 1
UCMR Statistical Design August 2001

Table 2. Distribution of Small Systems Required to Conduct Assessment Monitoring and

Screening Survey in Each State/Tribe/Territory

State/Tribes/

Territories

Population Served by

Small Systems

(10,000 or less people)1

(Pn)

Number of Small Systems

Conducting Assessment

Monitoring,2

(An)

Number of Small Systems

Conducting Screening

Surveys,3

(Sn)

17

Maryland 463,283 8 2

Massachusetts 713,312 12 3

Michigan 1,372,119 24 13

Minnesota 912,075 16 8

Mississippi 1,687,841 30 9

Missouri 1,129,714 20 8

Montana 343,389 6 3

Nebraska 471,233 8 4

Nevada 216,851 4 1

New Hampshire 343,257 6 2

New Jersey 934,202 16 6

New Mexico 449,245 8 6

New York 1,700,436 29 14

North Carolina 1,257,791 22 11

North Dakota 199,303 4 2

Ohio 1,595,309 28 7

Oklahoma 853,024 15 5

Oregon 585,945 11 6

Pennsylvania 2,131,859 37 19

Puerto Rico 493,374 9 4

Rhode Island 56,834 2 0

South Carolina 644,915 11 7

South Dakota 219,176 4 2

Tennessee 823,726 14 9

Texas 3,989,818 71 28

Utah 385,852 7 4

Vermont 238,493 4 3

Virgin Islands 92,555 2 1

Virginia 917,521 16 7

Washington 1,013,103 17 10

Washington DC6 0 00

West Virginia 547,661 10 6
UCMR Statistical Design August 2001

Table 2. Distribution of Small Systems Required to Conduct Assessment Monitoring and

Screening Survey in Each State/Tribe/Territory

State/Tribes/

Territories

Population Served by

Small Systems

(10,000 or less people)1

(Pn)

Number of Small Systems

Conducting Assessment

Monitoring,2

(An)

Number of Small Systems

Conducting Screening

Surveys,3

(Sn)

18

Wisconsin 1,193,154 21 12

Wyoming 153,712 3 2

Total 45,071,031 800 360

1 The distribution of samples above is based on the population and water system information in the 1999 Needs Survey

database inventory. 2 This column represents the total number of small systems allocated in individual States/Tribes from the national

representative sample of 800 systems. 3 There are 360 small systems shown for two Screening Surveys (180 for Screening Survey 1 and 180 for Screening

Survey 2) . Note that each Screening Survey Group of 120 large systems will also be required to monitor. Therefore,

there is a total of 300 small and large systems (a total of 600 Screening Survey systems) in each Survey. 4 The number of Tribal water systems includes Tribal systems in each of the 10 EPA Regions. Tribal systems were

aggregated as a State to ensure that Tribal systems were represented in the national representative sample of small

systems in the UCMR. 5 U.S. Territories include American Samoa, Guam, Northern Mariana Islands, Puerto Rico, and the Virgin Islands.

Territories were aggregated as a State to ensure that Territories were represented in the national representative sample

of small systems in the UCMR. 6 The Washington DC water supply is provided exclusively by large PWSs.

1. An initial allocation was computed for each State, in proportion to that State’s population

served by small systems.

2. All allocations were rounded up to the next largest integer, and any allocations less than two

were increased to two. Each State was allocated at least two systems, but the total number

of allocated systems increased to more than 800 systems.

3. Systems were removed one at a time from various States, in such a way as to minimize the

increase in variance of an overall exposure estimate and keep all State allocations at or

greater than two, until the total allocation was reduced again to 800.

The resulting State allocations are shown in Table 2. The results are very close to what one would

get by simply rounding the population-weighted allocations to the nearest integers.

Given the small individual State sample size, no statistically valid conclusions may be drawn at the

State level. However, EPA still considers it important that all States are represented and have the

opportunity to participate in the UCMR. Some contaminants, such as some pesticides, may only be

used intensively in specific regions of the country. It is possible that with the relatively small

number of systems in the representative sample, monitoring may miss contaminants with such

targeted regional use patterns. However, including systems in every State in approximate proportion

to the population served should ensure that contaminants with regional use patterns, to the extent that

they potentially contaminate water supplies, are proportionately represented by the national sampling

design.
UCMR Statistical Design August 2001

19

4.2.2 Calculation of Category Sampling Probabilities

Once systems are allocated to States, they must be allocated to categories of system size, system

type, and source water type, within each State. This allocation is computed not in terms of fixed

sample sizes, but by choosing the probability of drawing each system from each category. In this

way, systems from even the smallest categories have some chance of being sampled.

To see how the sampling probabilities were chosen, consider first a simple allocation in which the

probability of drawing from each category is proportional to the population served in that category.

As described above, this allocation gives the most precise overall national exposure estimates.

Table 3 shows the results of such an allocation, in terms of the expected number of systems sampled

from each category, and the resulting margins of error. For CWSs, an overall exposure estimate of

1% would have a margin of error of ± 0.97%, or a confidence interval of 0.03% to 1.97%, with 99%

confidence. This is slightly better than the first data quality objective described in Section 4.1. On

the other hand, the margins of error in the size-by-source-water-type categories are as high as ± 12%,

so that not much information is gathered about some categories. Similarly for NTNCWS, the margin

of error for an overall exposure estimate is ± 2% at 95% confidence, well within the first data quality

objective; but within smaller categories the margin of error is as high as ± 19%.

Table 3. Sample Allocation Proportional to Population Served: Expected

Number of Systems Drawn From Each Category, and Resulting

Margins of Error for Exposure Estimates

System Type Size Category

Ground

WaterSupplied

Systems

Surface

WaterSupplied

Systems

Total

n 1 error 2 n 1 error 2 n 1 error 2

CWSs

 500 and Under 78 ±3.0 5 ±12.1 83 ±2.9

 501 to 3,300 228 ±1.7 46 ±3.8 274 ±1.6

 3,301 to 10,000 237 ±1.7 111 ±2.5 348 ±1.4

Total 543 ±1.1 162 ±2.0 705 ±0.97

NTNCWSs

 500 and Under 40 ±3.1 1 ±17.4 42 ±3.0

 501 to 3,300 44 ±3.0 3 ±10.8 47 ±2.9

 3,301 to 10,000 5 ±8.8 1 ±19.0 6 ±8.0

Total 89 ±2.1 6 ±8.3 95 ±2.0

 Rows and columns do not add up to totals due to rounding. 

1

 n = expected number of samples drawn.

2

 error = expected normal-theory margin of error, in percent, when the estimated exposure fraction is 

1%, at 99% confidence for CWSs and 95% confidence for NTNCWSs.

 Note: The population-weighted distribution of samples is based on population and water system 

information from the 1999 Needs Survey database inventory. 
UCMR Statistical Design August 2001

20

Table 3 shows that there is room for improvement in the proportional allocation. By shifting some

sampling effort into the categories with smaller allocations, more information can be collected about

those categories. This would reduce the widest margins of error. For example for CWSs, systems

could be shifted into the smallest surface water stratum. The cost would be to gather less information

about the other categories, and also increase the error in the overall estimate. But if the systems are

reallocated, the widest margin of error can be minimized (the UCMR’s second data quality

objective), while keeping the overall margin of error at or below 1% (the first data quality objective).

Appendix A describes the procedure for reallocating PWSs as described above, in order to meet the

first two data quality objectives. Starting from the proportional allocation shown in Table 3,

sampling probabilities are reduced in the categories with the narrowest margins of error, and

increased in the categories with the widest margins of error. As the sampling plan moves farther

away from the proportional allocation in Table 3, the overall margin of error increases. The

procedure stops when further reallocation would cause the overall margin of error to exceed 1% for

CWS, or 2.5% for NTNCWS.

Using this procedure, sampling probabilities for Assessment Monitoring were derived for the

categories of system size, system type, and source water type, to satisfy the first two data quality

objectives described in Section 4.1. The third data quality objective, sampling at least 2 systems per

State or Territory, was already satisfied by allocating systems to States in Section 4.2.1. The

resulting sampling probabilities are provided in Appendix B. Table 4 shows a summary of the

results. Compared to Table 3, systems were shifted to the smallest surface water stratum for CWSs,

Table 4. Sample Allocation for Assessment Monitoring: Expected Number of

Systems Drawn from Each Category, and Resulting Margins of

Error for Exposure Estimates

System Type Size Category

Ground

WaterSupplied

Systems

Surface

WaterSupplied

Systems

Total

n 1 error 2 n 1 error 2 n 1 error 2

CWSs

 500 and Under 72 ±3.1 47 ±4.1 119 ±2.9

 501 to 3,300 218 ±1.8 41 ±4.1 259 ±1.6

 3,301 to 10,000 225 ±1.7 102 ±2.6 327 ±1.4

Total 515 ±1.1 190 ±2.1 705 ±1.00

NTNCWSs

 500 and Under 31 ±3.9 10 ±9.2 41 ±3.8

 501 to 3,300 31 ±3.8 9 ±9.2 41 ±3.6

 3,301 to 10,000 5 ±9.2 8 ±9.2 13 ±7.8

Total 68 ±2.6 28 ±6.0 95 ±2.50

Rows and columns do not add up to totals due to rounding.

1

 n = expected number of samples drawn.

2

 error = expected normal-theory margin of error, in percent, when the estimated exposure fraction is 

 1%, at 99% confidence for CWSs and 95% confidence for NTNCWSs.
UCMR Statistical Design August 2001

21

and to the various surface water strata for NTNCWSs. As a result, the maximum margin of error

in any of the categories decreased from 12.1% to 4.1% for CWSs, and from 19.0% to 9.2% for

NTNCWSs. Although still somewhat high, these errors represent the best that can be achieved with

a sample of 800 small systems, while maintaining a good overall exposure estimate. The resulting

sample allocation reflects the difficulty of obtaining precise information in all categories of systems

from a limited sample. At the same time, the margins of error for overall exposure estimates

increased to exactly 1% for CWSs and 2.5% for NTNCWSs, meeting the first data quality objective.

Margins of error in some categories also increased slightly, by up to 0.8%.

The methodology used to derive the sampling probabilities requires some simplifying assumptions.

As a result, the margins of error in Table 4 are only approximately correct. The methodology and

its limitations are described in detail in Appendix A. An important simplifying assumption is that

once a system is selected for sampling, the presence or absence of a contaminant can be determined

with certainty. Of course this assumption is not true; if a contaminant is not detected in a system in

a finite number of samples, it may never be present there, or it may only have been absent or

undetectable when the samples were taken. Because the derivation or the sampling probabilities

ignore this source of uncertainty, the margins of error tend to be underestimated. Occurrence

estimates may also turn out to be negatively biased, since contaminants that are present will not

always be detected in a finite number of samples. To account for this additional uncertainty would

require data or assumptions about the frequency and spatial and temporal variability of occurrence,

as well as the spatial distribution of samples. Such information was not available for the design of

the sampling plan. Once sampling takes place and some occurrence data are available, corrected

confidence intervals and occurrence estimates may be computed.

Due to the small sample size of the NTNCWSs in the ground water and surface water categories

within each size category (Categories 1 through 3), statistical conclusions about NTNCWSs must

be analyzed with caution. Conclusions about NTNCWSs cannot be based on source water type since

the margin of error would be too great. Note that since the actual allocation of systems to each

Table 5. National Representative Sample Distributed by System Size Category and

Water Source Type as Selected for the Initial SMPs 

Size Category

(by population

served)

Number of 

CWSs

Number of

NTNCWSs

Subtotal of All

Systems by Water

Source Type Total

Ground

Water

Surface

Water

Ground

Water

Surface

Water

Ground

Water

Surface

Water

 Category 1 500 and

Under 76 51 36 8 112 59 171

 Category 2 501 to

3,000 208 38 30 7 238 45 283

 Category 3 3,001 to

10,000 230 106 4 6 234 112 346

Total 514 195 70 21 584 216 800 
UCMR Statistical Design August 2001

22

service size category was randomized, the number of systems selected to monitor for each service

size category were different from the expected sample allocation once the random number generator

was used, as described in more detail in Section 5. Table 5 shows the composition of the actual

national representative sample of 800 systems as selected for the initial SMPs. Once each State

reviewed their initial SMP, the sampling distribution was expected to change. For instance, if a State

had only one ground water system serving 25-500 people which was selected to monitor for the

UCMR and this system was inactive (and had no replacement systems), this system was likely

replaced by a system in the State within another service size and/or water source category

(replacement systems are discussed further in Section 5). The number of systems that monitor for

the UCMR within each stratum will be included in future EPA documents that describe sampling

results.

4.3 Statistical Implications of the Sampling Plan

Once system selection, sampling, chemical analysis, and reporting are complete, EPA will estimate

occurrence and exposure of the 12 List 1 contaminants (see Section 8, Assessment Monitoring), and

their associated margins of error. These estimates will take into account the nature of the sampling

plan, in particular the different probabilities of sampling from systems in different strata. In this

section the occurrence and exposure estimates and two different kinds of confidence intervals are

described, which take the sampling plan into account. This section provides only a summary; a

complete description is provided in Appendix A.

4.3.1 Occurrence and Exposure Estimates

When some systems are more likely to be sampled than others, an unbiased estimate of occurrence

or exposure has to take the sampling probabilities into account, by giving less weight to those

systems that are more likely to be sampled. An estimator that does this is:

μ$ = (2)

=

∑ Wc y

p

ii i

i 1 i

800

where

E stands for “summation”;

i are the sampled systems, 1,...,800;

yi = 1 if the contaminant occurs in system i, 0 otherwise;

Wi is the weight given to system i

= population served by system i, for exposure estimates; or 1, for occurrence estimates;

pi is the probability of choosing system i;

ci is a constant, computed in Appendix A.

For example, for an exposure estimate, a sampled system receives more weight in equation (2) if it

serves more people (greater Wi), and less weight if it is more likely to be chosen under the sampling

plan (larger pi in the denominator). Because of the weighting in equation (2), some systems were

made more likely to be sampled in order to meet the UCMR’s data quality criteria, as described in

Section 4.2, without incurring any bias in the exposure or occurrence estimates. (The constant ci in

equation (2) performs a similar function to n-1 in an ordinary arithmetic mean, correcting for the total

number of observations in the sample. Details and a more precise definition of are provided in μ$

Appendix A.)
UCMR Statistical Design August 2001

23

There is an overlap between the populations served by CWSs and NTNCWSs. In the absence of

information about the number of people obtaining their drinking water from CWSs or NTNCWSs

and their degree of exposure, there is no way to combine exposure estimates from these two classes

of systems in the right proportions to reflect people’s total exposure. For this reason, exposure

estimates will be computed separately for CWSs and NTNCWSs, and will not be combined into a

single overall exposure estimate.

