U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2011–5153

National Water-Quality Assessment Program

Quality of Major Ion and Total Dissolved Solids Data 

from Groundwater Sampled by the National Water-Quality 

Assessment Program, 1992–2010
Cover. Small-capacity stock well located near Jackson, Wyoming. (Photograph by Michael G. Rupert, U.S. Geological Survey.)
Quality of Major Ion and Total Dissolved 

Solids Data from Groundwater Sampled by 

the National Water-Quality Assessment 

Program, 1992–2010

By Eliza L. Gross, Bruce D. Lindsey, and Michael G. Rupert

National Water-Quality Assessment Program

Scientific Investigations Report 2011–5153

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2012

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Suggested citation:

Gross, E.L., Lindsey, B.D., and Rupert, M.G., 2012, Quality of major ion and total dissolved solids data from 

groundwater sampled by the National Water-Quality Assessent Program, 1992–2010: U.S. Geological Survey 

Scientific Investigations Report 2011–5153, 26 p.
iii

Foreword

The U.S. Geological Survey (USGS) is committed to providing the Nation with reliable scientific information that helps to enhance and protect the overall quality of life and that 

facilitates effective management of water, biological, energy, and mineral resources (http://

www.usgs.gov/). Information on the Nation’s water resources is critical to ensuring long-term 

availability of water that is safe for drinking and recreation and is suitable for industry, irrigation, and fish and wildlife. Population growth and increasing demands for water make the 

availability of that water, measured in terms of quantity and quality, even more essential to the 

long-term sustainability of our communities and ecosystems.

The USGS implemented the National Water-Quality Assessment (NAWQA) Program in 

1991 to support national, regional, State, and local information needs and decisions related to 

water-quality management and policy (http://water.usgs.gov/nawqa). The NAWQA Program 

is designed to answer: What is the quality of our Nation’s streams and groundwater? How are 

conditions changing over time? How do natural features and human activities affect the quality of streams and groundwater, and where are those effects most pronounced? By combining 

information on water chemistry, physical characteristics, stream habitat, and aquatic life, the 

NAWQA Program aims to provide science-based insights for current and emerging water issues 

and priorities. From 1991 to 2001, the NAWQA Program completed interdisciplinary assessments and established a baseline understanding of water-quality conditions in 51 of the Nation’s river basins and aquifers, referred to as Study Units (http://water.usgs.gov/nawqa/studies/

study_units.html).

National and regional assessments are ongoing in the second decade (2001–2012) of the 

NAWQA Program as 42 of the 51 Study Units are selectively reassessed. These assessments extend the findings in the Study Units by determining water-quality status and trends at sites that 

have been consistently monitored for more than a decade, and filling critical gaps in characterizing the quality of surface water and groundwater. For example, increased emphasis has been 

placed on assessing the quality of source water and finished water associated with many of the 

Nation’s largest community water systems. During the second decade, NAWQA is addressing 

five national priority topics that build an understanding of how natural features and human activities affect water quality, and establish links between sources of contaminants, the transport 

of those contaminants through the hydrologic system, and the potential effects of contaminants 

on humans and aquatic ecosystems. Included are studies on the fate of agricultural chemicals, 

effects of urbanization on stream ecosystems, bioaccumulation of mercury in stream ecosystems, effects of nutrient enrichment on aquatic ecosystems, and transport of contaminants 

to public-supply wells. In addition, national syntheses of information on pesticides, volatile 

organic compounds (VOCs), nutrients, trace elements, and aquatic ecology are continuing. 

The USGS aims to disseminate credible, timely, and relevant science information to address practical and effective water-resource management and strategies that protect and restore 

water quality. We hope this NAWQA publication will provide you with insights and information to meet your needs, and will foster increased citizen awareness and involvement in the 

protection and restoration of our Nation’s waters. 

The USGS recognizes that a national assessment by a single program cannot address all 

water-resource issues of interest. External coordination at all levels is critical for cost-effective 

management, regulation, and conservation of our Nation’s water resources. The NAWQA 

Program, therefore, depends on advice and information from other agencies—Federal, State, 

regional, interstate, Tribal, and local—as well as nongovernmental organizations, industry, academia, and other stakeholder groups. Your assistance and suggestions are greatly appreciated.

William H. Werkheiser

USGS Associate Director for Water
iv

Contents

Foreword ........................................................................................................................................................iii

Abstract...........................................................................................................................................................1

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

Purpose and Scope ..............................................................................................................................2

Environmental and Quality-Control Data ...................................................................................................2

Types of Quality-Control Samples ......................................................................................................2

Compilation of Data ..............................................................................................................................2

Methods of Data Analysis ............................................................................................................................5

Methods Used to Determine Contamination Bias...........................................................................5

Methods Used to Determine Sampling Variability ..........................................................................5

Quality of Major Ion and Total Dissolved Solids Data..............................................................................6

Contamination Bias...............................................................................................................................6

Sampling Variability..............................................................................................................................9

Trends in Sampling Variability....................................................................................................9

Confidence Intervals .................................................................................................................23

Implications for Interpreting Environmental Data..................................................................................23

Potential Effects of Contamination Bias .........................................................................................24

Potential Effects of Sampling Variability.........................................................................................24

Summary........................................................................................................................................................25

Acknowledgments.......................................................................................................................................25

References Cited..........................................................................................................................................25
v

Figures

1. Graphs showing yearly proportion of reported values above the common maximum 

reporting level for calcium, magnesium, sodium, and potassium field blank data 

with 95-percent confidence interval error bars ......................................................................7

2. Graphs showing yearly proportion of reported values above the common maximum 

reporting level for chloride, sulfate, fluoride, and silica field blank data 

with 95-percent confidence interval error bars ......................................................................8

3. Graph showing yearly proportion of reported values above the common maximum 

reporting level for total dissolved solids field blank data with 95-percent confidence 

interval error bars.........................................................................................................................9

4. Graph showing upper 99-percent confidence limit for percentiles of chloride 

contamination in all groundwater samples based on data from field blanks.....................9

5. Graphs used to select low and high ranges of calcium and magnesium replicate 

concentrations used to determine sampling variability of analytes 

in groundwater samples............................................................................................................10

6. Graphs used to select low and high ranges of sodium and potassium replicate 

concentrations used to determine sampling variability of analytes 

in groundwater samples............................................................................................................11

7. Graphs used to select low and high ranges of chloride and sulfate replicate 

concentrations used to determine sampling variability of analytes 

in groundwater samples............................................................................................................12

8. Graphs used to select low and high ranges of fluoride and silica replicate 

concentrations used to determine sampling variability of analytes 

in groundwater samples............................................................................................................13

9. Graphs used to select low and high ranges of total dissolved solids replicate 

concentrations used to determine sampling variability of analytes 

in groundwater samples............................................................................................................14

10. Time-series plot showing a linear trend in the standard deviation of chloride 

replicates that had a mean concentration less than 100 milligrams per liter ..................17

11. Time-series plot with 95-percent confidence interval error bars and a regression 

line fit with 95-percent confidence interval limits showing a linear trend in the 

yearly average standard deviation of chloride replicates that had a mean 

concentration less than 100 milligrams per liter ...................................................................18

12. Graphs used to select low and high ranges of calcium replicate concentrations 

used to determine sampling variability of calcium in groundwater samples 

collected from 1997 through 2009 ............................................................................................19
vi

Tables

1. Number of quality-control groundwater samples collected in each of the 48 National 

Water-Quality Assessment Program study units that were used for the data analysis 

in this report...................................................................................................................................3

2. Upper 99-percent confidence limits for contamination by analytes in specified 

percentiles of all groundwater samples based on data from field blanks prepared 

at groundwater sample collection sites and maximum affected concentrations 

calculated based on the 99-percent upper confidence limit for the 95th percentile........4