4.3.2 Margins of Error

The error ranges in Table 5 were computed using the statistical formulas shown in Appendix A,

using the sampling probabilities and a normal approximation to the estimation error. The normal

approximation is valid when the expected number of detections is large enough. The expected

number of detections is n*p, where n is the number of systems selected and p is the fraction of

systems in which the contaminant occurs. In order for the normal approximation to hold, Casella

and Berger (1990) recommend n*p$5, while Parzen (1960) recommends n*p$10. For CWSs in

Table 5, where n = 705 and p = 0.01, n* p = 7.05. By this measure, the normal approximation may

not be valid. Moreover, Table 5 shows a clear problem with the normal approximation: the error

bounds are so wide that they include negative occurrence fractions within the margin of error. For

example, among very small ground water CWSs in Table 5, when the observed fraction of systems

with a contaminant is 1 percent, a 99% confidence interval for the true fraction is 1% ± 3.1%, or

[!2.1%, 4.1%]. This interval allows the possibility of a negative fraction of occurrence, which

cannot logically occur. The interval may be truncated to [0, 4.1%], but the need to truncate suggests

that the normal approximation does not lead to an accurate confidence interval.

The normal-based confidence interval is only one of several possible confidence intervals for an

estimated proportion. Newcombe (1998) compares seven such intervals, including two varieties of

the normal interval. Of these, the Wilson score interval without continuity correction (Wilson, 1927)

has good statistical properties (e.g., the stated confidence level is approximately correct for a wide

range of n and p), is simple to compute, and unlike the normal interval, always gives confidence

limits between 0 and 1. Given an estimated occurrence fraction p from a sample of size n, the

Wilson score interval for p is computed as shown in equation (A-13) of Appendix A.

Table 6 compares the normal and Wilson confidence intervals for CWS, still assuming an estimated

occurrence fraction of p = 0.01, and using the expected sample sizes summarized in Table 3. A

simple interpretation of these intervals is that the normal interval equals p, the estimated fraction,

plus or minus some amount, while the Wilson interval is approximately p times or divided by some

amount. For example, for very small ground water CWSs, the Wilson interval is [0.1%, 11.2%], or

about 1% x / ÷ 11. So according to the Wilson interval, the true occurrence fraction lies somewhere

between 0.1% and 11.2%, with 99% confidence. By comparison, the normal interval for this

example is -2.1% to 4.1%. Although the Wilson interval in this example is wider than the normal

interval, it is more believable in part because it does not include negative occurrence values.

The normal-based error ranges in Tables 3 and 4 are useful as a rough guide to the expected

precision of an estimated occurrence fraction. Moreover, the normal approximation yields the

simple formula in equation (1) for estimating the sample size needed to achieve a given precision

with given confidence. However, when computing confidence intervals for the estimated proportion,

the Wilson score interval is preferred, both because of its good statistical properties and because it

avoids the possibility of including negative occurrence values.
UCMR Statistical Design August 2001

24

Table 6. Comparison of 99% Normal and Wilson Score Confidence Intervals for

Exposure Estimates in CWSs under Assessment Monitoring

Size Category Ground WaterSupplied SystemsSurface WaterSupplied SystemsAll

Normal Confidence Intervals

500 and under [-2.1, 4.1] [-3.1, 5.1] [-19, 3.9]

501 to 3,300 [-0.8, 2.8] [-3.1, 5.1] [-0.6, 2.6]

3,301 to 10,000 [-0.7, 2.7] [-1.6, 3.6] [-0.4, 2.4]

All [-0.1, 2.1] [-1.1, 3.1] [0.0, 2.0]

Wilson Score Confidence Intervals

500 and under [0.1, 11.2] [0.1, 17.9] [0.1, 10.3]

501 to 3,300 [0.2, 4.8] [0.1, 18.2] [0.2, 4.3]

3,301 to 10,000 [0.2, 4.7] [0.1, 8.4] [0.3, 3.7]

All [0.3, 2.9] [0.2, 6.2] [0.4, 2.6]

Confidence intervals are in percent, when the estimate exposure fraction is 1%.

5. Selecting Systems for the Initial Plan List and the Replacement List in Each State

EPA selected the PWSs for the national representative sample through a two-staged random

selection process. Once the number of Assessment Monitoring systems were selected for each State,

EPA selected the individual stratum from which the systems would be selected. The individual

systems within each stratum were then selected. The sampling process is described in detail below.

EPA first calculated the probability of selecting each stratum for both CWSs and NTNCWSs

together (i.e., so that the cumulative probability of selecting any stratum from an individual State

equals one). The method of computing the sampling probabilities was described in Section 4.2. A

random number generator was then used to allocate the systems to strata of system type, system size,

and source water type. For instance, for a State that is allotted 10 PWSs for the UCMR sample, the

random number generator was run 10 times and was then compared to the cumulative probability

of selection to designate the strata from which the individual PWSs were selected.

In the example shown in Table 7 for the State of Colorado, the random number generator was run

ten times, returning the following set of numbers: 0.793739, 0.474497, 0.245539, 0.647118,

0.558134, 0.647613, 0.416625, 0.889291, 0.94107, and 0.457243. Based on comparing these

randomly generated numbers to the cumulative probability column in Table 7, one PWS was a

surface water based CWS serving 25-500 people, one was a ground water based CWS serving 501-

3,300 people, three were surface water based CWSs serving 501-3,300 people, two were ground 
UCMR Statistical Design August 2001

25

Table 7. Cumulative Probability of Selection by Stratum for Colorado

System Type System Size Water Source Probability Cumulative

Probability

Expected

Number of

Systems

Actual

Number of

Systems

CWS 25-500 GW 0.089138 0.089138 1 1

CWS 25-500 SW 0.188764 0.277903 2 1

CWS 501-3300 GW 0.166154 0.444056 2 0

CWS 501-3300 SW 0.138157 0.582213 1 3

CWS 3301-10000 GW 0.129963 0.712176 1 2

CWS 3301-10000 SW 0.21383 0.926007 2 2

NTNCWS 25-500 GW 0.002338 0.928344 0 0

NTNCWS 25-500 SW 0.008918 0.937263 0 0

NTNCWS 501-3300 GW 0.001276 0.938538 0 0

NTNCWS 501-3300 SW 0.001898 0.940436 0 1

NTNCWS 3301-10000 GW 0 0.940436 0 0

NTNCWS 3301-10000 SW 0.059564 1.000000 1 0

water based CWSs serving 3,301-10,000 people, two were surface water based CWSs serving 3,301-

10,000 people and one was a surface water based NTNCWS serving 501-3,300 people. When the

random number does not exactly match the cumulative probability, the random number was

“rounded” up to the next category. The number of systems to be selected from each stratum was

calculated with replacement. This means that each stratum in the State could be selected more than

one time. 

Table 7 also shows the expected number of systems to be allocated to each stratum within the State.

The “Expected Number of Systems” column shows the sample distribution if the sample were

selected solely based on the proportion of the population served by each stratum. The actual

sampling distribution based on using the random number generator is shown in the next column.

Appendix B shows the cumulative probabilities of selection, as well as the expected and actual

number of systems that were allocated to each State for the Assessment Monitoring portion of the

UCMR.

Once systems were allocated to each stratum, systems were then chosen at random from the strata.

To ensure that the systems selected from each stratum were representative of population served, the

probability of selection for each system was taken to be proportional to its population served within

that stratum. For example, a system that served 5% of all people in the stratum of Category 1 ground

water systems in Nebraska would have a 5% chance of being drawn when a system was selected

from that stratum. For systems not to be selected twice, each time a system is selected it is removed

from consideration in its stratum, and the system selection probabilities are re-computed. This is

called sampling without replacement. (Although the systems are sampled without replacement, the

stratum sampling probabilities in Section 4.2 were derived under the assumption of sampling with

replacement. This assumption makes the calculation tractable, at the cost of introducing some error.

The error is small enough to be ignored; see the discussion in Section A.5. in Appendix A.

The Initial SMP included detailed tables with the total number of systems allocated to a State

through this two-staged random selection process. The alternate/replacement list is a list of

additional systems that were randomly selected to replace primary systems in the SMP if necessary.
UCMR Statistical Design August 2001

26

Primary systems were replaced when the primary system was found to be inactive (i.e., the system

closed, merged, or now purchases all of its water from another system). Primary systems could have

also been replaced for other reasons, but the State should have already submitted a request and the

reasons the systems were removed to EPA with their modified SMP. 

EPA randomly selected two alternate/replacement systems for each primary system for every State.

A supplemental replacement list was also generated for each State. The replacement lists were

generated individually to select one replacement for each system selected to monitor for the UCMR.

Once the first replacement list was generated, the second set of replacement systems was selected.

This ensured that each system selected to monitor for the UCMR had two replacement systems

selected from the appropriate stratum. These systems were selected in the same manner as the initial

system list. The third, or general replacement list consisted of a randomly selected number of PWSs

from the remaining PWSs in the State, regardless of system size category, source water type, and

system type. For example, if a ground water based CWS serving 501-3,300 people was inactive, and

if both replacement systems selected for that system were inactive, any system remaining in the

sample frame list may be randomly selected to monitor for the UCMR regardless of system type,

size, and source water type.

6. Selecting Systems for the State Plan

Each State, Tribe, and territory had 60 days to review the initial plan list. The State/Tribe either:

(1) accepted the selections as its SMP and notified the Regional Administrator of its acceptance or

(2) proposed changes to the initial plan list and selected alternates from the replacement list,

including the reasons for the changes, informing the Regional Administrator of the proposed

changes; or (3) took no action within 60 days, which allowed the Regional Administrator to specify

the portion of the representative sample applicable to the State as its SMP. In the second case, the

Regional Administrator had 60 days to work with the State to develop a suitable plan, if problems

were encountered. The Reference Guide for the Unregulated Contaminant Monitoring Regulation

(EPA 815-R-01-023) provides a more detailed discussion of the SMP process. 

Any system(s) removed from the Initial SMP list must be replaced by the system(s) assigned as

replacement systems. If the State determines that both replacement systems are no longer active, the

first active system on the supplemental replacement list becomes the replacement system. 

Each State/Tribe/EPA Region reviewed their SMP to determine that the systems selected have the

appropriate operational status. The State/Tribe/EPA Region then submitted its representative sample

listing to the EPA Regional Office, with all changes from the initial list marked and the reasons for

any changes noted. 

States/Tribes may also sample additional systems. However, any additional PWSs sampled will not

be combined with those of the representative sample for the purpose of computing national estimates

of exposure and occurrence. EPA cannot pay for the testing of these additional systems. These

additional systems, though providing useful information, will bias the national set of systems if

included with those selected using the stated national criteria. However, if the States provide the

results of such monitoring, EPA will receive the data through SDWIS for input to the NCOD.
UCMR Statistical Design August 2001

27

7. Index System Monitoring

EPA identified 30 CWSs in the lower 48 States from the representative sample of small systems to

be “Index” systems. Five systems were selected from each size and source water stratum. The data

collected from the Index Systems will be used partly for added quality control and to better

characterize monitoring results and operating characteristics of small systems. These systems will

be monitored every year during the five year UCMR-listing cycle. This will provide detailed

information regarding temporal variation during the course of UCMR monitoring, as well as possible

effects related to operational changes. EPA will pay for this monitoring, and will provide for

sampling equipment, labor for sample collection, shipment of samples, testing and analysis.

Additional water quality and operational data from these systems may be collected at the same time,

with minimal burden to the systems. The Index Systems were selected so that they are located within

watersheds that have been studied extensively under the United States Geological Survey’s (USGS)

National Water Quality Assessment Program. This allows both the EPA and the USGS to share

information on source water and finished water quality in watersheds across the US. Table 8 shows

the number of systems chosen in each size category as Index Systems from the representative

sample.

Table 8. Distribution of Index Systems in the Representative

Sample

Size Category Number of 

Non-Index Systems

Number of 

Index Systems

 Ground Water

 500 and Under 71 5

 501 to 3,000 203 5

 3,001 to 10,000 225 5

 Surface Water

 500 and Under 46 5

 501 to 3,000 33 5

 3,001 to 10,000 101 5

 Number of Systems

 in the Representative

 Sample

679 30

Note: The distribution of samples indicated above is based on the 1999 Needs Survey database

inventory. 
UCMR Statistical Design August 2001

28

8. Assessment Monitoring

The first component of the UCMR is Assessment Monitoring which will be conducted by all of the

large CWSs and NTNCWSs (except those large systems that purchase all of their water from another

PWS), and by a statistically representative sample of 800 small CWSs and NTNCWSs (except those

small systems that purchase all of their water from another PWS). Assessment Monitoring will be

conducted for the 12 UCMR (1999) List 1 contaminants (listed in §141.40(a)(3) Table 1, UCMR

(1999) List 1). One-third of the representative sample (267 systems) will monitor in each of the

three Assessment Monitoring years (2001 to 2003). This sampling distribution is designed to

facilitate laboratory scheduling and other logistical considerations. The small systems were

delegated to a sampling year by random selection with a 33 percent probability that each system

would be selected in each of the three years. The year for the first system was randomly selected,

then the year for the rest of the systems were chronologically ordered. For instance, the random

number generator selected the year 2002 as the sampling year for the first system. The second

system was then assigned the year 2003, and the third system was assigned 2001, until each system

in the sample had an assigned monitoring year. 

After the sampling year was selected, the sampling months were randomly selected for the systems,

with four samples per year for surface water (and GUDI) systems and two samples per year for

ground water systems. The first month was selected randomly as described above for the sampling

year, then subsequent months were assigned consecutively. One sampling period must be during the

most vulnerable period (May 1 through July 31), as designated in the regulation. Specification of

the monitoring year and month not only facilitates scheduling of laboratory resources, but also

ensures that sampling covers vulnerable periods and all seasons to assess some aspect of temporal

occurrence patterns. To provide States with flexibility in determining vulnerable periods, EPA

allowed the State to modify the vulnerable period for some or all systems in their SMP. The State

should have notified EPA of the reasons for the change. EPA specified the sampling date as the 15th

of each month, plus or minus two weeks. Systems may sample at any time during the month, as long

as all subsequent samples are taken on the same day. The second ground water sample may be taken

within 5 to 7 months of the initial vulnerable period sample. While Index Systems sample during

all five years of the UCMR cycle, each Index System was also assigned an “official” sample year.

Only the data from the official sample year will be used in the national summary of results from

Assessment Monitoring, for consistency with the sample design.

The UCMR does not specify any particular year for Assessment Monitoring for the large PWSs, but

does specify that they must conduct their monitoring within the first three years (2001-2003) of the

UCMR cycle. EPA expects that large system UCMR monitoring for unregulated contaminants will

coincide, whenever possible, with required monitoring for regulated contaminants. Since monitoring

schedules for regulated chemicals depend on system size and detection history, compliance schedules

vary significantly. EPA recognizes that although it will be desirable to collect UCMR samples

concurrently with compliance samples for regulated chemical contaminants, sometimes it may be

difficult to coordinate the two sampling events. Large systems are required to bear the costs of

sampling, testing and reporting the results, and coincident monitoring may help reduce the burden.

9. Screening Surveys

The second component of the UCMR includes the Screening Surveys. Each Screening Survey will

be conducted at a combined total of approximately 300 PWSs randomly selected from the pool of

systems required to conduct Assessment Monitoring. Screening Survey monitoring will be

conducted for the UCMR (1999) List 2 contaminants for which analytical methods have been

developed, but may need to be further refined before large-scale Assessment Monitoring is
UCMR Statistical Design August 2001

29

conducted. There are 15 unregulated contaminants on the UCMR (1999) List 2. Fourteen of these

contaminants are chemical contaminants, and one is a microbiological contaminant. These

contaminants are listed in §141.40(a)(3) Table 1, UCMR (1999) List 2. 

The Screening Surveys are being conducted to assess contaminant occurrence in PWSs, and not to

determine exposure assessment by population (as is the purpose of Assessment Monitoring). EPA

estimates that there will be two different groups of systems involved in the Screening Surveys. Each

group will be comprised of 300 large and small CWSs and NTNCWSs. Small systems will conduct

the first Screening Survey in the year 2001, while large systems will conduct the Screening Survey

in 2002 for the contaminants identified in the List 2 rule. EPA expects that Aeromonas will be

monitored in 2003, since the analytical method will not be completed before the first Screening

Survey. Sampling schedules have been established, in part, to enable Screening Survey samples to

be collected coincident with the Assessment Monitoring samples whenever possible to minimize the

burden to small systems. Large systems are responsible for coordinating their Screening Survey

sample selection with Assessment Monitoring. 

EPA is examining general thresholds to evaluate Screening Survey results, relative to the margin of

error in the sample. For example, if a contaminant occurs over a certain threshold (i.e., in a

percentage of systems/population served), the contaminant may then be placed on the Assessment

Monitoring list and monitored in the next round of the UCMR by all large systems and a

representative sample of small systems. If the contaminant occurrence is below this threshold, it is

possible that no further testing will be required. Factors such as health effects levels will also need

to be considered; hence, thresholds may vary by contaminant.

Systems were selected from all the size and water source categories. However, selection was not

proportionately weighted by population served, or by the proportion of systems in each size category.

If the sample was weighted by population served, a disproportionate number of large systems would

be included in the Screening Surveys. If the sample were weighted by the number of systems in each

size category, a disproportionate number of small systems would be represented. Therefore, each

size category was given equal importance with 60 systems selected from each size category, with the

selected systems distributed evenly between surface water and ground water systems, wherever

possible (i.e., 30 ground water, and 30 surface water systems were targeted to be selected to monitor

for each Screening Survey. Note, however, that there were not enough very small (serving less than

500 people) systems in the sample to select a full 30 systems in this category for each Screening

Survey year. Only 20 very small surface water systems were selected to monitor for UCMR (1999)

List 2 contaminants in 2001. However, the extra 10 systems were selected from the very small

ground water category, so that a total of 40 systems will monitor for the Screening Survey in 2001.

This results in 180 small systems and 120 large systems in each of the Screening Surveys (i.e., a total

of 360 small systems and 240 large systems in the two Screening Surveys). To make national

occurrence or exposure estimates, the resultant data will need to be weighted in relation to these

sample distributions.

Table 9 illustrates the allocation of systems in each size category in each group for each Screening

Survey and the associated margin of errors of estimation at the 99 and 95 percent confidence levels

to evaluate the measurement precision for the sample of 300 systems. Even though there are a total

of 600 systems involved, there will be, as noted, two Screening Surveys performed, by two mutually

exclusive groups of systems, analyzing water samples for two different sets of contaminants. 
UCMR Statistical Design August 2001

30

Table 9. Allocation of Systems for Screening Surveys by Size Category

with the Associated Confidence Levels and Margins of Error

Size Category

Ground WaterSupplied SystemsSurface WaterSupplied Systems All

n 1 99% 2 95% 2 n 1 99% 2 95% 2 n 1 99% 2 95% 2

 500 and Under 40 ±4.1 ±3.1 20 ±5.7 ±4.4 60 ±3.3 ±2.5

 501 to 3,300 45 ±3.8 ±2.9 15 ±6.6 ±5.0 60 ±3.3 ±2.5

 3,301 to 10,000 30 ±4.7 ±3.6 30 ±4.7 ±3.6 60 ±3.3 ±2.5

 Subtotal 

 Small Systems 115 ±2.4 ±1.8 65 ±3.2 ±2.4 180 ±1.9 ±1.5

 10,001 to 50,000 30 ±4.7 ±3.6 30 ±4.7 ±3.6 60 ±3.3 ±2.5

 50,001 and over 30 ±4.7 ±3.6 30 ±4.7 ±3.6 60 ±3.3 ±2.5

 Subtotal 

 Large Systems 60 ±3.3 ±2.5 60 ±3.3 ±2.5 120 ±2.3 ±1.8

 All 175 ±1.9 ±1.5 125 ±2.3 ±1.7 300 ±1.5 ±1.1

1

 Values in the columns with the heading of “n” indicate the number of PWSs allocated to a specific system

size category. 2

 These column headings indicate the confidence level used for evaluation. The values preceded by “±”

listed in these columns are the normal-theory margins of error, in percent, associated with the given

confidence level (either 99% or 95%). Error calculations in the table assume an estimated occurrence

fraction of p = 0.01.

Results from the Screening Surveys are likely only suitable for aggregate national estimates given

the 99 percent confidence level and ± 1.5% margin of error. Only aggregated national estimates are

appropriate because the error margin may be too large in small subcategories (e.g., surface or ground

water systems in a given size category) to be conclusive, particularly in cases where no detections

occur. For example, in very small surface water systems, if a contaminant does not occur in the

screening survey, there is a 95% chance that the national occurrence fraction of that contaminant is

less than 4.4%. Note also that since the total number of systems allocated to each size category is

equal (60 systems per category), the monitoring results will have to be weighted by the proportion

of the population served within each service size category. Monitoring results will have to be

carefully analyzed to correctly assess the possible implications of such results. 

To implement the Screening Surveys, EPA selected 180 small PWSs from the set of 267 systems

(i.e., one-third of the 800 systems in the national representative sample), scheduled to conduct

Assessment Monitoring in 2001 (for the first group) and again in 2003 (for the second group).

Although a Screening Survey is not currently scheduled for 2002, systems were still selected for this

year (in case it was necessary to conduct a Screening Survey in 2002). The probability of a system

being selected for Assessment Monitoring (A) in any given year is 267/800, or Pn(A)=33%. 
UCMR Statistical Design August 2001

31

Given that a system was first selected for Assessment Monitoring (A) in any given year n, the

probability of that system also being selected for Screening Survey (S), is:

(3).

Overall, there was a 22% probability that a system would be selected for the Screening Survey and

Assessment Monitoring in the same year (67% chance of being selected for Screening Surveys,

multiplied by a 33% chance of being selected for Assessment Monitoring). However, if the first

Screening Survey is conducted in the year 2002, the systems selected to conduct Assessment

Monitoring in the year 2001 have no chance of being selected for a Screening Survey. Overall, there

is a 45% chance for a small system to be selected for both Assessment Monitoring and a Screening

Survey simultaneously. Therefore, the probability of a system being selected only for Assessment

Monitoring is estimated as 55%. Figure 2 depicts the number of systems and the probability of a

system being selected for Assessment Monitoring and a Screening Survey.

Similarly, for the large CWSs and NTNCWSs, the probability of a system being required to

participate in a Screening Survey (S) is:

(4).

Therefore, there is approximately a 9% probability that a large system will be chosen for a Screening

Survey.

Again, based on the proportion of population served by small CWSs and NTNCWSs in each State,

the number of systems selected for the two groups of Screening Surveys (Sn) in each State/Tribe n,

is calculated as:

(5).

where Pni is the population served by small systems in State/Tribe n in category i, and NPi is the total

national population served in system category i, and Zi is the total number of systems required to

conduct the survey in that category i. 

Figure 2 illustrates the allocation of systems conducting Assessment Monitoring and two Screening

Surveys in each State/Tribe based on the population served by the systems.

10. Pre-Screen Testing

The third monitoring component of the UCMR is Pre-Screen Testing. EPA established this third

tier of the UCMR monitoring with its stakeholders for contaminants of concern for which analytical

methods are in the early stages of development and/or whose methods are currently too expensive

for wide-scale monitoring. Pre-Screen Testing may also address contaminants that have recently

emerged or been identified as a concern, such as through the Governors’ petition process. The

purpose of this monitoring component will be to determine whether the methods in early

development will provide adequate analytical results in conditions under which the contaminants are
UCMR Statistical Design August 2001

32

most likely to occur. There are nine contaminants on the UCMR (1999) List 3, including seven

microbiological contaminants and two radiological contaminants. The complete list may be found

in §141.40(a)(3) Table 1, UCMR (1999) List 3.

EPA will ask each State to identify a list of between 5 and 25 systems that might be most vulnerable

to the UCMR (1999) List 3 Pre-Screen Testing contaminants. EPA will define a process to select

up to 200 large and small PWSs from the list of systems nominated by States. The Pre-Screen

Testing will use analytical results from a small sample to evaluate and improve methods, and to

conduct an initial assessment of occurrence. Given the small number of Pre-Screen Testing systems,

the monitoring results cannot be used to estimate national occurrence of UCMR (1999) List 3

contaminants in a statistically rigorous manner. EPA will provide further guidance on Pre-Screen

Testing contaminants after the List 3 Rule is promulgated.
UCMR Statistical Design August 2001

33

800

Representative

Systems

(100%)

266 systems

(33% of 800 system)

267 systems

(33% of 800 systems)

267 systems

(33% of 800 systems)

Assessment Monitoring

 +

Screening Survey

(45%)*

Assessment 

Monitoring

Only

(55%)*

180 systems

(67% of 267 or 22.5% of

800 systems)

180 systems

(67% of 267 or 22.5% of

800 systems)

87 systems

(33% of 267 or

11% of

800 systems)

266 systems

(33% of 800 

systems)

2001

2002

2003

UCMR

Monitoring

Year

Assessment

Monitoring

in any

given year

* Overall Probability (over three years)

87 systems

(33% of 267 or 11% of

800 systems)

Figure 2. Number and Probability of Small Systems Chosen for Assessment Monitoring and

Screening Surveys for the UCMR Years 2001-2003
UCMR Statistical Design August 2001

34

11. References

Casella, G. and Berger, R. (1990), Statistical Inference, Pacific Grove, Ca, Wadsworth.

Cochran, W. G. (1977), Sampling Techniques (3rd ed.), New York, Wiley.

The MathWorks, Inc. (1996), Using MATLAB, Natick, MA.

The MathWorks, Inc. (1999), Optimization Toolbox User’s Guide, Natick, MA. 

Newcombe, R.G. (1998), “Two-sided confidence intervals for the single proportion:

comparison of seven methods,” Statistics in Medicine, 17: 857-872.

Parzen, E. (1960), Modern Probability Theory and Its Applications, New York: Wiley.

Wilson, E.B. (1927), “Probable inference, the law of succession, and statistical

inference,” Journal of the American Statistical Association, 22: 209-212.
UCMR Statistical Design August 2001

Appendix A

Statistical Theory and Optimal Choice of Probabilities

for Probability-Weighted Estimation

This appendix presents some statistical theory for the methods of estimation, confidence intervals,

and selection of sampling probabilities that were used to derive the sampling plan for Assessment

Monitoring, as described in Section 4. The theory is presented here in order to show that, subject

to the approximations described in Section A.5, the sampling plan will provide occurrence and

exposure estimates that meet the UCMR’s data quality objectives of accuracy and precision, as

described in Section 4.

The discussion below requires that the reader be familiar with basic statistical theory, for example

as in Casella and Berger (1991). It extends some of the sampling theory of Cochran (1977), but

does not require that the reader be familiar with that book.

A.1 Probability-Weighted Estimation

Suppose we have a population of N systems of interest. For example, we could consider the population of N = 63,869 small PWSs in the United States and Territories. Fix a single contaminant of

interest. For each system i = 1, . . . , N, let yi = 1 if the contaminant occurs at any time in system

i, or 0 otherwise. We want to estimate the weighted mean

μ =

X

N

i=1

Wi yi (A-1)

where the Wi are given weights. For example, if Wiis the number of people served by system

i, then μ is the number of people exposed to the contaminant. If S is a subset of systems and

Wi = 1{i ∈ S}/#{S}, where 1{A} equals 1 if the event A is true or 0 if A is false, and #{S} is the

number of systems in S, then μ is the fraction of systems in S that have some occurrence of the

contaminant.

In order to estimate μ, consider the following sampling scheme. We draw D independent samples.

The d-th sample consists of nd i.i.d. system numbers Id1, . . . , Idnddrawn with replacement from

the distribution P(Id1 = i) = pdi , where pd1, . . . , pd N are given probabilities, PN

i=1

pdi = 1.

The systems numbered Id1, . . . , Idnd

are then sampled, and yId1, . . . , yIdnd

are obtained. The total

number of systems sampled is n =

PD

d=1

nd .

A-1
UCMR Statistical Design August 2001

To compute an unbiased estimate of μ using this sampling scheme, let qdi = 1{pdi > 0}, ci = PD

d=1

ndqdi−1, and

μˆ =

X

D

d=1

Xnd

j=1



W yc

pd



Id j

. (A-2)

Here 

W yc

pd



i

is a simplified notation for Wi yi ci

pdi

. This notation simplifies formulas and is used

repeatedly below.

We call μˆ the probability-weighted estimator of μ, given the sampling probabilities pdi . μˆ includes

two bias corrections: ci acts like n

−1

in a sample mean, correcting for the total number of possible

observations on a system; and p

−1

di gives greater weight to observations that are expected to be

drawn less often within a sample. In order for cito be defined, we require that PD

d=1

ndqdi > 0 for

each i. This is equivalent to assuming that each system has positive probability of being sampled

at least once.

Cochran (1977, Section 9A.3) considers μˆ in the case D = 1. He calls μˆ the “probability proportional to p” estimator. A special case is probability proportional to size (pps), in which pdi ∝ Wi

.

In this case systems are sampled in proportion to their weight in μ, and when D = 1 the estimator

is just the sample mean, μˆ = n

−1 Pn

j=1

yIj

. The pps estimator is easily shown to be the minimum

variance unbiased estimator of μ when there are no constraints on the ps.

The following Theorem gives properties of μˆ. See also Cochran (1977, Section 9A.3) for the case

D = 1.

Theorem 1. Let μd =

PN

i=1

(W ycqd )i and μˆ d = n

−1

d

Pnd

j=1



W yc

pd



Id j

.

(a) μˆ is an unbiased estimate of μ.

(b) Var(μ)ˆ =

PD

d=1

nd

PN

i=1

pdi  W yc

pd



i

− μd

2

.

(c) An unbiased estimate of Var(μ)ˆ is Vˆ(μ)ˆ =

PD

d=1

nd

nd−1

Pnd

j=1

 W yc

pd



Id j

− ˆμd

2

.