3. Replicate set reporting levels and number of nondetects for each analyte ......................4

4. Estimates of sampling variability for analytes in groundwater samples collected 

from 1992 to 2009.........................................................................................................................16

5. Estimates of sampling variability for analytes in groundwater samples collected 

from 1992 to 2009 and changes in estimates of sampling variability for 1992–96 

and 1997–2009 for the standard deviation of potassium, chloride, and fluoride, 

and for both the standard deviation and relative standard deviation of calcium, 

magnesium, sodium, sulfate, and silica ..................................................................................20

6. Changes in sampling variability for calcium in groundwater samples collected 

from 1992 to 2009.........................................................................................................................21

7. Most appropriate sampling variabilities for application to environmental data 

on the basis of low and high concentrations and year........................................................22

Abbreviations, Acronyms, and Conversion Factors

mg/L milligrams per liter

NAWQA National Water-Quality Assessment

QC quality control

RSD relative standard deviation

SMCL Secondary Maximum Contaminant Level

UCL upper confidence limit

USEPA U.S. Environmental Protection Agency

USGS U.S. Geological Survey

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C=(°F-32)/1.8

Concentrations of chemical constituents in water are given in milligrams per liter (mg/L), which 

is approximately equal to parts per million.
Quality of Major Ion and Total Dissolved Solids Data 

from Groundwater Sampled by the National Water-Quality 

Assessment Program, 1992–2010

By Eliza L. Gross, Bruce D. Lindsey, and Michael G. Rupert

Abstract

Proper interpretation of water quality requires consideration of the effects that contamination bias and sampling 

variability might have on measured analyte concentrations. 

The effect of contamination bias and sampling variability on 

major ion and total dissolved solids data in water samples 

collected in 48 of the 52 National Water-Quality Assessment 

Program study units from 1992 to 2010 is discussed in this 

report. Contamination bias and sampling variability can occur 

as a result of sample collection, processing, shipping, and 

analysis. Contamination bias can adversely affect interpretation of measured concentrations in comparison to standards 

or criteria. Sampling variability can help determine the 

reproducibility of an individual measurement or whether two 

measurements are different. 

Field blank samples help determine the frequency and 

magnitude of contamination bias, and replicate samples 

help determine the sampling variability (error) of measured 

analyte concentrations. Quality control data were evaluated 

for calcium, magnesium, sodium, potassium, chloride, sulfate, 

fluoride, silica, and total dissolved solids. A 99-percent upper 

confidence limit is calculated from field blanks to assess the 

potential for contamination bias. For magnesium, potassium, 

chloride, sulfate, and fluoride, potential contamination in 

more than 95 percent of environmental samples is less than or 

equal to the common maximum reporting level. Contamination bias has little effect on measured concentrations greater 

than 4.74 mg/L (milligrams per liter) for calcium, 14.98 mg/L 

for silica, 4.9 mg/L for sodium, and 120 mg/L for total dissolved solids. Estimates of sampling variability are calculated 

for high and low ranges of concentration for major ions and 

total dissolved solids. Examples showing the calculation of 

confidence intervals and how to determine whether measured differences between two water samples are significant 

are presented.

Introduction

The U.S. Geological Survey’s (USGS) National-Water 

Quality Assessment (NAWQA) Program was implemented in 

1991 in order to describe current water-quality conditions and 

how they are changing and to improve scientific and public 

understanding of natural and human factors impacting those 

conditions. These objectives are being achieved through extensive monitoring within 52 study units, which consist of large 

river basin and aquifer systems throughout the United States. 

In Cycle I (1991–2001) and Cycle II (2002–12), much of the 

work involved gathering comparable information on water 

quality in both surface water and groundwater. 

Estimates of contamination bias and sampling variability 

resulting from sample collection, processing, shipment, and 

laboratory analysis are needed to quantify how much variability in water-quality measurements can be explained by field 

and laboratory methods, as compared to environmental factors 

(Mueller and Titus, 2005). Quality-control (QC) samples, 

such as field blank or replicate samples, are collected at the 

same time as the environmental samples in order to evaluate 

contamination bias and sampling variability. Contamination 

bias is the systematic error that can occur during sample collection, processing, shipping, or laboratory analysis. Contaminants can be introduced into water samples by exposure to 

airborne gases and particulates or from inadequately cleaned 

sample collection or analytical equipment (Mueller and Titus, 

2005). Variability is the degree of random error in independent 

measurements of the same quantity, and “sampling variability” 

(termed by Mueller, 1998, p. vii) is the variability introduced 

by sample collection, field processing, shipping, and laboratory analysis. Contamination bias and sampling variability 

are evaluated by collecting and analyzing QC samples. The 

frequency and magnitude of contamination bias are determined from field blank samples, and the sampling variability of measured analyte concentrations is determined from 
2 Quality of Data from Groundwater Sampled by the National Water-Quality Assessment Program, 1992–2010

replicate samples. The distribution of concentrations in field 

blank samples is used to estimate the potential distribution 

of contamination in the environmental samples. Similarly, 

the distribution of variability in the replicate sets is used to 

estimate potential sampling variability in the results from 

environmental samples. Estimates from a particular set of 

field blanks or replicates can be applied to a particular set of 

environmental samples to describe similar sample collection 

and analytical methods, sample collection site characteristics, and sample collection during a specific time period.

Purpose and Scope

This report describes the quality of major ion and total 

dissolved solids data in groundwater samples collected in 48 

of the 52 NAWQA study units from 1992 to 2010. The QC 

analysis is used to (1) describe the frequency and magnitude 

of contamination using field blank samples; (2) evaluate 

sampling variability of the groundwater-quality data using 

replicate samples; and (3) identify potential effects of bias 

and sampling variability in interpreting the major ion and 

total dissolved solids data. Major ions reviewed in this report 

include calcium, magnesium, sodium, potassium, chloride, sulfate, fluoride, and silica. Although bicarbonate and 

carbonate are also major ions, these were not included in the 

study since they are computed from field measurement of 

alkalinity rather than laboratory measurements.

Environmental and Quality-Control 

Data

This report evaluates major ion and total dissolved 

solids data from groundwater and QC samples collected 

during 1992–2010 at locations within 48 of the 52 NAWQA 

study units. Contamination bias and sampling variability 

were assumed to be the same or similar in all 48 NAWQA 

study units even though this may not necessarily always be 

the case. The number of field blank and replicate samples 

used in this report from each study unit are listed in table 1. 

Groundwater samples were collected using the protocols 

for the collection of QC samples for NAWQA study-unit 

investigations documented by Koterba and others (1996) 

and were analyzed at the USGS National Water Quality 

Laboratory (NWQL) in Denver, Colorado (Shelton, 1994; 

U.S. Geological Survey, variously dated). Chemical analysis 

results on QC samples and associated environmental samples 

were compiled from the USGS’s NAWQA Data Warehouse 

(http://water.usgs.gov/nawqa/data). Data used in this report 

were retrieved from the NAWQA Data Warehouse during 

March 2010 and reviewed for consistency to identify and 

correct errors.

Types of Quality-Control Samples

A blank is a QC water sample that is intended to be free 

of and not interfere with the determination of the analytes of 

interest (Mueller and Titus, 2005). Blank samples are used to 

test for bias that could result from contamination during any 

stage of the sample collection and analysis process. A field 

blank is a specific type of blank sample used to demonstrate 

that (1) equipment has been adequately cleaned to remove 

contamination introduced from water samples obtained at 

previous sites; (2) sample collection and processing have not 

resulted in contamination; and (3) sample handling, shipping, 

and laboratory analysis have not introduced contamination 

(Mueller and Titus, 2005). Field blank samples are the only 

type of QC blank samples evaluated in this study.