Note. When pdi = 0, we define μˆ in (A-2) to replace p

−1

di by an arbitrary number. This leaves

the estimator unchanged, since the affected systems are sampled with probability zero. But in

Theorem 1(b) and below it allows us to write pdi/pdi = 0 when pdi = 0.

A-2
UCMR Statistical Design August 2001

Proof of Theorem 1. First prove some facts about μd and μˆ d :

μ =

X

i

(W yc)i

X

d

nd qdi =

X

d

nd

X

i

(W ycqd )i =

X

d

ndμd , (A-3)

μˆ =

X

d

ndμˆ d , (A-4)

E(μˆ d ) = E



W yc

pd



Id1

=

X

i

pdi 

W yc

pd



i

=

X

i

(W ycqd )i = μd , (A-5)

Var(μˆ d ) = n

−1

d VarW yc

pd



Id1



= n

−1

d

X

i

pdiW yc

pd



i

− μd

2

. (A-6)

(a) Eμˆ =

P

d

nd Eμˆ d =

P

d

ndμd = μ, by (A-4), (A-5), and (A-3).

(b) Var(μ)ˆ =

P

d

n

2

d Var(μˆ d ) by (A-4); apply (A-6).

(c) Let vˆd =

Pnd

j=1

 W yc

pd



Id j

− ˆμd

2

. Standard results give Evˆd = (nd − 1) Var W yc

pd



Id j



=

nd (nd − 1) Var(μˆ d ), so EVˆ(μ)ˆ =

P

d

nd

nd−1

Evˆd =

P

d

n

2

d Var(μˆ d ) = Var(μ)ˆ by (A-4).

A.2 Stratified Sampling

Suppose now that the N systems are divided into T strata. The s-th stratum contains Ns systems,

so N =

PT

s=1 Ns

. For the purposes of the UCMR, a stratum is a combination of State or Territory

(1 of 56), system size (1, 2, or 3), source water type (GW or SW), and system type (CWS or

NTNCWS). Thus there are T = 56 × 3 × 2 × 2 = 672 strata. We could also consider smaller sets

of strata, for example just the 6 size-by-source-water-type strata.

Instead of a single system number i, each system is now identified by a stratum number s and a

system number h within stratum s. This is just a relabeling of the systems, so the development of

Section A.1 still holds, with i and I replaced everywhere by (s, h) and (S, H). The estimand is

μ =

PT

s=1

PNs

h=1 Wsh ysh, and in the d-th sample we draw i.i.d. stratum and system number pairs

(Sd1, Hd1), . . . , (Sdnd

, Hdnd

) using P(Sd1 = s, Hd1 = h) = pdsh.

An important special case is when the mean weights Wsh and sampling probabilities pdsh are the

same for all systems h within a stratum. That is, assume

Assumption 1. Wsh = Ws and pdsh = pds for all d, s, and h.

In this case let rds be the probability of drawing the next system from stratum s: then rds =

P(Sd1 = s) =

P

h

pdsh = Ns pds, so μˆ becomes

μˆ =

X

D

d=1

Xnd

j=1



Uc

rd



Sd j

y(S,H)d j (A-7)

A-3
UCMR Statistical Design August 2001

where the new mean weights are Us = WsNs. The Us have a “per stratum” interpretation instead

of “per system.” For example, if before Wsh was the number of people served by system h in

stratum s, now Usis the number of people served by all of stratum s.

From here forward we consider only the special case of Assumption 1. This has the advantage that

instead of simultaneously drawing S and H using pdsh, we can now think of first drawing a stratum

number S with probabilities rds, then drawing a system number within S from a uniform distribution on {1, . . . , NS}. Since the system numbers are uniformly distributed within each stratum, we

do not have to compute their probabilities and will concentrate on the strata.

A.3 Optimal Choice of Probabilities

In this section we describe a procedure for choosing the sampling probabilities rds in order to

minimize the variance of certain mean estimates, subject to upper bounds on the variance of other

mean estimates. Some simplifying assumptions are required in order to solve the problem. We first

formulate the optimization as a nonlinear programming problem, and then describe some details

of the implementation.

A.3.1 Problem Formulation

Let

P

μ1, . . . , μE+F be means of interest, each determined by a given set of weights: μi =

s,h Wish ysh. Suppose that a set of samples will be drawn as described in Section A.1, and each

μi will then be estimated by μˆi as in (A-7). The problem in this section is to find sampling probabilities rds that minimize the maximum variance of μˆ 1, . . . ,μˆ E, subject to given upper bounds

on the variances of μˆ E+1, . . . ,μˆ E+F. If R = [rds]

D T

d=1,s=1

is the matrix of sampling probabilities,

then we want R that solves

min

R

max {Var(μˆ 1), . . . , Var(μˆ E)}

s.t. Var(μˆ E+i) 6 ui, i = 1, . . . , F

R1 = 1

R > 0

(A-8)

The variance bounds ui could be chosen, for example, to give normal-theory confidence intervals

of no more than a specified width at a specified confidence.

The first simplifying assumption is that mean weights and sampling probabilities are constant

within each stratum. This is Assumption 1 of the previous section. Assumption 1 poses no problem

for estimating occurrence, since then we are just counting systems and every system in a stratum

can receive the same weight. On the other hand for estimating exposure, Assumption 1 is restrictive

since each system should be weighted by its number of customers, which varies within a stratum.

Under Assumption 1 we are forced instead to use, say, the mean number of customers per system

in each stratum. However, if the strata are based sufficiently on size so that most of the variation in

A-4
UCMR Statistical Design August 2001

system size is between and not within strata, then the restriction due to Assumption 1 will be mild.

Moreover, if information were available about the size distribution within each stratum, a different

assumption could be substituted to use that information. Similarly, other assumptions could be

substituted about the proportions of the pdsh.

Under Assumption 1, the argument of Section A.2 can be applied to Theorem 1(b) to give

Var(μˆi) =

X

d,s

nd

 

U

2

i

c

2qd y ̄

rd

!

s

−

X

d

nd

 X

s

(Ui cqd y ̄)s

!2

(A-9)

where y ̄s = N

−1

s

PNs

h=1

ysh. The only unknowns in (A-9) are y ̄s and rds (since for the purposes of

optimization, qds := 1{rds > 0} are assumed to be given as part of the problem). In order to leave

only rds unknown, we make the next simplifying assumption:

Assumption 2. y ̄s = ρ for all s and some ρ ∈ [0, 1].

The user has to specify a value of ρ. The results of the optimization will be valid only for this

value. For example, the user could choose to optimize the sampling plan for contaminants which

occur on average in ρ = 1% of systems, as in Section 4.

Assumption 2 says that the fraction of occurrence is identical in each stratum. This is obviously

unrealistic, but is a reasonable default in the absence of other information. Again, any other assumption that simplifies or summarizes the effect of the y’s could also be used. For example, the

y ̄’s could be assumed to depend in a simple way on mean system size in each stratum.

Using (2), we can rewrite (A-9) as

Var(μˆi) = ρ

X

d,s

aids

rds

− ρ

2

bi (A-10)

where aids = nd (U

2

i

cqd )s and bi =

P

d

nd

P

s

(Ui cqd )s

2

. We can now rewrite (A-8) in matrix

form. For each i, let ai be a 1×DT row vector of the aids: ai = [ai11, . . . , ai1T , . . . , ai D1, . . . , ai DT ].

In the same way, arrange the rds and r

−1

ds into DT × 1 column vectors r and r

−1

, respectively. Let

A1 = [a

0

1

. . . a

0

E

]

0

, A2 = [a

0

E+1

. . . a

0

E+F

]

0

, b1 = [b1, . . . , bE]

0

, b2 = [bE+1, . . . , bE+F]

0

, and

u = [u1, . . . , uF]

0

. Then (A-8) can be written as

min

r

max (ρA1r

−1 − ρ2

b1)

s.t. ρA2r

−1 6 ρ2

b2 + u

Sr = 1

r > 0

(A-11)

where S is a matrix of 1’s and 0’s such that Sr is the same as R1 (in fact S = ID ⊗ 11×T , where ⊗

is the Kronecker or tensor product).

A-5
UCMR Statistical Design August 2001

Problem (A-11) is a nonlinear program, with both a nonlinear objective function and nonlinear

constraints. It has to be solved numerically. Fortunately, the nonlinearity in (A-11) is not too

bad: each minimax objective and constraint is a linear function of either r or r

−1

. Solution with

nonlinear programming software is therefore more or less routine. The next subsection describes

some details of the implementation.

A.3.2 Implementation

We programmed the optimization described above in Matlab (The MathWorks, Inc., 1996), a matrix computation language. For the optimization step we used the fminimax function in Matlab’s

Optimization Toolbox (The MathWorks, Inc., 1999).

The optimization requires that the user provide the following input:

• The number of systems and number of people served in each of the 672 sampling strata.

For the UCMR this information came from the 1999 Drinking Water Infrastructure Needs

Survey, as described in Section 2.

• A skeletal sampling plan:

– D, the number of independent samples;

– n1, . . . , nD, the numbers of systems in each sample;

– qds, the indicators of positive sampling probabilities. If qds = 1, then the optimization

searches for the optimal positive probability rds of drawing from stratum s during each

draw in the d-th sample. If qds = 0, then the optimization sets rds = 0, so no systems

will be drawn from stratum s during the d-th sample.

• ρ, the assumed occurrence fraction in each stratum.

• Wis, the response weights for the means of interest. In our implementation each mean may

have either occurrence or exposure weights in any combination of strata. Each mean is also

identified as being either part of the minimax objective or subject to a variance constraint.

• ui, the upper bounds for the variance constraints. We parameterized ui by a desired confidence level and half-width of a normal-theory confidence interval.

There are P

d,s

qds probabilities to optimize over, or at most DT probabilities. With T = 672

strata and multiple samples, this number can easily become large enough to prevent the optimization from converging quickly or at all. Some experimentation is required in order to find a sampling

plan for which the optimization succeeds. We tried several unsuccessful plans before arriving at

the following successful two-step procedure:

1. Determine the number of systems to draw from each State, by adjusting the populationweighted allocation as described in Section 4.2.1.

A-6
UCMR Statistical Design August 2001

2. Specify a sampling plan with D = 56 samples, one for each State and Territory. The number of systems in each sample (= State) is determined in Step 1. Each sample allows positive sampling probability in each of the 12 system-type-by-source-water-type-by-systemsize strata within its State or Territory, and zero sampling probability in all other States and

Territories.

This plan allows 56×12 = 672 positive sampling probabilities. The resulting optimal probabilities

are tabulated in Appendix B.

In order to help the optimization converge, we simplified the problem further by partitioning it into

two subproblems, one for CWSs and one for NTNCWSs. The minimax objectives and variance

constraints already break down in this way, since each of the target means (e.g. Size 1 GW CWSs)

puts positive weight either only on CWSs, or only on NTNCWSs. In order to partition the probability constraints, we imposed a further constraint, which is our last simplifying assumption for

the optimization:

Assumption 3. The sums of the CWS and NTNCWS sampling probabilities in each sample (= State)

are proportional to the respective populations served.

For example in Texas, CWSs serve 93.2% of the population, so by design each system allocated to

Texas has a 93.2% chance of being drawn as a CWS, as Appendix B confirms.

Using Assumption 3, the optimization may be decomposed from a single problem in 672 unknowns, into separate CWS and NTNCWS optimizations each in 336 unknowns. The resulting

subproblems are solved in about 3 hours each on a 400 MHz Pentium-II computer. Note however that even if Assumption 3 were not required, solving the two subproblems is not equivalent to

solving the original problem, because we now perform two separate minimax optimizations, which

give different optimal values. As a result the widest confidence interval for CWSs in Table 5 is

narrower than for NTNCWSs. We consider this difference to be an advantage: it reflects a decision

that CWSs, which serve more people, should comprise a larger proportion of the systems sampled

for the UCMR.

A.4 Confidence Intervals

A normal-theory 100(1 − α)% confidence interval for μˆ may be computed in the usual way as

μˆ ± z1−α/2

q

Vˆ(μ)ˆ , where Vˆ(μ)ˆ is the variance estimate defined in Theorem 1.

Under simple random sampling, the Wilson score confidence interval without continuity correction

(Newcombe, 1998; Wilson, 1927) for a proportion ρ is derived by using the normal interval to find

A-7
UCMR Statistical Design August 2001

the range of parameter values for which the parameter estimate is plausible:

ρˆ ∈ ρ ± z

p

ρ(1 − ρ)/n

⇔ ρ ∈



2nρˆ + z

2 ± z

q

z

2 + 4nρ(ˆ 1 − ˆρ).

2(n + z

2

) (A-12)

so (A-12) defines the Wilson score confidence interval for ρ. Under Assumptions 1 and 2, the same

derivation can be applied to a probability-weighted estimator with stratified sampling. Writing

(A-10) as Var(ρ)ˆ = V1ρ − V2ρ

2

, we have

ρˆ ∈ ρ ± z

q

V1ρ − V2ρ

2

⇔ ρ ∈



2ρˆ + V1z

2 ± z

q

V

2

1

z

2 + 4(V1ρˆ − V2ρˆ2

)

.

2(1 + V2z

2

) (A-13)

so (A-13) may be considered an approximate Wilson score confidence interval for ρ. The interval

is only approximate because it requires Assumptions 1 and 2.

A.5 Problems

The method described in this Appendix has the following weaknesses.

1. The theory assumes that systems are sampled with replacement, while the sampling plan for

Assessment Monitoring (Sections 4 and 8 above) uses sampling without replacement. When the

sampling fraction n/N is small, the sampling probabilities under sampling without replacement

do not change much from one sample to the next, so the difference between the two methods

is small. In Section 4, the sampling fraction is 800/63,869, or about 1.25%, which is probably

small enough to ignore. By comparison, in simple random sampling, a sampling fraction of this

size reduces standard errors by about 0.6%, and is commonly ignored.

2. The optimization forces the probability of drawing a CWS or NTNCWS to be proportional

to the population served by CWSs and NTNCWSs in each State (Assumption 3). So about

88% of the systems selected for Assessment Monitoring will be CWSs, since CWSs serve 88%

of the total population served by small systems. Although this constraint was imposed for

computational reasons as described in Section A.3.2, it agrees with the principle of sampling in

proportion to the population served.

3. The optimization assumes that the mean weights and sampling probabilities are constant within

each stratum (Assumption 1). As discussed in Section A.3, this assumption is mildly restrictive

for exposure estimates, where weights and probabilities should increase with system size, which

varies mostly between strata but also somewhat within strata.

4. The optimization also assumes that the occurrence fraction ρ is the same in each stratum (Assumption 2). As argued in Section A.3, this assumption is unrealistic but is a reasonable default

in the absence of information about how occurrence depends on stratum properties. Even if

A-8
UCMR Statistical Design August 2001

such information were available, it would probably be different for each contaminant and so

again Assumption 2 is a reasonable default.

5. The optimization depends on a user-specified value of ρ. If a new value of ρ is hypothesized,

the optimization must be rerun. Moreover a single sampling plan has to be used for many contaminants, which will occur with different frequencies; so the sampling plan will be suboptimal

for most contaminants. The sensitivity of the optimal sampling plan to the assumed value of ρ

has not been tested.

6. Theorem 1 ignores sampling error in the yi’s. It assumes that once the system number is chosen,

we can go to the system and observe y without error. This is a classical assumption in sampling,

but it does not hold in this case. The response yi equals 1 if the contaminant of interest occurs

at detectable levels at any time in system i, or 0 otherwise. But of course yi cannot be observed

without error: a finite number of samples is drawn from each system, and instead of yi we

observe yˆi, which equals 1 if the contaminant is observed in our few samples, or 0 otherwise.

The approximation of yi by yˆiintroduces bias and additional variance. In particular, yˆi will

be negatively biased for yi

, since we will often miss a contaminant which is only occasionally

present.

In order to study the effect of yˆi on the present theory, one needs either data or assumptions

about the frequency of occurrence of the contaminant of interest above the level of interest; the

number of samples taken from each system; the number of sampling locations within systems;

and temporal and spatial variability of contaminant occurrence across sampling locations. Such

data will be available once the sampling program is complete, and more accurate and conservative confidence intervals can be computed at that time.

A-9
UCMR Statistical Design August 2001

A-10
UCMR Statistical Design August 2001

Appendix B

Expected and Total Number of Systems Selected for Assessment Monitoring
UCMR Statistical Design August 2001

B-2

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

4 Alaska CWS 25-500 GW 0.103141 0.103141 0 1

Alaska CWS 25-500 SW 0.527185 0.630325 1 2

Alaska CWS 501-3300 GW 0.112833 0.743158 1 1

Alaska CWS 501-3300 SW 0.061396 0.804554 0 0

Alaska CWS 3301-10000 GW 0.068704 0.873258 1 0

Alaska CWS 3301-10000 SW 0.126742 1.000000 1 0

Alaska NTNCWS 25-500 GW 0.000000 1.000000 0 0

Alaska NTNCWS 25-500 SW 0.000000 1.000000 0 0

Alaska NTNCWS 501-3300 GW 0.000000 1.000000 0 0

Alaska NTNCWS 501-3300 SW 0.000000 1.000000 0 0

Alaska NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Alaska NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

14 Alabama CWS 25-500 GW 0.012354 0.012354 0 0

Alabama CWS 25-500 SW 0.003231 0.015585 0 1

Alabama CWS 501-3300 GW 0.274297 0.289882 4 2

Alabama CWS 501-3300 SW 0.023398 0.313280 0 1

Alabama CWS 3301-10000 GW 0.538540 0.851820 8 10

Alabama CWS 3301-10000 SW 0.111429 0.963250 2 1

Alabama NTNCWS 25-500 GW 0.001197 0.964446 0 0

Alabama NTNCWS 25-500 SW 0.009440 0.973886 0 0

Alabama NTNCWS 501-3300 GW 0.006425 0.980312 0 0

Alabama NTNCWS 501-3300 SW 0.019688 1.000000 0 0

Alabama NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Alabama NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

13 Arkansas CWS 25-500 GW 0.048335 0.048335 1 1

Arkansas CWS 25-500 SW 0.037493 0.085827 0 1

Arkansas CWS 501-3300 GW 0.281970 0.367797 4 3

Arkansas CWS 501-3300 SW 0.065464 0.433261 1 0

Arkansas CWS 3301-10000 GW 0.380083 0.813343 5 5

Arkansas CWS 3301-10000 SW 0.165064 0.978408 2 3

Arkansas NTNCWS 25-500 GW 0.001920 0.980327 0 0

Arkansas NTNCWS 25-500 SW 0.012133 0.992460 0 0

Arkansas NTNCWS 501-3300 GW 0.002293 0.994752 0 0

Arkansas NTNCWS 501-3300 SW 0.005248 1.000000 0 0

Arkansas NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Arkansas NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

2 American

Samoa CWS 25-500 GW 0.278403 0.278403 1 1
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-3

American

Samoa CWS 25-500 SW 0.636275 0.914677 1 1

American

Samoa CWS 501-3300 GW 0.000000 0.914677 0 0

American

Samoa CWS 501-3300 SW 0.085323 1.000000 0 0

American

Samoa CWS 3301-10000 GW 0.000000 1.000000 0 0

American

Samoa CWS 3301-10000 SW 0.000000 1.000000 0 0

American

Samoa NTNCWS 25-500 GW 0.000000 1.000000 0 0

American

Samoa NTNCWS 25-500 SW 0.000000 1.000000 0 0

American

Samoa NTNCWS 501-3300 GW 0.000000 1.000000 0 0

American

Samoa NTNCWS 501-3300 SW 0.000000 1.000000 0 0

American

Samoa NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

American

Samoa NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

12 Arizona CWS 25-500 GW 0.108010 0.108010 1 2

Arizona CWS 25-500 SW 0.058390 0.166401 0 0

Arizona CWS 501-3300 GW 0.284651 0.451052 3 2

Arizona CWS 501-3300 SW 0.023234 0.474286 0 1

Arizona CWS 3301-10000 GW 0.366545 0.840831 4 7

Arizona CWS 3301-10000 SW 0.016569 0.857400 0 0

Arizona NTNCWS 25-500 GW 0.021645 0.879045 0 0

Arizona NTNCWS 25-500 SW 0.019254 0.898299 0 0

Arizona NTNCWS 501-3300 GW 0.077477 0.975776 1 0

Arizona NTNCWS 501-3300 SW 0.005127 0.980903 0 0

Arizona NTNCWS 3301-10000 GW 0.019097 1.000000 0 0

Arizona NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

48 California CWS 25-500 GW 0.091801 0.091801 4 6

California CWS 25-500 SW 0.145704 0.237505 0 10

California CWS 501-3300 GW 0.170920 0.408425 8 7

California CWS 501-3300 SW 0.058824 0.467249 3 2

California CWS 3301-10000 GW 0.280015 0.747264 13 10

California CWS 3301-10000 SW 0.129795 0.877059 6 8

California NTNCWS 25-500 GW 0.022186 0.899245 1 1
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-4

California NTNCWS 25-500 SW 0.020841 0.920085 1 0

California NTNCWS 501-3300 GW 0.022424 0.942510 1 2

California NTNCWS 501-3300 SW 0.011769 0.954278 1 1

California NTNCWS 3301-10000 GW 0.012763 0.967041 1 0

California NTNCWS 3301-10000 SW 0.032959 1.000000 2 1

10 Colorado CWS 25-500 GW 0.089138 0.089138 0 0

Colorado CWS 25-500 SW 0.188764 0.277903 0 1

Colorado CWS 501-3300 GW 0.166154 0.444056 2 1

Colorado CWS 501-3300 SW 0.138157 0.582213 1 3

Colorado CWS 3301-10000 GW 0.129963 0.712176 1 2

Colorado CWS 3301-10000 SW 0.213830 0.926007 2 2

Colorado NTNCWS 25-500 GW 0.002338 0.928344 0 0

Colorado NTNCWS 25-500 SW 0.008918 0.937263 0 0

Colorado NTNCWS 501-3300 GW 0.001276 0.938538 0 0

Colorado NTNCWS 501-3300 SW 0.001898 0.940436 0 0

Colorado NTNCWS 3301-10000 GW 0.000000 0.940436 0 0

Colorado NTNCWS 3301-10000 SW 0.059564 1.000000 1 1

6 Connecticut CWS 25-500 GW 0.195981 0.195981 0 1

Connecticut CWS 25-500 SW 0.006058 0.202039 0 0

Connecticut CWS 501-3300 GW 0.166513 0.368552 1 0

Connecticut CWS 501-3300 SW 0.037219 0.405771 0 1

Connecticut CWS 3301-10000 GW 0.101240 0.507011 1 0

Connecticut CWS 3301-10000 SW 0.176568 0.683578 1 2

Connecticut NTNCWS 25-500 GW 0.153652 0.837230 1 0

Connecticut NTNCWS 25-500 SW 0.000000 0.837230 0 0

Connecticut NTNCWS 501-3300 GW 0.162770 1.000000 1 2

Connecticut NTNCWS 501-3300 SW 0.000000 1.000000 0 0

Connecticut NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Connecticut NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

2 Delaware CWS 25-500 GW 0.177268 0.177268 0 1

Delaware CWS 25-500 SW 0.000000 0.177268 0 0

Delaware CWS 501-3300 GW 0.381717 0.558986 1 0

Delaware CWS 501-3300 SW 0.000000 0.558986 0 0

Delaware CWS 3301-10000 GW 0.239315 0.798300 1 1

Delaware CWS 3301-10000 SW 0.000000 0.798300 0 0

Delaware NTNCWS 25-500 GW 0.060765 0.859066 0 0

Delaware NTNCWS 25-500 SW 0.000000 0.859066 0 0
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-5

Delaware NTNCWS 501-3300 GW 0.078519 0.937585 0 0

Delaware NTNCWS 501-3300 SW 0.062415 1.000000 0 0

Delaware NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Delaware NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

32 Florida CWS 25-500 GW 0.107618 0.107618 0 3

Florida CWS 25-500 SW 0.000000 0.107618 0 0

Florida CWS 501-3300 GW 0.350597 0.458215 11 8

Florida CWS 501-3300 SW 0.001696 0.459910 0 0

Florida CWS 3301-10000 GW 0.394205 0.854115 13 17

Florida CWS 3301-10000 SW 0.016435 0.870550 1 0

Florida NTNCWS 25-500 GW 0.058549 0.929099 2 2

Florida NTNCWS 25-500 SW 0.000000 0.929099 0 0

Florida NTNCWS 501-3300 GW 0.060849 0.989949 2 1

Florida NTNCWS 501-3300 SW 0.000000 0.989949 0 0

Florida NTNCWS 3301-10000 GW 0.010051 1.000000 0 1

Florida NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

22 Georgia CWS 25-500 GW 0.123473 0.123473 0 3

Georgia CWS 25-500 SW 0.075460 0.198932 0 5

Georgia CWS 501-3300 GW 0.216882 0.415814 5 3

Georgia CWS 501-3300 SW 0.076029 0.491843 2 1

Georgia CWS 3301-10000 GW 0.205910 0.697753 5 4

Georgia CWS 3301-10000 SW 0.233809 0.931562 5 4

Georgia NTNCWS 25-500 GW 0.014761 0.946323 0 1

Georgia NTNCWS 25-500 SW 0.016129 0.962453 0 1

Georgia NTNCWS 501-3300 GW 0.017752 0.980205 0 0

Georgia NTNCWS 501-3300 SW 0.017194 0.997399 0 0

Georgia NTNCWS 3301-10000 GW 0.002601 1.000000 0 0

Georgia NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

1 Guam CWS 25-500 GW 0.000000 0.000000 0 0

Guam CWS 25-500 SW 0.000000 0.000000 0 0

Guam CWS 501-3300 GW 0.000000 0.000000 0 0

Guam CWS 501-3300 SW 0.000000 0.000000 0 0

Guam CWS 3301-10000 GW 0.000000 0.000000 0 0

Guam CWS 3301-10000 SW 1.000000 1.000000 1 1

Guam NTNCWS 25-500 GW 0.000000 1.000000 0 0

Guam NTNCWS 25-500 SW 0.000000 1.000000 0 0

Guam NTNCWS 501-3300 GW 0.000000 1.000000 0 0
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-6

Guam NTNCWS 501-3300 SW 0.000000 1.000000 0 0

Guam NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Guam NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

3 Hawaii CWS 25-500 GW 0.044055 0.044055 0 0

Hawaii CWS 25-500 SW 0.013192 0.057247 0 0

Hawaii CWS 501-3300 GW 0.348328 0.405574 1 1

Hawaii CWS 501-3300 SW 0.018984 0.424558 0 0

Hawaii CWS 3301-10000 GW 0.442170 0.866728 1 2

Hawaii CWS 3301-10000 SW 0.086899 0.953627 1 0

Hawaii NTNCWS 25-500 GW 0.029826 0.983453 0 0

Hawaii NTNCWS 25-500 SW 0.002279 0.985732 0 0

Hawaii NTNCWS 501-3300 GW 0.014268 1.000000 0 0

Hawaii NTNCWS 501-3300 SW 0.000000 1.000000 0 0

Hawaii NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Hawaii NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

16 Iowa CWS 25-500 GW 0.108789 0.108789 0 2

Iowa CWS 25-500 SW 0.009389 0.118178 0 1

Iowa CWS 501-3300 GW 0.421654 0.539832 7 9

Iowa CWS 501-3300 SW 0.022059 0.561891 1 3

Iowa CWS 3301-10000 GW 0.338653 0.900544 5 1

Iowa CWS 3301-10000 SW 0.061586 0.962131 1 0

Iowa NTNCWS 25-500 GW 0.016414 0.978545 0 0

Iowa NTNCWS 25-500 SW 0.003658 0.982203 0 0

Iowa NTNCWS 501-3300 GW 0.017797 1.000000 0 0

Iowa NTNCWS 501-3300 SW 0.000000 1.000000 0 0

Iowa NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Iowa NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

8 Idaho CWS 25-500 GW 0.124816 0.124816 0 1

Idaho CWS 25-500 SW 0.199402 0.324217 0 1

Idaho CWS 501-3300 GW 0.181250 0.505467 1 0

Idaho CWS 501-3300 SW 0.050444 0.555911 1 1

Idaho CWS 3301-10000 GW 0.245922 0.801833 2 5

Idaho CWS 3301-10000 SW 0.036241 0.838074 0 0

Idaho NTNCWS 25-500 GW 0.044504 0.882578 1 0

Idaho NTNCWS 25-500 SW 0.037115 0.919693 0 0

Idaho NTNCWS 501-3300 GW 0.042032 0.961725 0 0

Idaho NTNCWS 501-3300 SW 0.008380 0.970105 0 0
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-7

Idaho NTNCWS 3301-10000 GW 0.029895 1.000000 0 0

Idaho NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

28 Illinois CWS 25-500 GW 0.072244 0.072244 0 0

Illinois CWS 25-500 SW 0.010088 0.082331 0 0

Illinois CWS 501-3300 GW 0.320482 0.402813 9 10

Illinois CWS 501-3300 SW 0.036115 0.438927 1 1

Illinois CWS 3301-10000 GW 0.360524 0.799451 10 15

Illinois CWS 3301-10000 SW 0.105342 0.904793 3 1

Illinois NTNCWS 25-500 GW 0.020272 0.925065 1 0

Illinois NTNCWS 25-500 SW 0.010566 0.935631 0 0

Illinois NTNCWS 501-3300 GW 0.020635 0.956266 1 1

Illinois NTNCWS 501-3300 SW 0.005094 0.961359 0 0

Illinois NTNCWS 3301-10000 GW 0.006049 0.967408 0 0

Illinois NTNCWS 3301-10000 SW 0.032592 1.000000 1 0

20 Indiana CWS 25-500 GW 0.046374 0.046374 0 1

Indiana CWS 25-500 SW 0.001670 0.048044 0 0

Indiana CWS 501-3300 GW 0.292420 0.340464 6 2

Indiana CWS 501-3300 SW 0.015509 0.355973 0 0

Indiana CWS 3301-10000 GW 0.424877 0.780850 8 14

Indiana CWS 3301-10000 SW 0.076221 0.857071 2 1

Indiana NTNCWS 25-500 GW 0.063461 0.920532 2 1

Indiana NTNCWS 25-500 SW 0.021198 0.941730 0 0

Indiana NTNCWS 501-3300 GW 0.054268 0.995998 1 1

Indiana NTNCWS 501-3300 SW 0.004002 1.000000 0 0

Indiana NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Indiana NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