Replicates are two or more QC samples that are collected 

or processed in such a manner that the replicate samples are 

thought to be essentially identical in composition (Mueller 

and Titus, 2005). Replicate samples are used to measure the 

sampling variability introduced during sample processing and 

analysis. Sequential replicates (multiple replicate samples 

collected at the same location one right after the other) were 

collected for this study. In addition to sampling variability, 

sequential replicates can include a small amount of environmental variability, though this is generally negligible for 

groundwater samples since wells are pumped until conditions 

are stable prior to sample collection.

Compilation of Data

Field blank data with multiple reporting levels were 

aggregated for each analyte in relation to the highest or most 

frequently used reporting level, which is referred to in this 

report as a “common maximum reporting level” (Apodaca 

and others, 2006). For each analyte (except for total dissolved 

solids) the highest reporting level in the field blank samples 

was used as a common maximum reporting level because 

these levels were consistent with detection limits observed in 

1993–2010 blind spike samples collected through the USGS 

Branch of Quality System’s Inorganic Blind Spike Sample 

Project. The most frequently used reporting level was used 

as the common maximum reporting level for total dissolved 

solids because only one groundwater sample represented the 

highest reporting level, and the highest reporting level was 

not consistent with any of the total dissolved solids detection 

limits observed in 1993–2010 blind spike samples collected 

through the Inorganic Blind Spike Sample Project. Common maximum reporting levels for each analyte are listed in 

table 2. A single common reporting level can lead to loss of 

information because some quantified results will be censored, 

especially for analytes with multiple reporting levels that 

are less than the defined common maximum reporting level. 

Since only slight differences occurred among reporting levels 
Environmental and Quality-Control Data 3

Table 1. Number of quality-control groundwater samples collected in each of the 48 National Water-Quality 

Assessment Program study units that were used for the data analysis in this report.

Study-unit 

abbreviation Study-unit name Number of field blanks

Number of 

replicate sets

ACAD Acadian-Pontchartrain Drainages 15 32

ACFB Apalachicola-Chattahoochee-Flint River Basin 19 43

ALBE Albemarle-Pamlico Drainage Basin 30 21

ALMN Allegheny and Monongahela River Basins 13 13

CAZB Central Arizona Basins 42 26

CCYK Central Columbia Plateau - Yakima River Basin 28 22

CNBR Central Nebraska Basins 30 20

CONN Connecticut, Housatonic, and Thames River Basins 35 19

COOK Cook Inlet Basin 7 2

DELR Delaware River Basin 16 6

EIWA Eastern Iowa Basins 33 41

GAFL Georgia-Florida Coastal Plain 18 30

GRSL Great Salt Lake Basins 43 23

HDSN Hudson River Basin 16 9

HPGW High Plains Regional Groundwater Study 59 55

KANA Kanawha - New River Basins 16 1

LERI Lake Erie - Lake Saint Clair Drainages 15 16

LINJ Long Island - New Jersey Coastal Drainages 47 34

LIRB Lower Illinois River Basin 40 17

LSUS Lower Susquehanna River Basin 0 17

MISE Mississippi Embayment 26 23

MOBL Mobile River Basin 15 12

NECB New England Coastal Basins 39 14

NROK Northern Rockies Intermontane Basins 23 14

NVBR Las Vegas Valley Area and the Carson and Truckee River Basins 32 17

OAHU Oahu 8 4

OZRK Ozark Plateaus 18 16

PODL Potomac River Basin and Delmarva Peninsula 38 64

PUGT Puget Sound Basin 17 13

REDN Red River of the North Basin 26 30

RIOG Rio Grande Valley 31 28

SACR Sacramento River Basin 29 20

SANA Santa Ana Basin 18 19

SANJ San Joaquin-Tulare Basins 46 55

SANT Santee River Basin and Coastal Drainages 41 25

SCTX South-Central Texas 49 32

SOFL Southern Florida 28 14

SPLT South Platte River Basin 44 43

TENN Tennessee River Basin 22 17

TRIN Trinity River Basin 16 19

UCOL Upper Colorado River Basin 25 15

UIRB Upper Illinois River Basin 22 13

UMIS Upper Mississippi River Basin 16 27

USNK Upper Snake River Basin 32 27

WHMI White, Great, and Little Miami River Basins 37 36

WILL Willamette Basin 22 2

WMIC Western Lake Michigan Drainages 5 20

YELL Yellowstone River Basin 12 11

Total 1,259 1,077
4 Quality of Data from Groundwater Sampled by the National Water-Quality Assessment Program, 1992–2010

for each analyte, censoring field blank data to the appropriate 

common maximum reporting level removed minor inconsistencies caused by multiple reporting levels.

Replicate data were not censored to a common maximum 

reporting level because sampling variability of replicates can 

only be analyzed when both samples in a replicate pair have 

detections. Reporting levels and the number of nondetections 

in replicate sets for all analytes are listed in table 3. Replicate 

sets consisting of all nondetections were excluded from the 

analysis of sampling variability (Martin, 2002). In addition, 

replicate pairs with detections in one sample but not in both 

were excluded from analysis due to inconsistency in detections. Less than 4 percent of the replicate pairs for fluoride 

represent pairs with uncertain detections, and less than 1 percent of replicate pairs represent pairs with uncertain detections 

for all other analytes.

Table 2. Upper 99-percent confidence limits for contamination by analytes in specified percentiles of all groundwater samples 

based on data from field blanks prepared at groundwater sample collection sites and maximum affected concentrations calculated 

based on the 99-percent upper confidence limit for the 95th percentile.

[mg/L, milligrams per liter]

Analyte

Number 

of field 

blanks

Common 

maximum 

reporting 

level 

(mg/L)

Field blanks with 

reported values greater 

than the common 

maximum reporting level

Upper 99-percent confidence limit 

(mg/L)

Maximum 

affected 

concentration 

(mg/L) Number Percent 75th 

percentile

90th 

percentile

95th 

percentile

99th 

percentile

Calcium 1,253 0.10 181 14.4 0.1 0.18 0.47 3.5 4.74

Magnesium 1,253 .10 23 1.8 0.1 0.1 0.1 1.7 1.00

Sodium 1,253 .20 84 6.7 0.2 0.2 0.5 4.4 4.90

Potassium 1,104 .24 9 0.8 0.24 0.24 0.24 2.30 2.40

Chloride 1,100 .30 17 1.5 0.3 0.3 0.3 1.7 3.00

Sulfate 1,099 .31 10 0.9 0.31 0.31 0.31 1.89 3.10

Fluoride 1,100 .20 4 0.4 0.2 0.2 0.2 0.2 2.00

Silica 1,253 .20 121 9.7 0.2 0.29 1.50 10 14.98

Total dissolved solids 1,083 10 52 4.8 10 10 12 33 120.00

Table 3. Replicate set reporting levels and number of nondetects for each analyte.

[bold indicates most common reporting level for each analyte; mg/L, milligrams per liter]

Analyte

Total number 

of replicate 

sets

Reporting levels

Number of replicate 

sets with nondetects 

for both 

groundwater samples

Number of replicate 

sets with nondetects 

for one 

groundwater sample

Number of 

replicate sets 

used for study

Calcium 1,045 0.02 0 1 1,044

Magnesium 1,045 0.01 0 3 1,042

Sodium 1,045 0.2 0 3 1,042

Potassium 1,045 0.1, 0.06 6 5 1,034

Chloride 1,044 1.0, 0.1 0 3 1,041

Sulfate 1,074 0.31, 0.18, 0.1, 0.01 20 6 1,048

Fluoride 1,043 0.5, 0.2, 0.171, 0.17, 0.16, 0.131, 0.123, 

0.12, 0.115, 0.104, 0.101, 0.1, 0.096, 

0.091, 0.08, 0.078, 0.06, 0.058, 0.055, 

0.053, 0.051, 0.019, 0.007

289 36 718

Silica 1,042 0.1, 0.01 0 2 1,040

Total dissolved solids 1,008 10 1 0 1,007
Methods of Data Analysis 5

Methods of Data Analysis

Contamination bias and sampling variability can be evaluated through statistical analysis of field blank and replicate 

samples, respectively. The primary purpose of evaluating contamination bias and sampling variability is to determine their 

effects on interpretation of the associated environmental data.