12 Kansas CWS 25-500 GW 0.079950 0.079950 0 2

Kansas CWS 25-500 SW 0.060355 0.140304 0 0

Kansas CWS 501-3300 GW 0.370682 0.510986 4 4

Kansas CWS 501-3300 SW 0.113083 0.624069 2 1

Kansas CWS 3301-10000 GW 0.174180 0.798249 2 4

Kansas CWS 3301-10000 SW 0.169657 0.967906 2 1

Kansas NTNCWS 25-500 GW 0.007580 0.975485 0 0

Kansas NTNCWS 25-500 SW 0.009514 0.984999 0 0

Kansas NTNCWS 501-3300 GW 0.015001 1.000000 0 0

Kansas NTNCWS 501-3300 SW 0.000000 1.000000 0 0

Kansas NTNCWS 3301-10000 GW 0.000000 1.000000 0 0
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-8

Kansas NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

9 Kentucky CWS 25-500 GW 0.018156 0.018156 0 0

Kentucky CWS 25-500 SW 0.057626 0.075782 0 1

Kentucky CWS 501-3300 GW 0.088308 0.164090 1 0

Kentucky CWS 501-3300 SW 0.124368 0.288458 1 2

Kentucky CWS 3301-10000 GW 0.139996 0.428453 1 2

Kentucky CWS 3301-10000 SW 0.509989 0.938442 5 4

Kentucky NTNCWS 25-500 GW 0.008458 0.946900 0 0

Kentucky NTNCWS 25-500 SW 0.027535 0.974435 0 0

Kentucky NTNCWS 501-3300 GW 0.004291 0.978726 0 0

Kentucky NTNCWS 501-3300 SW 0.021274 1.000000 0 0

Kentucky NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Kentucky NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

27 Louisiana CWS 25-500 GW 0.070882 0.070882 0 3

Louisiana CWS 25-500 SW 0.013489 0.084371 0 1

Louisiana CWS 501-3300 GW 0.360128 0.444499 10 12

Louisiana CWS 501-3300 SW 0.018921 0.463420 1 0

Louisiana CWS 3301-10000 GW 0.414728 0.878148 11 6

Louisiana CWS 3301-10000 SW 0.058840 0.936988 2 1

Louisiana NTNCWS 25-500 GW 0.005874 0.942862 0 0

Louisiana NTNCWS 25-500 SW 0.013111 0.955973 0 0

Louisiana NTNCWS 501-3300 GW 0.013590 0.969562 0 0

Louisiana NTNCWS 501-3300 SW 0.005822 0.975385 0 0

Louisiana NTNCWS 3301-10000 GW 0.000000 0.975385 0 0

Louisiana NTNCWS 3301-10000 SW 0.024615 1.000000 1 4

12 Massachusetts CWS 25-500 GW 0.030041 0.030041 0 0

Massachusetts CWS 25-500 SW 0.006699 0.036740 0 0

Massachusetts CWS 501-3300 GW 0.144887 0.181627 2 2

Massachusetts CWS 501-3300 SW 0.024759 0.206386 0 1

Massachusetts CWS 3301-10000 GW 0.603425 0.809810 7 7

Massachusetts CWS 3301-10000 SW 0.100924 0.910734 1 1

Massachusetts NTNCWS 25-500 GW 0.037313 0.948048 1 0

Massachusetts NTNCWS 25-500 SW 0.000000 0.948048 0 0

Massachusetts NTNCWS 501-3300 GW 0.048693 0.996741 1 1

Massachusetts NTNCWS 501-3300 SW 0.000000 0.996741 0 0

Massachusetts NTNCWS 3301-10000 GW 0.003259 1.000000 0 0

Massachusetts NTNCWS 3301-10000 SW 0.000000 1.000000 0 0
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-9

8 Maryland CWS 25-500 GW 0.098108 0.098108 0 1

Maryland CWS 25-500 SW 0.062991 0.161098 0 0

Maryland CWS 501-3300 GW 0.233629 0.394727 2 3

Maryland CWS 501-3300 SW 0.035363 0.430090 0 0

Maryland CWS 3301-10000 GW 0.163664 0.593754 1 0

Maryland CWS 3301-10000 SW 0.096850 0.690604 1 1

Maryland NTNCWS 25-500 GW 0.113191 0.803794 1 1

Maryland NTNCWS 25-500 SW 0.008687 0.812481 0 0

Maryland NTNCWS 501-3300 GW 0.174751 0.987232 1 0

Maryland NTNCWS 501-3300 SW 0.000000 0.987232 0 0

Maryland NTNCWS 3301-10000 GW 0.012768 1.000000 0 2

Maryland NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

6 Maine CWS 25-500 GW 0.080051 0.080051 0 0

Maine CWS 25-500 SW 0.080540 0.160591 1 1

Maine CWS 501-3300 GW 0.210100 0.370691 0 1

Maine CWS 501-3300 SW 0.133374 0.504065 1 0

Maine CWS 3301-10000 GW 0.125473 0.629538 1 0

Maine CWS 3301-10000 SW 0.149065 0.778603 1 1

Maine NTNCWS 25-500 GW 0.122935 0.901537 1 3

Maine NTNCWS 25-500 SW 0.058997 0.960535 0 0

Maine NTNCWS 501-3300 GW 0.027121 0.987656 0 0

Maine NTNCWS 501-3300 SW 0.012344 1.000000 0 0

Maine NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Maine NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

24 Michigan CWS 25-500 GW 0.088378 0.088378 0 2

Michigan CWS 25-500 SW 0.009233 0.097611 0 0

Michigan CWS 501-3300 GW 0.286533 0.384144 7 10

Michigan CWS 501-3300 SW 0.023687 0.407831 1 1

Michigan CWS 3301-10000 GW 0.256976 0.664808 6 5

Michigan CWS 3301-10000 SW 0.063746 0.728554 2 2

Michigan NTNCWS 25-500 GW 0.159639 0.888193 4 3

Michigan NTNCWS 25-500 SW 0.000000 0.888193 0 0

Michigan NTNCWS 501-3300 GW 0.096246 0.984439 2 1

Michigan NTNCWS 501-3300 SW 0.000000 0.984439 0 0

Michigan NTNCWS 3301-10000 GW 0.015561 1.000000 0 0

Michigan NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

16 Minnesota CWS 25-500 GW 0.097146 0.097146 0 2
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-10

Minnesota CWS 25-500 SW 0.002208 0.099353 0 0

Minnesota CWS 501-3300 GW 0.457793 0.557147 7 5

Minnesota CWS 501-3300 SW 0.010180 0.567327 0 0

Minnesota CWS 3301-10000 GW 0.324204 0.891531 5 7

Minnesota CWS 3301-10000 SW 0.058047 0.949578 1 0

Minnesota NTNCWS 25-500 GW 0.033979 0.983557 1 2

Minnesota NTNCWS 25-500 SW 0.001830 0.985387 0 0

Minnesota NTNCWS 501-3300 GW 0.005726 0.991113 0 0

Minnesota NTNCWS 501-3300 SW 0.008887 1.000000 0 0

Minnesota NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Minnesota NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

20 Missouri CWS 25-500 GW 0.089997 0.089997 0 3

Missouri CWS 25-500 SW 0.047255 0.137252 0 0

Missouri CWS 501-3300 GW 0.307287 0.444539 6 7

Missouri CWS 501-3300 SW 0.046065 0.490604 1 0

Missouri CWS 3301-10000 GW 0.331344 0.821948 7 5

Missouri CWS 3301-10000 SW 0.109887 0.931835 2 3

Missouri NTNCWS 25-500 GW 0.012704 0.944539 0 2

Missouri NTNCWS 25-500 SW 0.021993 0.966532 0 0

Missouri NTNCWS 501-3300 GW 0.030450 0.996982 1 0

Missouri NTNCWS 501-3300 SW 0.000000 0.996982 0 0

Missouri NTNCWS 3301-10000 GW 0.003018 1.000000 0 0

Missouri NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

2 Marianna

Islands CWS 25-500 GW 0.424375 0.424375 0 1

Marianna

Islands CWS 25-500 SW 0.000000 0.424375 0 0

Marianna

Islands CWS 501-3300 GW 0.575625 1.000000 1 1

Marianna

Islands CWS 501-3300 SW 0.000000 1.000000 0 0

Marianna

Islands CWS 3301-10000 GW 0.000000 1.000000 0 0

Marianna

Islands CWS 3301-10000 SW 0.000000 1.000000 0 0

Marianna

Islands NTNCWS 25-500 GW 0.000000 1.000000 0 0

Marianna

Islands NTNCWS 25-500 SW 0.000000 1.000000 0 0
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-11

Marianna

Islands NTNCWS 501-3300 GW 0.000000 1.000000 0 0

Marianna

Islands NTNCWS 501-3300 SW 0.000000 1.000000 0 0

Marianna

Islands NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Marianna

Islands NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

30 Mississippi CWS 25-500 GW 0.054848 0.054848 0 2

Mississippi CWS 25-500 SW 0.000395 0.055243 0 0

Mississippi CWS 501-3300 GW 0.536246 0.591489 16 20

Mississippi CWS 501-3300 SW 0.000000 0.591489 0 0

Mississippi CWS 3301-10000 GW 0.355742 0.947231 11 6

Mississippi CWS 3301-10000 SW 0.000000 0.947231 0 0

Mississippi NTNCWS 25-500 GW 0.010244 0.957475 0 0

Mississippi NTNCWS 25-500 SW 0.000000 0.957475 0 0

Mississippi NTNCWS 501-3300 GW 0.025558 0.983032 1 2

Mississippi NTNCWS 501-3300 SW 0.000000 0.983032 0 0

Mississippi NTNCWS 3301-10000 GW 0.016968 1.000000 0 0

Mississippi NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

6 Montana CWS 25-500 GW 0.176760 0.176760 0 1

Montana CWS 25-500 SW 0.109912 0.286672 0 1

Montana CWS 501-3300 GW 0.225216 0.511888 1 1

Montana CWS 501-3300 SW 0.081293 0.593181 0 0

Montana CWS 3301-10000 GW 0.147776 0.740957 1 1

Montana CWS 3301-10000 SW 0.146475 0.887433 1 1

Montana NTNCWS 25-500 GW 0.059815 0.947248 1 0

Montana NTNCWS 25-500 SW 0.024406 0.971654 0 0

Montana NTNCWS 501-3300 GW 0.028346 1.000000 0 1

Montana NTNCWS 501-3300 SW 0.000000 1.000000 0 0

Montana NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Montana NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

22 North Carolina CWS 25-500 GW 0.156723 0.156723 4 3

North Carolina CWS 25-500 SW 0.045023 0.201746 0 1

North Carolina CWS 501-3300 GW 0.195084 0.396830 4 2

North Carolina CWS 501-3300 SW 0.052233 0.449063 1 2

North Carolina CWS 3301-10000 GW 0.227239 0.676301 5 6

North Carolina CWS 3301-10000 SW 0.163587 0.839889 4 6

North Carolina NTNCWS 25-500 GW 0.061479 0.901368 1 0
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-12

North Carolina NTNCWS 25-500 SW 0.009916 0.911284 0 1

North Carolina NTNCWS 501-3300 GW 0.066654 0.977938 1 0

North Carolina NTNCWS 501-3300 SW 0.020225 0.998163 1 1

North Carolina NTNCWS 3301-10000 GW 0.001837 1.000000 0 0

North Carolina NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

4 North Dakota CWS 25-500 GW 0.107831 0.107831 1 0

North Dakota CWS 25-500 SW 0.014230 0.122061 0 1

North Dakota CWS 501-3300 GW 0.511024 0.633085 2 3

North Dakota CWS 501-3300 SW 0.049591 0.682676 0 0

North Dakota CWS 3301-10000 GW 0.220790 0.903466 1 0

North Dakota CWS 3301-10000 SW 0.079568 0.983034 0 0

North Dakota NTNCWS 25-500 GW 0.001980 0.985014 0 0

North Dakota NTNCWS 25-500 SW 0.014986 1.000000 0 0

North Dakota NTNCWS 501-3300 GW 0.000000 1.000000 0 0

North Dakota NTNCWS 501-3300 SW 0.000000 1.000000 0 0

North Dakota NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

North Dakota NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

8 Nebraska CWS 25-500 GW 0.152090 0.152090 0 1

Nebraska CWS 25-500 SW 0.000000 0.152090 0 0

Nebraska CWS 501-3300 GW 0.426111 0.578202 3 3

Nebraska CWS 501-3300 SW 0.014720 0.592922 0 0

Nebraska CWS 3301-10000 GW 0.307693 0.900615 3 3

Nebraska CWS 3301-10000 SW 0.044192 0.944807 1 0

Nebraska NTNCWS 25-500 GW 0.024216 0.969023 0 1

Nebraska NTNCWS 25-500 SW 0.000000 0.969023 0 0

Nebraska NTNCWS 501-3300 GW 0.016591 0.985614 0 0

Nebraska NTNCWS 501-3300 SW 0.000000 0.985614 0 0

Nebraska NTNCWS 3301-10000 GW 0.014386 1.000000 0 0

Nebraska NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

6 New

Hampshire CWS 25-500 GW 0.179653 0.179653 0 1

New

Hampshire CWS 25-500 SW 0.059689 0.239342 0 0

New

Hampshire CWS 501-3300 GW 0.211377 0.450719 1 1

New

Hampshire CWS 501-3300 SW 0.082279 0.532998 0 2

New

Hampshire CWS 3301-10000 GW 0.100470 0.633468 1 1
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-13