Methods Used to Determine Contamination Bias

The purpose of analyzing field blanks is to estimate the 

amount of contamination that might have been introduced 

during the collection, processing, shipping, and analyzing of 

environmental samples. The frequency and distribution of 

contamination identified in field blank samples is assumed to 

apply to environmental samples because both samples were 

collected, processed, shipped, and analyzed in the same way, 

at the same or similar sites, and during the same time period. 

Ideally, the bias introduced by contamination will be so small 

that concentrations in field blanks are less than the laboratory 

detection limit (Mueller and Titus, 2005).

Field blank data collected during the sample collection 

period were analyzed for temporal trends to determine if contamination bias changed over time. The proportion of reported 

values above the common maximum reporting level was 

calculated for each year from 1993 to 2009 for each analyte. 

The upper and lower 95-percent confidence intervals for each 

yearly proportion were calculated and plotted as error bars surrounding the proportion, and the plotted data were analyzed to 

evaluate trends over time.

To assess the potential for contamination at or above the 

common maximum reporting level for each analyte, upper 

confidence limits (UCLs) were constructed for percentiles 

of the distribution of concentration in the field blanks. The 

UCL is the maximum contamination expected in a specified percentage of water samples. Therefore, the 99-percent 

UCL for the 95th percentile indicates that with 99-percent 

confidence, the resulting amount of contamination would be 

exceeded in no more than 5 percent of water samples. The 

99-percent UCL at the 95th percentile also can be explained 

as the maximum contamination expected in 95 percent of the 

samples with only a 1-percent chance that the contamination 

has been underestimated.

Statistical techniques that assume normality when 

calculating the UCL are not applicable since the distribution 

of concentrations in field blanks can be highly skewed. A 

method described by Hahn and Meeker (1991) is appropriate 

for skewed data and can be used to determine a distributionfree UCL for a percentile. The UCL is calculated using order 

statistics, which rank data values from small to large, and a 

binomial probability (Mueller and Titus, 2005). Mueller and 

Titus include an example of this calculation (Mueller and 

Titus, 2005, p. 4 and 6). A one-sided 99-percent UCL was 

calculated at the 75th, 90th, 95th, and 99th percentiles for 

analyte concentrations in field blanks using the SAS statistical 

software (SAS Institute Inc., 1990).

Methods Used to Determine Sampling 

Variability

Sampling variability can be estimated by using some 

measure of the dispersion of repeated measurements, such as 

the standard deviation of field replicates (Mueller and Titus, 

2005). Because sampling variability of replicates can only be 

determined when both samples in a pair have detections, only 

replicate pairs with detections were included (Apodaca and 

others, 2006). Sampling variability of replicate data was analyzed according to different statistical measures over different 

concentration ranges. Over a low range of concentrations, 

standard deviation of replicates generally is uniform, but at 

higher concentrations, standard deviation tends to increase in 

proportion to concentration (Mueller and Titus, 2005). Within 

this high range, the relative standard deviation (RSD), defined 

as the standard deviation divided by the mean concentration, 

is generally uniform. The RSD is also known as the coefficient 

of variation (Mueller and Titus, 2005).

Sampling variability over the range of observed concentrations can be approximated by dividing the replicate data 

into segments where either the standard deviation or the RSD 

is relatively constant (Anderson, 1987). Over the low-concentration range, sampling variability is estimated as the average 

standard deviation of replicates; over the high-concentration 

range, sampling variability is estimated as the average RSD 

(Mueller and Titus, 2005). Selection of high and low concentration ranges can be performed using graphical analysis of 

standard deviation and RSD in relation to mean concentration 

for each replicate set. Approximate boundary values between 

ranges can be determined by the change in slope of a curve, 

such as a spline smooth (SAS Institute Inc., 1990) or loess 

(local regression) curve (S-Plus, 2002) through the center of 

the data. Adjustments could be necessary if the average lowrange standard deviation and high-range RSD do not intersect 

at the boundary.

Standard deviation and RSD of replicates were analyzed 

for temporal trends using Kendall’s tau-b, which is a nonparametric measure of association based on concordances and 

discordances in paired observations (SAS Institute Inc., 1990). 

Where temporal trends were statistically significant (p < 0.1), 

changes in laboratory methods, reported concentrations, or 

sample collection techniques were examined and data were 

further analyzed to calculate appropriate sampling variabilities 

for each analyte.

After calculating sampling variability for low- and highconcentration ranges of replicate data, confidence intervals 
6 Quality of Data from Groundwater Sampled by the National Water-Quality Assessment Program, 1992–2010

can be determined for any one measurement. The confidence 

interval for a concentration measured in a single water sample 

is defined as:

[CL ,CU] = C ± Z(1 – α/2) σ , (1)

where

CL,CU are the lower and upper limits of 

concentration for the 100(1 – α)-percent 

confidence interval,

C is the individual measured concentration,

Z is the ordinate if the normal curve (Z-value) 

contains 100(1 – α) percent of the 

distribution,

α is the probability that the confidence interval 

does not include the true concentration, 

and 

σ is the sampling variability for the measured 

concentration.

If the measured concentration is in the low range, σ 

is the average standard deviation of replicates within that 

range. If the measured concentration is in the high range, 

σ = C (RSD/100). 

The error inherent in a single measurement of concentration due to sampling variability is represented in 

equation 1 by the term Z(1 – α/2) σ. It is not possible, with 

100(1 – α)-percent confidence, to determine whether the concentration in the water sample exceeds the standard if a single 

measurement differs from a standard by less than this error.

For a mean concentration (C) from multiple water samples, the confidence interval for the true mean is calculated:

[ , ] C C C Z( / ) n L U = ± 1 2 −a

σ , (2)

where

n is the number of water samples,

C is the mean concentration for these water 

samples, and the other variables are as 

previously defined in equation 1. 

Again, the second term of equation 2 represents the error 

due to sampling variability, but in this instance it includes 

the number of water samples as well as the standard deviation. Thus, the error inherent in a mean concentration due 

to sampling variability can be decreased by collecting more 

water samples. This error can be considered the minimum that 

is typically achievable for determining a mean concentration 

in the absence of environmental variability. A determination of 

statistical significance is unlikely for a difference between two 

mean concentrations that is less than the sum of their inherent errors; therefore, small but true environmental differences 

might not be detected (Mueller and Titus, 2005, p. 7).

Quality of Major Ion and Total 

Dissolved Solids Data

Groundwater samples were analyzed for the following 

analytes:

• calcium

• magnesium

• sodium

• potassium

• chloride

• sulfate

• fluoride

• silica

• total dissolved solids dried at 180°C

The QC samples collected to analyze the quality of the 

NAWQA data included field blanks prepared using inorganic 

grade laboratory blank waters that were pumped through 

the groundwater sample collection equipment using pumps 

designed to prevent contamination. Groundwater replicates 

were collected sequentially as water was pumped from 

the well.

Contamination Bias

The relation between analyte concentrations and the dates 

on which field blanks were collected was analyzed to identify 

possible temporal trends in contamination. Plots were created 

showing the proportion of reported values above the common 

maximum reporting level and their 95-percent confidence 

intervals for years 1993–2009 (figs. 1–3). Since only a few 

groundwater samples were available for 1992 and 2010, data 

from these years were omitted. Year-by-year plots of magnesium, potassium, chloride, sulfate, fluoride, and total dissolved 

solids show that proportions of reported values above the 

common maximum threshold and a majority of their upper 

confidence levels were consistently below 0.25 from 1993 

to 2009. Calcium, silica, and sodium had higher proportions 

from 1993–95 than for the remaining years, which also corresponds with the time period when sample collection began. 