New

Hampshire CWS 3301-10000 SW 0.134734 0.768202 1 0

New

Hampshire NTNCWS 25-500 GW 0.129265 0.897467 1 0

New

Hampshire NTNCWS 25-500 SW 0.000000 0.897467 0 0

New

Hampshire NTNCWS 501-3300 GW 0.102533 1.000000 1 1

New

Hampshire NTNCWS 501-3300 SW 0.000000 1.000000 0 0

New

Hampshire NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

New

Hampshire NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

16 New Jersey CWS 25-500 GW 0.041427 0.041427 0 1

New Jersey CWS 25-500 SW 0.000000 0.041427 0 0

New Jersey CWS 501-3300 GW 0.180334 0.221761 3 4

New Jersey CWS 501-3300 SW 0.006606 0.228367 0 0

New Jersey CWS 3301-10000 GW 0.435798 0.664165 7 7

New Jersey CWS 3301-10000 SW 0.043850 0.708015 1 2

New Jersey NTNCWS 25-500 GW 0.105685 0.813700 2 2

New Jersey NTNCWS 25-500 SW 0.001010 0.814710 0 0

New Jersey NTNCWS 501-3300 GW 0.140774 0.955484 2 0

New Jersey NTNCWS 501-3300 SW 0.018795 0.974279 0 0

New Jersey NTNCWS 3301-10000 GW 0.025721 1.000000 0 0

New Jersey NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

8 New Mexico CWS 25-500 GW 0.147242 0.147242 0 1

New Mexico CWS 25-500 SW 0.069756 0.216998 0 2

New Mexico CWS 501-3300 GW 0.268916 0.485914 2 3

New Mexico CWS 501-3300 SW 0.044185 0.530099 1 0

New Mexico CWS 3301-10000 GW 0.310844 0.840944 2 0

New Mexico CWS 3301-10000 SW 0.077038 0.917981 1 0

New Mexico NTNCWS 25-500 GW 0.020732 0.938713 0 0

New Mexico NTNCWS 25-500 SW 0.024464 0.963178 0 0

New Mexico NTNCWS 501-3300 GW 0.031415 0.994593 0 2

New Mexico NTNCWS 501-3300 SW 0.005407 1.000000 0 0

New Mexico NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

New Mexico NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

4 Nevada CWS 25-500 GW 0.096624 0.096624 1 0

Nevada CWS 25-500 SW 0.061023 0.157648 0 0
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-14

Nevada CWS 501-3300 GW 0.316982 0.474630 1 3

Nevada CWS 501-3300 SW 0.025688 0.500317 0 0

Nevada CWS 3301-10000 GW 0.301061 0.801378 1 0

Nevada CWS 3301-10000 SW 0.064865 0.866243 1 0

Nevada NTNCWS 25-500 GW 0.030812 0.897055 0 0

Nevada NTNCWS 25-500 SW 0.028647 0.925702 0 1

Nevada NTNCWS 501-3300 GW 0.032687 0.958389 0 0

Nevada NTNCWS 501-3300 SW 0.011499 0.969888 0 0

Nevada NTNCWS 3301-10000 GW 0.030112 1.000000 0 0

Nevada NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

29 New York CWS 25-500 GW 0.105270 0.105270 0 1

New York CWS 25-500 SW 0.119826 0.225096 0 1

New York CWS 501-3300 GW 0.212439 0.437535 6 8

New York CWS 501-3300 SW 0.099139 0.536674 3 1

New York CWS 3301-10000 GW 0.128412 0.665086 4 4

New York CWS 3301-10000 SW 0.182485 0.847570 5 6

New York NTNCWS 25-500 GW 0.025672 0.873242 1 4

New York NTNCWS 25-500 SW 0.012511 0.885754 1 0

New York NTNCWS 501-3300 GW 0.039152 0.924905 1 2

New York NTNCWS 501-3300 SW 0.013069 0.937975 0 0

New York NTNCWS 3301-10000 GW 0.007687 0.945661 0 0

New York NTNCWS 3301-10000 SW 0.054339 1.000000 2 2

28 Ohio CWS 25-500 GW 0.060154 0.060154 0 1

Ohio CWS 25-500 SW 0.021562 0.081715 0 0

Ohio CWS 501-3300 GW 0.247273 0.328989 0 6

Ohio CWS 501-3300 SW 0.045966 0.374955 1 0

Ohio CWS 3301-10000 GW 0.308339 0.683294 9 12

Ohio CWS 3301-10000 SW 0.141144 0.824438 4 4

Ohio NTNCWS 25-500 GW 0.071715 0.896153 2 2

Ohio NTNCWS 25-500 SW 0.004899 0.901052 0 0

Ohio NTNCWS 501-3300 GW 0.056505 0.957557 2 1

Ohio NTNCWS 501-3300 SW 0.035977 0.993534 1 0

Ohio NTNCWS 3301-10000 GW 0.006466 1.000000 0 2

Ohio NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

15 Oklahoma CWS 25-500 GW 0.053578 0.053578 0 3

Oklahoma CWS 25-500 SW 0.129226 0.182804 0 0

Oklahoma CWS 501-3300 GW 0.235046 0.417850 3 1
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-15

Oklahoma CWS 501-3300 SW 0.135236 0.553087 2 2

Oklahoma CWS 3301-10000 GW 0.110855 0.663942 2 3

Oklahoma CWS 3301-10000 SW 0.310569 0.974511 5 6

Oklahoma NTNCWS 25-500 GW 0.004712 0.979223 0 0

Oklahoma NTNCWS 25-500 SW 0.016061 0.995284 0 0

Oklahoma NTNCWS 501-3300 GW 0.000876 0.996160 0 0

Oklahoma NTNCWS 501-3300 SW 0.000000 0.996160 0 0

Oklahoma NTNCWS 3301-10000 GW 0.003840 1.000000 0 0

Oklahoma NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

11 Oregon CWS 25-500 GW 0.105427 0.105427 0 0

Oregon CWS 25-500 SW 0.124548 0.229975 0 1

Oregon CWS 501-3300 GW 0.189055 0.419030 2 3

Oregon CWS 501-3300 SW 0.126690 0.545720 2 1

Oregon CWS 3301-10000 GW 0.136664 0.682384 2 1

Oregon CWS 3301-10000 SW 0.194845 0.877229 2 3

Oregon NTNCWS 25-500 GW 0.057707 0.934936 1 2

Oregon NTNCWS 25-500 SW 0.012444 0.947380 0 0

Oregon NTNCWS 501-3300 GW 0.025242 0.972622 0 0

Oregon NTNCWS 501-3300 SW 0.027378 1.000000 0 0

Oregon NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Oregon NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

37 Pennsylvania CWS 25-500 GW 0.090515 0.090515 0 4

Pennsylvania CWS 25-500 SW 0.064085 0.154600 1 3

Pennsylvania CWS 501-3300 GW 0.200824 0.355424 8 4

Pennsylvania CWS 501-3300 SW 0.064166 0.419591 0 3

Pennsylvania CWS 3301-10000 GW 0.183790 0.603380 7 4

Pennsylvania CWS 3301-10000 SW 0.172501 0.775881 6 8

Pennsylvania NTNCWS 25-500 GW 0.082633 0.858514 3 5

Pennsylvania NTNCWS 25-500 SW 0.023604 0.882118 1 1

Pennsylvania NTNCWS 501-3300 GW 0.080900 0.963018 3 4

Pennsylvania NTNCWS 501-3300 SW 0.029903 0.992921 1 1

Pennsylvania NTNCWS 3301-10000 GW 0.007079 1.000000 0 0

Pennsylvania NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

9 Puerto Rico CWS 25-500 GW 0.030068 0.030068 0 0

Puerto Rico CWS 25-500 SW 0.367728 0.397797 0 2

Puerto Rico CWS 501-3300 GW 0.096501 0.494298 1 0

Puerto Rico CWS 501-3300 SW 0.126482 0.620780 1 1
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-16

Puerto Rico CWS 3301-10000 GW 0.163618 0.784398 2 3

Puerto Rico CWS 3301-10000 SW 0.140299 0.924697 1 2

Puerto Rico NTNCWS 25-500 GW 0.002643 0.927340 0 0

Puerto Rico NTNCWS 25-500 SW 0.013930 0.941269 0 0

Puerto Rico NTNCWS 501-3300 GW 0.034820 0.976089 1 1

Puerto Rico NTNCWS 501-3300 SW 0.000000 0.976089 0 0

Puerto Rico NTNCWS 3301-10000 GW 0.023911 1.000000 0 0

Puerto Rico NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

2 Rhode Island CWS 25-500 GW 0.102141 0.102141 0 0

Rhode Island CWS 25-500 SW 0.000000 0.102141 0 0

Rhode Island CWS 501-3300 GW 0.119044 0.221185 0 1

Rhode Island CWS 501-3300 SW 0.075209 0.296394 0 0

Rhode Island CWS 3301-10000 GW 0.166570 0.462964 1 1

Rhode Island CWS 3301-10000 SW 0.151757 0.614721 1 0

Rhode Island NTNCWS 25-500 GW 0.139146 0.753868 0 0

Rhode Island NTNCWS 25-500 SW 0.000000 0.753868 0 0

Rhode Island NTNCWS 501-3300 GW 0.144328 0.898196 0 0

Rhode Island NTNCWS 501-3300 SW 0.000000 0.898196 0 0

Rhode Island NTNCWS 3301-10000 GW 0.101804 1.000000 0 0

Rhode Island NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

11 South Carolina CWS 25-500 GW 0.074769 0.074769 0 0

South Carolina CWS 25-500 SW 0.000000 0.074769 0 0

South Carolina CWS 501-3300 GW 0.219103 0.293873 2 3

South Carolina CWS 501-3300 SW 0.054199 0.348072 1 0

South Carolina CWS 3301-10000 GW 0.272259 0.620330 3 0

South Carolina CWS 3301-10000 SW 0.277753 0.898083 3 6

South Carolina NTNCWS 25-500 GW 0.012816 0.910900 0 0

South Carolina NTNCWS 25-500 SW 0.005474 0.916373 0 1

South Carolina NTNCWS 501-3300 GW 0.011296 0.927669 0 0

South Carolina NTNCWS 501-3300 SW 0.015615 0.943284 0 1

South Carolina NTNCWS 3301-10000 GW 0.000000 0.943284 0 0

South Carolina NTNCWS 3301-10000 SW 0.056716 1.000000 1 0

4 South Dakota CWS 25-500 GW 0.123446 0.123446 1 0

South Dakota CWS 25-500 SW 0.114364 0.237810 1 1

South Dakota CWS 501-3300 GW 0.336164 0.573974 0 2

South Dakota CWS 501-3300 SW 0.065505 0.639479 0 0

South Dakota CWS 3301-10000 GW 0.271831 0.911310 1 1
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-17

South Dakota CWS 3301-10000 SW 0.067799 0.979109 0 0

South Dakota NTNCWS 25-500 GW 0.003200 0.982309 0 0

South Dakota NTNCWS 25-500 SW 0.016996 0.999305 0 0

South Dakota NTNCWS 501-3300 GW 0.000695 1.000000 0 0

South Dakota NTNCWS 501-3300 SW 0.000000 1.000000 0 0

South Dakota NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

South Dakota NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

14 Tennessee CWS 25-500 GW 0.010921 0.010921 0 0

Tennessee CWS 25-500 SW 0.039598 0.050519 0 2

Tennessee CWS 501-3300 GW 0.132222 0.182741 2 2

Tennessee CWS 501-3300 SW 0.091572 0.274314 2 0

Tennessee CWS 3301-10000 GW 0.172997 0.447311 2 0

Tennessee CWS 3301-10000 SW 0.527512 0.974823 7 10

Tennessee NTNCWS 25-500 GW 0.001157 0.975979 0 0

Tennessee NTNCWS 25-500 SW 0.004805 0.980785 0 0

Tennessee NTNCWS 501-3300 GW 0.000531 0.981316 0 0

Tennessee NTNCWS 501-3300 SW 0.018684 1.000000 0 0

Tennessee NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Tennessee NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

7 Tribes CWS 25-500 GW 0.202971 0.202971 2 2

Tribes CWS 25-500 SW 0.147933 0.350904 0 2

Tribes CWS 501-3300 GW 0.338683 0.689587 2 1

Tribes CWS 501-3300 SW 0.046713 0.736299 0 0

Tribes CWS 3301-10000 GW 0.170082 0.906381 1 0

Tribes CWS 3301-10000 SW 0.055832 0.962213 1 1

Tribes NTNCWS 25-500 GW 0.017954 0.980167 0 0

Tribes NTNCWS 25-500 SW 0.000000 0.980167 0 0

Tribes NTNCWS 501-3300 GW 0.019833 1.000000 0 1

Tribes NTNCWS 501-3300 SW 0.000000 1.000000 0 0

Tribes NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Tribes NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

71 Texas CWS 25-500 GW 0.080530 0.080530 0 8

Texas CWS 25-500 SW 0.032271 0.112801 0 3

Texas CWS 501-3300 GW 0.336133 0.448935 24 19

Texas CWS 501-3300 SW 0.034461 0.483395 2 0

Texas CWS 3301-10000 GW 0.346726 0.830121 25 29

Texas CWS 3301-10000 SW 0.102709 0.932830 7 4
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-18

Texas NTNCWS 25-500 GW 0.009594 0.942424 1 1

Texas NTNCWS 25-500 SW 0.011363 0.953787 1 1

Texas NTNCWS 501-3300 GW 0.012236 0.966023 1 2

Texas NTNCWS 501-3300 SW 0.013273 0.979297 1 1

Texas NTNCWS 3301-10000 GW 0.004174 0.983471 0 0

Texas NTNCWS 3301-10000 SW 0.016529 1.000000 1 3

7 Utah CWS 25-500 GW 0.097464 0.097464 0 0

Utah CWS 25-500 SW 0.089084 0.186548 0 1

Utah CWS 501-3300 GW 0.292421 0.478969 2 2

Utah CWS 501-3300 SW 0.042900 0.521869 0 0

Utah CWS 3301-10000 GW 0.322360 0.844229 2 2

Utah CWS 3301-10000 SW 0.100653 0.944882 1 2

Utah NTNCWS 25-500 GW 0.011787 0.956669 0 0

Utah NTNCWS 25-500 SW 0.011496 0.968165 0 0

Utah NTNCWS 501-3300 GW 0.011412 0.979577 0 0

Utah NTNCWS 501-3300 SW 0.000000 0.979577 0 0

Utah NTNCWS 3301-10000 GW 0.020423 1.000000 0 0

Utah NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

16 Virginia CWS 25-500 GW 0.110551 0.110551 0 4

Virginia CWS 25-500 SW 0.098994 0.209545 0 1

Virginia CWS 501-3300 GW 0.126866 0.336411 2 5

Virginia CWS 501-3300 SW 0.084950 0.421361 1 0

Virginia CWS 3301-10000 GW 0.056914 0.478275 1 0

Virginia CWS 3301-10000 SW 0.209323 0.687598 3 2

Virginia NTNCWS 25-500 GW 0.088632 0.776230 2 1

Virginia NTNCWS 25-500 SW 0.018261 0.794490 0 0

Virginia NTNCWS 501-3300 GW 0.139405 0.933895 2 0

Virginia NTNCWS 501-3300 SW 0.052778 0.986673 1 3

Virginia NTNCWS 3301-10000 GW 0.013327 1.000000 0 0

Virginia NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

2 Virgin Islands CWS 25-500 GW 0.000000 0.000000 0 0

Virgin Islands CWS 25-500 SW 0.203449 0.203449 0 1

Virgin Islands CWS 501-3300 GW 0.000000 0.203449 0 0

Virgin Islands CWS 501-3300 SW 0.009623 0.213072 0 0

Virgin Islands CWS 3301-10000 GW 0.000000 0.213072 0 0

Virgin Islands CWS 3301-10000 SW 0.007027 0.220099 0 0

Virgin Islands NTNCWS 25-500 GW 0.000000 0.220099 0 0
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-19