Sodium and silica also had proportions above 0.50 for 2005, 

but the proportions for 1996–2004 and 2006–09 remained 

fairly consistent. Overall, proportions of reported values above 

the common maximum reporting level and their 95-percent 

confidence intervals were (1) consistent for all of the years 

or (2) higher from 1993 to 1995, when the sample collection 
Quality of Major Ion and Total Dissolved Solids Data 7

Figure 1. Yearly proportion of reported values above the common maximum reporting level for calcium, magnesium, sodium, and 

potassium field blank data with 95-percent confidence interval error bars.

Sodium field blanks Potassium field blanks

Magnesium field blanks

Proportion of reported values above

the common maximum reporting level

0

0.25

0.50

0.75

1.00

Year

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Proportion of reported values above

the common maximum reporting level

0

0.25

0.50

0.75

1.00

Year

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Proportion of reported values above

the common maximum reporting level

0

0.25

0.50

0.75

1.00

Year

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Proportion of reported values above

the common maximum reporting level

0

0.25

0.50

0.75

1.00

Year

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Calcium field blanks

95-percent confidence interval 

error bars around the mean

EXPLANATION
8 Quality of Data from Groundwater Sampled by the National Water-Quality Assessment Program, 1992–2010

Figure 2. Yearly proportion of reported values above the common maximum reporting level for chloride, sulfate, fluoride, and silica 

field blank data with 95-percent confidence interval error bars.

Fluoride field blanks Silica field blanks

Sulfate field blanks

Proportion of reported values above

the common maximum reporting level

0

0.25

0.50

0.75

1.00

Year

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Proportion of reported values above

the common maximum reporting level

0

0.25

0.50

0.75

1.00

Year

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Proportion of reported values above

the common maximum reporting level

0

0.25

0.50

0.75

1.00

Year

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Proportion of reported values above

the common maximum reporting level

0

0.25

0.50

0.75

1.00

Year

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Chloride field blanks

95-percent confidence interval 

error bars around the mean

EXPLANATION
Quality of Major Ion and Total Dissolved Solids Data 9

program began, and were consistent for the remaining years, 

except for the high proportion for 2005 for silica and sodium. 

The distribution of proportions of reported values above the 

common maximum reporting level for each analyte did not 

appear to be due to an overall increase or decrease during the 

period of record, but could have been affected by changes in 

sample collection frequency and reporting level.

Data from all field blanks were used to calculate UCLs 

for selected percentiles of contamination, which were then 

assumed to be applicable to all environmental samples collected from 1992 to 2010. The 99-percent UCL was selected, 

and calculations were made for the 75th, 90th, 95th, and 99th 

percentiles (table 2). The potential contamination in groundwater is estimated to be no greater than the common maximum reporting level for all analytes in at least 75 percent of 

all samples. In at least 90 percent of all groundwater samples, 

potential contamination is estimated to be no greater than the 

common maximum reporting level for all analytes except 

calcium and silica in groundwater. Plots of the 99-percent 

UCLs show that potential contamination remains relatively 

low through at least the 95th percentiles for all analytes. For 

example, figure 4 shows potential contamination for chloride 

is not likely to exceed the common maximum reporting level 

of 0.30 mg/L in 97 percent of all groundwater samples.

Sampling Variability

Sampling variability within replicate samples collected at 

groundwater sites was estimated using the standard deviation 

over a low range of concentrations and the relative standard 

deviation (RSD) over a high range of concentrations. For each 

analyte, replicate standard deviation and RSD were graphed 

with the mean concentrations for each set of replicates in order 

to determine the division between low-range and high-range 

concentrations (figs. 5–9). Concentrations are shown on a 

logarithmic scale in the standard deviation graphs so that the 

lower range is emphasized. Each graph includes a smooth 

curve through the data points showing the general relation 

between concentrations and standard deviation or RSD. Where 

the smooth curve is roughly horizontal, there is no relation 

between concentrations and standard deviation or RSD. Over 

this range of concentration, sampling variability is considered 

constant. Divisions between low-range and high-range concentrations were defined by finding a point on the x-axis below 

which the curve for standard deviation or RSD was essentially 

horizontal and above which the curve for RSD was essentially 

horizontal. These boundary concentrations are represented on 

each graph with a vertical dashed line. Sampling variability for 

each analyte was estimated as the average standard deviation 

for the low range of concentrations or the average RSD for the 

high range of concentrations after low-range and high-range 

concentrations for each analyte were defined.

Trends in Sampling Variability

Temporal trends in the standard deviation and RSD were 

analyzed for each analyte in order to examine the stability 

of each sampling variability value over the period of record. 

Groundwater samples in the low range of mean concentration 

Figure 3. Yearly proportion of reported values above the common 

maximum reporting level for total dissolved solids field blank data 

with 95-percent confidence interval error bars. Proportion of reported values above the common maximum reporting level

0

0.25

0.50

0.75

1.00

Year

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Total dissolved solids field blanks

95-percent confidence interval 

error bars around the mean

EXPLANATION

Chloride concentration, in milligrams per liter

0.3

0.2

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

Percentile

40 50 60 70 80 90 100

Groundwater chloride concentrations by percentile

Common maximum reporting level

EXPLANATION

Figure 4. Upper 99-percent confidence limit for percentiles of 

chloride contamination in all groundwater samples based on data 

from field blanks.
Figure 5. Graphs used to select low and high ranges of calcium and magnesium replicate concentrations used to determine sampling variability groundwater samples. (Although values of concentration and standard deviation, by definition, cannot be negative, axes have been extended beof viewing data clustered at low values.)

Standard deviation of replicates, in milligrams per liter

0

10203040506070

Standard deviation of replicates, in milligrams per liter

0

102030

Mean concentration of replicates, in milligrams per liter

0.1 1 10 100 1,000

Calcium

Mean concentration of replicates, in m

0 100 200 300 400 

Mean concentration of replicates, in milligrams per liter

0.01 0.1 1 10 100 1,000

Mean concentration of replicates, in m

0 100 200 

Relative standard deviation of replicates, in percent

0

102030405060708090

100110120130140150

Calcium

Magnesium

Relative standard deviation of replicates, in percent

0

1020304050607080

Magnesium

EXPLANATION

Spline smooth curve through dataDivision between low and high concentrations
Figure 6. Graphs used to select low and high ranges of sodium and potassium replicate concentrations used to determine sampling variability ogroundwater samples. (Although values of concentration and standard deviation, by definition, cannot be negative, axes have been extended beof viewing data clustered at low values.)

Standard deviation of replicates, in milligrams per liter

0

102030405060708090

100

Standard deviation of replicates, in milligrams per liter

08

10

462

12

Mean concentration of replicates, in milligrams per liter

0.1 1 10 100 1,000 10,000

Sodium

Mean concentration of replicates, in m

0 1,000 2,

Mean concentration of replicates, in milligrams per liter

0.01 0.1 1 10 100

Mean concentration of replicates, in m

0 10 20 30 40 50 60 

Relative standard deviation of replicates, in percent

0

1020304050

Sodium

Potassium

Relative standard deviation of replicates, in percent

0

102030405060807090

100

Potassium

EXPLANATION

Spline smooth curve through dataDivision between low and high concentrations
Figure 7. Graphs used to select low and high ranges of chloride and sulfate replicate concentrations used to determine sampling variability of samples. (Although values of concentration and standard deviation, by definition, cannot be negative, axes have been extended below the origin data clustered at low values.)

Standard deviation of replicates, in milligrams per liter

0

102030405060709080

110100120130

Standard deviation of replicates, in milligrams per liter

0

120150

609030

110140170160

508020

100130

407010

180

Mean concentration of replicates, in milligrams per liter

0.1 1 10 100 1,000 10,000

Chloride

Mean concentration of replicates, in m

0 1,000 2,000 3,000 

Mean concentration of replicates, in milligrams per liter

0.01 0.1 1 10 100 1,000 10,000

Mean concentration of replicates, in m

0 1,000 2

Relative standard deviation of replicates, in percent

0

1020304050

Chloride

Sulfate

Relative standard deviation of replicates, in percent

0

10203040506070

Sulfate

EXPLANATION

Spline smooth curve through dataDivision between low and high concentrations
Figure 8. Graphs used to select low and high ranges of fluoride and silica replicate concentrations used to determine sampling variability of ansamples. (Although values of concentration and standard deviation, by definition, cannot be negative, axes have been extended below the origin data clustered at low values.)

Standard deviation of replicates, in milligrams per liter

0

0.10.20.30.40.50.60.70.90.81.21.01.41.11.31.5

Standard deviation of replicates, in milligrams per liter

0

102030

Mean concentration of replicates, in milligrams per liter

0.01 0.1 1 10

Fluoride

Mean concentration of replicates, in m

0 1 2 3 4 5 

Mean concentration of replicates, in milligrams per liter

1 10 100

Mean concentration of replicates, in m

0 10 20 30 40 50 

Relative standard deviation of replicates, in percent

0

2040608090

100110120

10305070

130

Fluoride

Silica

Relative standard deviation of replicates, in percent

0

20406080

100120150

1030507090

110130140 Silica

EXPLANATION

Spline smooth curve through dataDivision between low and high concentrations
14 Quality of Data from Groundwater Sampled by the National Water-Quality Assessment Program, 1992–2010

Figure 9. Graphs used to select low and high ranges of total dissolved 

solids replicate concentrations used to determine sampling variability of 

analytes in groundwater samples. (Although values of concentration and 

standard deviation, by definition, cannot be negative, axes have been 

extended below the origin for ease of viewing data clustered 

at low values.) Standard deviation of replicates, in milligrams per liter

0

10

20

30

Mean concentration of replicates, in milligrams per liter

1 10 100

Mean concentration of replicates, in milligrams per liter

0 10 20 30 40 50 60 70 80 90

Relative standard deviation of replicates, in percent

0

20

40

60

80

100

120

150

10

30

50

70

90

110

130

140

EXPLANATION

Spline smooth curve through data

Division between low and high concentrations

Total dissolved solids

Total dissolved solids
Quality of Major Ion and Total Dissolved Solids Data 15

were analyzed for trends in standard deviation, whereas 

groundwater samples in the high range of mean concentration 

were analyzed for trends in RSD. Trends were identified as 

statistically significant (p < 0.01) for 13 of the 18 measures of 

sampling variability listed in table 4 using the Mann-Kendall 

trend test. Statistically significant trends were identified for the 

standard deviation of potassium, chloride, and fluoride, and for 

both the standard deviation and RSD of calcium, magnesium, 

sodium, sulfate, and silica. 

For each of the analytes, the number of significant 

decimal places in the reported concentrations was increased 

in the beginning of 1997. Before the change in 1997, the 

magnitude of differences between pairs of replicate concentrations was limited to a small number of values, leading to 

linear patterns in standard deviations and RSDs before 1997, 

as shown in figure 10, for example: the difference between 

two rounded concentrations could be 0.0 or 0.1, but not 0.005. 

The trend shown in figure 10 is significant over the entire time 

period. Increasing the number of reported significant decimal 

places from 1997 to 2009 produces an apparently significant 

(downward or negative) trend over the entire time period for 

standard deviations and (or) RSDs of calcium, magnesium, 

sodium, potassium, chloride, sulfate, fluoride, and silica.

When the time periods before (1992–96) or after (1997–

2009) the change in reported significant decimal places are 

considered separately, there are no trends in sampling variability for 1997–2009 for any analyte except chloride (table 5). 

Thus, this indicates that the apparent trends for 1992–2009 

data for all other analytes are an artifact of the changes in the 

number of reported significant decimal places. A statistically 

significant trend (p < 0.01) is identified for standard deviation 

of the low-range chloride concentrations during 1997–2009 

(table 5). The average standard deviation was calculated for 

each year for chloride and plotted with error bars showing the 

95-percent confidence intervals along with the trend line and 

its 95-percent confidence interval limits (fig. 11). Because only 

two samples collected in 1992 had chloride concentrations of 

less than 100 mg/L, samples from this year were excluded. 

The error bars for each of the years show overlap with the 

trend line or its fitted 95-percent confidence interval limits, but 

it is apparent that 1997–2003 standard deviations are slightly 

higher than 2004–09 standard deviations (fig. 11). When 

1997–2003 and 2004–09 standard deviations for chloride are 

analyzed separately, there is no longer a significant trend for 

these time periods.

If calcium, magnesium, sodium, potassium, sulfate, 

fluoride, and silica replicates are restricted to those after 

the change in reported significant figures in 1997, divisions 

between low- and high-concentration ranges are better defined 

than the divisions derived from the data for the entire time 

period. Although divisions between low- and high-concentration ranges are more distinct, the concentrations for each division remain the same for all analytes except calcium (fig. 12). 

For calcium, divisions are at a slightly different concentration 

than the value that was selected for the entire time period (fig. 

12). For comparison, table 6 includes sampling variabilities for 

calcium computed for the entire time period using the original 

division at 100 mg/L and for the separate time periods using 

the more distinct division at 50 mg/L based on the 1997–2009 

data. Sampling variabilities over both concentration ranges are 

smaller for groundwater samples collected during 1997–2009 

for calcium based on the more distinct division. In addition, 

sampling variabilities over both concentration ranges are the 

same or smaller for groundwater samples collected during 

1997–2009 compared to 1992–96 for all other analytes except 

sodium within the low range. Because analytical methods 

were not changed from 1992 to 2009, it may be likely that if 

more significant figures had been reported during the earlier 

time period, sampling variabilities from 1992–96 would have 

been more similar to the 1997 to 2009 values. 

Appropriate sampling variabilities for high and low concentrations for each analyte were determined by the stability 

of sampling variability values over different periods of record. 

Stability of sampling variability was analyzed according to 

statistical significance of temporal trends. Time periods analyzed included the entire time period (1992–2009) and periods 

before and after the change in the number of reported significant decimal places (1992–96 and 1997–2009). The RSDs 

of potassium, chloride, and fluoride and both the standard 

deviation and RSD of total dissolved solids computed over 

the entire time period (1992–2009) are considered appropriate 

for application to environmental data (table 7). The standard 

deviation of potassium and fluoride and both the standard 

deviation and RSD of calcium, magnesium, sodium, sulfate, 

and silica computed for 1997–2009 replicates are considered 

appropriate for application to environmental data collected 

during the entire time period (table 7). Although trends in the 

sampling variability of chloride were identified for the entire 

time period and for 1997–2009, when 1997–2003 and 2004–

09 data were considered separately, the trend was no longer 

significant. Thus, average standard deviations computed separately for 1992–96, 1997–2003, and 2004–09 (table 7) are also 

considered appropriate for application to environmental data 

collected within those respective time periods.
Table 4. Estimates of sampling variability for analytes in groundwater samples collected from 1992 to 2009. [bold indicates p-value less than or equal to 0.01; mg/L, milligrams per liter; NS, correlation not significant – p-value greater than 0.01; <, less than] Analyte Low concentrations High concentrations Range (mg/L) Number of replicate sets Average sampling variability (standard deviation, in mg/L) Temporal trend Kendall Tau b Range (mg/L) Number of replicate sets Average sampling variability (relative standard deviation, in percent) 