Virgin Islands NTNCWS 25-500 SW 0.298099 0.518198 1 1

Virgin Islands NTNCWS 501-3300 GW 0.000000 0.518198 0 0

Virgin Islands NTNCWS 501-3300 SW 0.189741 0.707939 0 0

Virgin Islands NTNCWS 3301-10000 GW 0.000000 0.707939 0 0

Virgin Islands NTNCWS 3301-10000 SW 0.292061 1.000000 1 0

4 Vermont CWS 25-500 GW 0.151019 0.151019 0 1

Vermont CWS 25-500 SW 0.168637 0.319656 0 0

Vermont CWS 501-3300 GW 0.228719 0.548375 1 2

Vermont CWS 501-3300 SW 0.150632 0.699007 0 0

Vermont CWS 3301-10000 GW 0.144298 0.843305 0 0

Vermont CWS 3301-10000 SW 0.156398 0.999702 1 1

Vermont NTNCWS 25-500 GW 0.000298 1.000000 0 0

Vermont NTNCWS 25-500 SW 0.000000 1.000000 0 0

Vermont NTNCWS 501-3300 GW 0.000000 1.000000 0 0

Vermont NTNCWS 501-3300 SW 0.000000 1.000000 0 0

Vermont NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Vermont NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

17 Washington CWS 25-500 GW 0.199296 0.199296 4 4

Washington CWS 25-500 SW 0.063516 0.262812 0 1

Washington CWS 501-3300 GW 0.307767 0.570579 5 4

Washington CWS 501-3300 SW 0.048778 0.619357 1 1

Washington CWS 3301-10000 GW 0.252023 0.871380 4 4

Washington CWS 3301-10000 SW 0.047768 0.919148 1 0

Washington NTNCWS 25-500 GW 0.015331 0.934479 0 0

Washington NTNCWS 25-500 SW 0.018754 0.953233 0 0

Washington NTNCWS 501-3300 GW 0.014947 0.968180 0 1

Washington NTNCWS 501-3300 SW 0.031820 1.000000 1 2

Washington NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Washington NTNCWS 3301-10000 SW 0.000000 1.000000 0.0 0

21 Wisconsin CWS 25-500 GW 0.080289 0.080289 0 0

Wisconsin CWS 25-500 SW 0.000000 0.080289 0 0

Wisconsin CWS 501-3300 GW 0.325307 0.405597 7 8

Wisconsin CWS 501-3300 SW 0.001226 0.406822 0 0

Wisconsin CWS 3301-10000 GW 0.413393 0.820215 9 11

Wisconsin CWS 3301-10000 SW 0.007789 0.828004 0 0

Wisconsin NTNCWS 25-500 GW 0.105799 0.933804 2 2

Wisconsin NTNCWS 25-500 SW 0.000000 0.933804 0 0
UCMR Statistical Design August 2001

Appendix B. Probability of Selection, with Expected and Initial SMP

Systems Selected for Assessment Monitoring

Total

Number of

Systems

State/Territory System

Type System Size SourceType Probability CumulativeProbability

Expected #

of Systems

Actual # of

Systems

B-20

Wisconsin NTNCWS 501-3300 GW 0.066196 1.000000 1 0

Wisconsin NTNCWS 501-3300 SW 0.000000 1.000000 0 0

Wisconsin NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Wisconsin NTNCWS 3301-10000 SW 0.000000 1.000000 0 0

10 West Virginia CWS 25-500 GW 0.049667 0.049667 0 0

West Virginia CWS 25-500 SW 0.061836 0.111503 0 0

West Virginia CWS 501-3300 GW 0.154994 0.266497 2 0

West Virginia CWS 501-3300 SW 0.232457 0.498954 2 5

West Virginia CWS 3301-10000 GW 0.083186 0.582140 1 0

West Virginia CWS 3301-10000 SW 0.328074 0.910214 3 4

West Virginia NTNCWS 25-500 GW 0.011075 0.921289 0 0

West Virginia NTNCWS 25-500 SW 0.010705 0.931994 0 0

West Virginia NTNCWS 501-3300 GW 0.003917 0.935911 0 0

West Virginia NTNCWS 501-3300 SW 0.009707 0.945618 0 1

West Virginia NTNCWS 3301-10000 GW 0.000000 0.945618 0 0

West Virginia NTNCWS 3301-10000 SW 0.054382 1.000000 1 0

3 Wyoming CWS 25-500 GW 0.125408 0.125408 0 0

Wyoming CWS 25-500 SW 0.187899 0.313306 0 1

Wyoming CWS 501-3300 GW 0.145051 0.458358 1 1

Wyoming CWS 501-3300 SW 0.105977 0.564335 0 0

Wyoming CWS 3301-10000 GW 0.087057 0.651392 0 0

Wyoming CWS 3301-10000 SW 0.228394 0.879786 1 0

Wyoming NTNCWS 25-500 GW 0.008824 0.888609 0 0

Wyoming NTNCWS 25-500 SW 0.091474 0.980084 0 1

Wyoming NTNCWS 501-3300 GW 0.003474 0.983557 0 0

Wyoming NTNCWS 501-3300 SW 0.016443 1.000000 0 0

Wyoming NTNCWS 3301-10000 GW 0.000000 1.000000 0 0

Wyoming NTNCWS 3301-10000 SW 0.000000 1.000000 0 0
UCMR Statistical Design August 2001

C-1

Appendix C

Acronyms

CCL - Contaminant Candidate List

CFR - Code of Federal Regulations

CWS - community water system

EPA - Environmental Protection Agency

EPTDS - Entry Point to the Distribution System

GW - ground water

GUDI - ground water under the direct influence (of surface water)

NAWQA - National Water Quality Assessment Program

NCOD - National Drinking Water Contaminant Occurrence Database

NTNCWS - non-transient non-community water system

PA - Partnership agreement

PWS - Public Water System

SDWA - Safe Drinking Water Act

SDWIS - Safe Drinking Water Information System

SDWIS FED - the Federal Safe Drinking Water Information System

SMP - State monitoring plan

SW - surface water 

TNCWS - transient non-community water system

UCMR - Unregulated Contaminant Monitoring Regulation/Rule

USEPA - United States Environmental Protection Agency 
UCMR Statistical Design August 2001

C-2
UCMR Statistical Design August 2001

D-1

Appendix D

Definitions

Assessment Monitoring means sampling, testing, and reporting of listed contaminants that have

available analytical methods and for which preliminary data indicate their possible occurrence in

drinking water. Assessment Monitoring will be conducted for the UCMR (1999) List 1

contaminants.

Index Systems means a limited number of small CWSs and NTNCWSs, selected from the

Assessment Monitoring systems in State Plans, that will be required to provide more detailed and

frequent monitoring for the UCMR (1999) List 1 contaminants (§141.40(a)(6)). The Index Systems

will be selected to geographically coincide with watersheds and areas studied under the United States

Geological Survey’s National Water Quality Assessment program. In addition to the reporting

information required for Assessment Monitoring, the Index Systems must also report information

on system operating conditions (such as water source, pumping rates, and environmental setting)

(§141.40(a)(6)). These systems must monitor each year of the 5-year UCMR cycle, with EPA paying

for all reasonable monitoring costs (§141.40(a)(4)(i)(A)). This more detailed and frequent

monitoring will provide important information with which EPA can more fully evaluate the

conditions under which small systems operate.

Listed contaminant means a contaminant identified as an analyte in Table 1, 141.40(a)(3) of the

Unregulated Contaminant Monitoring Regulation (UCMR). To distinguish the current 1999 UCMR

listed contaminants from potential future UCMR listed contaminants, all references to UCMR

contaminant lists will identify the appropriate year in parenthesis immediately following the acronym

UCMR and before the referenced list. For example, the contaminants included in the UCMR (1999)

List include the component lists identified as UCMR (1999) List 1, UCMR (1999) List 2 and UCMR

(1999) List 3 contaminants.

Listing cycle means the 5-year period for which each revised UCMR list is effective and during

which no more than 30 unregulated contaminants from the list may be required to be monitored.

EPA is mandated to develop and promulgate a new UCMR List every 5 years.

Monitored systems means all community water systems serving more than 10,000 people, and the

national representative sample of community and non-transient non-community water systems

serving 10,000 or fewer people that are selected to be part of a State Plan for the UCMR. (Note that

for this round of Assessment Monitoring, systems that purchase their primary source of water are

not included in the monitoring.)

Monitoring (as distinct from Assessment Monitoring) means all aspects of determining the quality

of drinking water relative to the listed contaminants. These aspects include drinking water sampling

and testing, and the reviewing, reporting, and submission to EPA of analytical results.

Most vulnerable systems (or Systems most vulnerable) means a subset of 5 to not more than 25

systems of all monitored systems in a State that are determined by that State in consultation with the

EPA Regional Office to be most likely to have the listed contaminants occur in their drinking waters,

considering the characteristics of the listed contaminants, precipitation, system operation, and

environmental conditions (soils, geology and land use).
UCMR Statistical Design August 2001

D-2

Pre-Screen Testing means sampling, testing, and reporting of the listed contaminants that may have

newly emerged as drinking water concerns and, in most cases, for which methods are in an early

stage of development. Pre-Screen Testing will be conducted by a limited number of systems (up to

200). States will nominate up to 25 of the most vulnerable systems per State for Pre-Screen Testing.

The actual Pre-Screen Testing systems will be selected from the list of nominated systems through

the use of a random number generator. Pre-Screen Testing will be performed to determine whether

a listed contaminant occurs in sufficient frequency in the most vulnerable systems or sampling

locations to warrant its being included in future Assessment Monitoring or Screening Surveys. PreScreen Testing will be conducted for the UCMR (1999) List 3 contaminants. 

Random Sampling is a statistical sampling method by which each member of the population has an

equal probability (an equal random chance) of being selected as part of a sample (the sample being

a small subset of the population which represents the population as a whole).

Representative Sample (or National Representative Sample) means a small subset of all community

and non-transient non-community water systems serving 10,000 or fewer people which EPA selects

using a random number generator. The systems in the representative sample are selected using a

stratified random sampling process that ensures that this small subset of systems will proportionally

reflect (is “representative” of) the actual number of size- and water type-categories of all small

systems nationally. In finalizing State Plans, a State may substitute a system from the replacement

list for a system selected as part of the original representative sample, if a system on the

representative sample list in the State Plan is closed, merged or purchases water from another

system. 

Sampling means the act of collecting water from the appropriate location in a public water system

(from the applicable point from an intake or well to the end of a distribution line, or in some limited

cases, a residential tap) following proper methods for the particular contaminant or group of

contaminants.

Sampling Point means a unique location where samples are to be collected. 

Screening Survey means sampling, testing, and reporting of the List 2 contaminants. These

contaminants have analytical methods which have been recently developed, and have uncertain

potential for occurrence in drinking water. Under the final List 2 Rule (66 FR 2273), two Screening

Surveys will be conducted by a subset of approximately 180 small systems from the 800 small

systems conducting Assessment Monitoring. Screening Survey one will be conducted by small

systems during 2001 for the List 2 chemical contaminants. Screening Survey two will be conducted

by small systems during 2003 for the List 2 microbiological contaminant, Aeromonas. 

State means each of the fifty States, the District of Columbia, U.S. Territories, and Tribal lands. For

the national representative sample, Guam, the Commonwealth of Puerto Rico, the Northern Mariana

Islands, the Virgin Islands, American Samoa, and the Trust Territories of the Pacific Islands are each

treated as an individual State. All Tribal water systems in the U.S. which have status as a State under

Section 1451 of the Safe Drinking Water Act for this program will be considered collectively as one

State for the purposes of selecting a representative sample of small systems. 

State Monitoring Plan (or State Plan) means a State’s portion of the national representative sample

of CWSs and NTNCWSs serving 10,000 or fewer people which must monitor for unregulated

contaminants (Assessment Monitoring, Screening Survey(s) and Index Systems) and all large

systems (systems serving greater than 10,000 people) which are required to monitor for Screening

Survey contaminants. A State Plan may be developed by a State’s acceptance of EPA’s
UCMR Statistical Design August 2001

D-3

representative sample for that State, or by a State’s selection of systems from a replacement list for

systems specified in the first list that are closed, are merged, or purchase water from another system.

A State Plan also includes the process by which the State will inform each public water system of

its selection for the plan and of its responsibilities to monitor. A State Plan will also include the

systems required to conduct Pre-Screen Testing, selected from the State’s designation of vulnerable

systems. The State Plan may be part of the Partnership Agreement (PA) between the State and EPA.

Stratified Random Sampling is a procedure to draw a random sample from a population that has been

divided into subpopulations or strata, with each stratum comprised of a population subset sharing

common characteristics. Random samples are selected from each stratum proportional to that

stratum’s proportion of the entire population. The aggregate random sample (compiled from all the

strata samples) provides a random sample of the entire population that reflects the proportional

distribution of characteristics of the population. In the context of the UCMR, the population served

by public water systems was stratified by size (with size categories of 500 or fewer people served,

501 to 3,300 people served, and 3,301 to 10,000 people served) and by water source type supplying

the water system (ground water or surface water). This stratification was done to ensure that systems

randomly selected as nationally representative sample systems would proportionally reflect the actual

number of size and water type categories nationally.

Testing means, for the purposes of the UCMR and distinct from Pre-Screen Testing, the submission

and/or shipment of samples following appropriate preservation practices to protect the integrity of

the sample; the chemical, radiological, physical and/or microbiological analysis of samples; and the

reporting of the sample’s analytical results for evaluation. Testing is a subset of activities defined

as monitoring.

Unregulated contaminants means chemical, microbiological, radiological and other substances that

occur in drinking water or sources of drinking water that are not currently regulated under the federal

drinking water program. EPA has not issued standards for these substances in drinking water (i.e.,

maximum contaminant levels or treatment technology requirements). EPA is required by Congress

to establish a program to monitor for selected unregulated contaminants in public water systems to

determine whether they should be considered for future regulation to protect public health. The

selected contaminants are listed in 141.40(a)(3), Table 1, the UCMR List.

Vulnerable time (or vulnerable period) means the time (or, in some cases, the 3-month quarter) of

the year determined as the most likely to have the listed group of contaminants present at their

highest concentrations or densities in drinking water. The vulnerable determination, in the case of

the UCMR, is made by the EPA or by the State (under arrangement with the EPA) for a system,

subset of systems, or all systems in a State. The vulnerable determination is based on characteristics

of the contaminants, precipitation, system operations, and environmental conditions such as soil

types, geology, and land use. This determination does not indicate or imply that the listed

contaminants will be identified in the drinking water with certainty, but only that sampling

conducted during the vulnerable period presumably has the highest likelihood of identifying those

contaminants in higher concentrations relative to other sampling times of the year, if and when the

contaminants occur.
UCMR Statistical Design August 2001

D-4