 Correlation coefficent p-value Corr

coe

Calcium 0.13–100 862 0.648 0.11576 <.0001 100–623.75 182 1.3 0.2Magnesium .04–30 821 0.117 0.20812 <.0001 30–301.2 221 1.5 0.Sodium .47–100 921 0.258 0.16826 <.0001 100–2,400 121 1.4 0.2Potassium .10–10 981 0.065 0.05641 0.0093 10–91 53 2.3 Chloride .18–100 919 0.301 -0.0628 0.0048 100–4,132.37 122 1.5 Sulfate .09–100 883 0.197 0.0913 <.0001 100–2,753 165 0.7 0.2Fluoride .03–1 638 0.012 0.22437 <.0001 1–7.89 80 3.3 Silica 1.15–20 554 0.122 0.13835 <.0001 20–81.53 486 0.9 0.Total dissolved solids 14.5–1,000 932 7.052 NS 0.1042 1,000–9,015 75 3.2 
Quality of Major Ion and Total Dissolved Solids Data 17

Figure 10. Time-series plot showing a linear trend in the standard deviation of chloride replicates that had a mean concentration less 

than 100 milligrams per liter (mg/L). (Only standard deviations less than 5 mg/L are shown.)

Year

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Standard deviation of replicates, in milligrams per liter

0

1

2

3

4

5

EXPLANATION

Trend line
18 Quality of Data from Groundwater Sampled by the National Water-Quality Assessment Program, 1992–2010

Figure 11. Time-series plot with 95-percent confidence interval error bars and a regression line fit with 95-percent 

confidence interval limits showing a linear trend in the yearly average standard deviation of chloride replicates that 

had a mean concentration less than 100 milligrams per liter. Standard deviation of replicates, in milligrams per liter

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

Year

1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

Regression line

95-percent confidence interval limits fit for the regression line

95-percent confidence interval error bars around the mean

EXPLANATION
Quality of Major Ion and Total Dissolved Solids Data 19

Figure 12. Graphs used to select low and high ranges of calcium replicate 

concentrations used to determine sampling variability of calcium in 

groundwater samples collected from 1997 through 2009. (Although values 

of concentration and standard deviation, by definition, cannot be negative, 

axes have been extended below the origin for ease of viewing data 

clustered at low values.) Standard deviation of replicates, in milligrams per liter

0

10

20

30

40

Mean concentration of replicates, in milligrams per liter

0.1 1 10 100 1,000

Mean concentration of replicates, in milligrams per liter

0 100 200 300 400 500 600 700

Relative standard deviation of replicates, in percent

0

40

80

120

160

180

20

60

100

140

EXPLANATION

Spline smooth curve through data

Division between low and high concentrations

Calcium

Calcium
Table 5. Estimates of sampling variability for analytes in groundwater samples collected from 1992 to 2009 and changes in estimates of sampling vaand 1997–2009 for the standard deviation of potassium, chloride, and fluoride, and for both the standard deviation and relative standard deviation of csodium, sulfate, and silica.—Continued [bold indicates p-value less than or equal to 0.01; mg/L, milligrams per liter; NS, correlation not significant – p-value greater than 0.01; <, less than; --, not applicable] Analyte Time period Low concentrations High concentrati

Range (mg/L) Number of replicate sets Average sampling variability (standard deviation, in mg/L) Temporal trend Kendall Tau b Range (mg/L) Number of replicate sets Average samp

variability (relative stand

deviation, in percent) 

Correlation coefficent p-value 

Calcium 1992–2009 0.13–100 862 0.648 0.11576 <.0001 100–623.75 182 1.3 

1992–1996 0.13–100 260 1.117 NS 0.1761 100–535 55 1.2 1997–2009 0.13–100 602 0.445 NS 0.1267 100–623.75 127 1.3 

Magnesium 1992–2009 0.04–30 821 0.117 0.20812 <.0001 30–301.2 221 1.5 

1992–1996 0.04–30 253 0.118 NS 0.5457 30–205 60 2.4 1997–2009 0.04–30 568 0.116 NS 0.3639 30–301.2 161 1.1 

Sodium 1992–2009 0.47–100 921 0.258 0.16826 <.0001 100–2,400 121 1.4 

1992–1996 0.47–100 277 0.192 NS 0.0248 100–2,400 36 2.1 1997–2009 0.47–100 644 0.286 NS 0.0564 100–1,857 85 1.1 

Potassium 1992–2009 0.10–10 981 0.065 0.05641 0.0093 10–91 53 2.3 

1992–1996 0.10–10 299 0.068 NS 0.1171 -- -- -- 1997–2009 0.10–10 682 0.063 NS 0.7501 -- -- -- 

Chloride 1992–2009 0.18–100 919 0.301 -0.0628 0.0048 100–4,132.37 122 1.5 

1992–1996 0.18–100 286 0.417 NS 0.2215 -- -- -- 1997–2009 0.18–100 633 0.249 -0.20014 <.0001 -- -- -- 

Sulfate 1992–2009 .09–100 883 0.197 0.0913 <.0001 100–2,753 165 0.7 

1992–1996 .10–100 264 0.201 -0.129 0.0052 100–2,600 49 0.7 1997–2009 .09–100 619 0.196 NS 0.0353 100–2,753 116 0.7 
Table 5. Estimates of sampling variability for analytes in groundwater samples collected from 1992 to 2009 and changes in estimates of sampling vaand 1997–2009 for the standard deviation of potassium, chloride, and fluoride, and for both the standard deviation and relative standard deviation of csodium, sulfate, and silica.—Continued[bold indicates p-value less than or equal to 0.01; mg/L, milligrams per liter; NS, correlation not significant – p-value greater than 0.01; <, less than; --, not applicable]

Analyte Time period

Low concentrations High concentrati

Range 

(mg/L)

Number of 

replicate 

sets

Average sampling 

variability 

(standard 

deviation, 

in mg/L)

Temporal trend 

Kendall Tau b Range 

(mg/L)

Number of 

replicate 

sets

Average samp

variability 

(relative stand

deviation, 

in percent)

Correlation 

coefficent p-value 

Fluoride 1992–2009 0.03–1 638 0.012 0.22437 <.0001 1–7.89 80 3.3 

1992–1996 0.03–1 161 0.013 NS 0.0421 -- -- -- 1997–2009 0.03–1 477 0.012 NS 0.0769 -- -- -- 

Silica 1992–2009 1.15–20 554 0.122 0.13835 <.0001 20–81.53 486 0.9 

1992–1996 1.15–20 176 0.173 NS 0.1907 20–81.5 135 1.5 1997–2009 1.15–20 378 0.099 NS 0.0231 20–81.53 351 0.7 

Total dissolved solids 1992–2009 14.5–1,000 932 7.052 NS 0.1042 1,000–9,015 75 3.2 

1992–1996 -- -- -- -- -- -- -- -- 1997–2009 -- -- -- -- -- -- -- -- 

Table 6. Changes in sampling variability for calcium in groundwater samples collected from 1992 to 2009.[bold indicates p-value less than or equal to 0.01; mg/L, milligrams per liter; NS, correlation not significant – p-value greater than 0.01; <, less than]

Analyte Time period

Low concentrations High concentration

Range 

(mg/L)

Number of 

replicate 

sets

Average sampling 

variability 

(standard 

deviation, 

in mg/L)

Temporal trend 

Kendall Tau b Range 

(mg/L)

Number of 

replicate 

sets

Average sampling 

variability 

(relative standard 

deviation, 

in percent)

Correlation 

coefficent p-value 

Calcium 1992–2009 0.13–100 862 0.648 0.11576 <.0001 100–623.75 182 1.3 

1992–1996 0.13–50 135 1.075 NS 0.3814 50–535 181 1.4 1997–2009 0.13–50 329 0.202 NS 0.4707 50–623.75 399 1.1 
Table 7. Most appropriate sampling variabilities for application to environmental data on the basis of low and high concentrations and year. [mg/L, milligrams per liter; --, not applicable] Analyte Low concentrations High concentrations Appropriate application time period1 Range (mg/L) Number of replicate sets Average sampling variability (standard deviation, in mg/L) Appropriate application time period1 Range (mg/L) Number of replicate sets Averag

(relativ

Calcium 1992–2009 0.13–50 464 0.202 1992–2009 50–623.75 580 Magnesium 1992–2009 0.04–30 821 0.116 1992–2009 30–301.2 221 Sodium 1992–2009 0.47–100 921 0.286 1992–2009 100–1,857 121 Potassium 1992–2009 0.10–10 981 0.063 1992–2009 10–91 53 Chloride 1992–1996 0.2–100 286 0.417 1992–2009 100–4,132.37 122 

1997–2003 0.2–100 366 0.31946 -- -- -- 2004–2009 0.182–100 267 0.14344 -- -- -- 

Sulfate 1992–2009 0.09–100 883 0.196 1992–2009 100–2,753 165 Fluoride 1992–2009 0.032–1 638 0.012 1992–2009 1–7.89 80 Silica 1992–2009 1.15–20 554 0.099 1992–2009 20–81.53 486 Total dissolved solids 1992–2009 14.5–1,000 932 7.052 1992–2009 1,000–9,015 75 

1Appropriate application time periods are the same as computation time periods, except for the standard deviation of potassium and fluoride and both the standard deviation 

deviation (RSD) of calcium, magnesium, sodium, sulfate, and silica, which have a computation time period of 1997–2009.
Implications for Interpreting Environmental Data 23

Confidence Intervals

Confidence intervals can be calculated around measured 

concentrations for any analyte by using the estimated sampling variabilities from table 7 and the appropriate Z statistic 

from a table of normal deviates. For a 95-percent confidence 

interval, α = 0.05 and Z(1 – σ/2) = 1.96. Confidence limits can 

be calculated for an individual measurement using equation 1 

and the mean of multiple measurements using equation 2. For 

example, if calcium in a groundwater sample has a measured 

concentration of 3 mg/L, the estimated sampling variability 

for the low concentration range from table 7 is 0.202 mg/L. 

A 95-percent confidence interval for the true concentration, 

based on this estimate, can be determined using equation 1:

[CL ,CU] = 3 ± 1.96 (0.202). (3)

Thus, the inherent error of the measurement is 

±0.396 mg/L or ±13.2 percent of the measured concentration.

For a higher calcium concentration, such as 90 mg/L, 

the 95-percent confidence interval can be calculated using 

the same equation with a sampling variability from table 7 of 

1.1 percent for the high-concentration range:

[ , ] . ( . C C ) L U = ± 90 1 96 90 1 1

100 . (4)

The inherent error of this measurement is ±1.9 mg/L or 

±2.2 percent of the measured concentration.

In addition, a 95-percent confidence interval for a mean 

calcium concentration of 3 mg/L in 10 groundwater samples 

can be determined using equation 2:

[ , ] . ( . C C ) L U = ±3 1 96 0 202

10 . (5)

The inherent error for 10 measurements is estimated to 

be ±0.13 mg/L or ±4.2 percent of the measured concentration. 

This represents the potential measurement error if calcium 

concentrations were exactly the same in all 10 groundwater 

samples. The actual standard deviation would probably be 

increased by other factors, such as environmental variability 

among groundwater samples. As a result, sampling variability for a mean characterizes the expected lower limit of 

overall variability.

Confidence intervals can also be used to determine 

whether two groundwater-quality measurements are significantly different. Confidence intervals can be calculated for 

two individual measurements in order to determine whether 

their difference can be attributed solely to sampling variability. 

If the computed confidence intervals for the two measurements overlap, then the difference is within the uncertainty 

of sampling variability. On the other hand, if the computed 

confidence intervals for the two measurements do not overlap, 

then a difference in concentration is indicated at the selected 

level of confidence.

In the example previously provided, the inherent 

error of the first calcium measurement of 3 mg/L was 

±0.396 mg/L, which means that the measurement has a 

95-percent confidence interval ranging from 2.6 mg/L to 

3.4 mg/L. The inherent error of another low concentration 

of calcium such as 4 mg/L, which differs from the previous 

measurement by only 1 mg/L, is ±.396 mg/L. This means 

that the measurement has a 95-percent confidence interval 

ranging from 3.6 mg/L to 4.4 mg/L. Because the ranges of 

these two confidence intervals do not overlap, the conclusion is that a data user can be 95 percent confident that the 

concentrations of calcium in the two water samples are 

different, even though they differ by only 1 mg/L. If the 

concentrations of interest had differed by less than 1 mg/L, 

the range of the 95-percent confidence intervals would have 

overlapped. Thus, the data user could have concluded with 

95-percent confidence that the concentrations of calcium in 

the two water samples were not truly different and that the 

difference resulted from sampling variability.

Analyte concentrations in the high range need to differ by more than 1 mg/L to be considered different. For 

instance, the previously provided example resulted in an 

inherent error of ±1.9 mg/L for a calcium measurement of 

90 mg/L and a 95-percent confidence interval ranging from 

88.1 to 91.9 mg/L. A high concentration of calcium such 

as 94 mg/L, which differs from 90 mg/L by 4 mg/L, has an 

inherent error of ±2.0 mg/L and a 95-percent confidence 

interval ranging from 92.0 to 96.0 mg/L. Since these confidence intervals do not overlap, a data user can be 95 percent 

confident that the concentrations of 90 and 94 mg/L are 

different. If these concentrations had differed by less than 

4 mg/L, the 95-percent confidence intervals would have 

overlapped and the concentrations would not be considered 

truly different.

Implications for Interpreting 

Environmental Data

Proper interpretation of environmental data such as 

NAWQA data involves analysis of the influence of contamination bias and sampling variability on major ion and total 

dissolved solids concentrations measured in groundwater. 

Because field blanks are collected in a manner similar to the 

way environmental samples are collected, field blanks can 

be used to determine the contamination bias associated with 

environmental samples, which provides a more comprehensive understanding of environmental data. Sampling 

variability is critical in determining the reproducibility of an 

individual measurement or whether two measurements are 

different. Both contamination bias and sampling variability 

are important variables in assessing the quality of environmental groundwater-quality data.
24 Quality of Data from Groundwater Sampled by the National Water-Quality Assessment Program, 1992–2010

Potential Effects of Contamination Bias

The distribution of concentrations in field blank samples 

is used to estimate the potential distribution of contamination 

in the environmental samples. Typically, the effect of contamination bias on a measured value can be ignored if potential 

contamination is less than 10 percent of a measured value, 

so the largest measured concentration that might be affected, 

hereafter termed “maximum affected concentration,” is estimated as 10 times the potential contamination (Mueller and 

Titus, 2005). A measure of the uncertainty in field blank contamination is provided through calculation of the 95-percent 

UCL (table 2). The UCL provides an uncertainty estimate for a 

percentile and is used as a conservative estimate of contamination at that percentile. This uncertainty measure can be used in 

evaluating the need to consider contamination in the analysis 

and interpretation of the major ion and total dissolved solids 

environmental groundwater-quality data.

Maximum affected concentrations were calculated for 

analytes and are listed in table 2. For calcium, potential contamination was no more than 0.4784 in at least 95 percent of 

all groundwater samples, so the maximum affected calcium 

concentration in environmental samples is 4.74 mg/L. Concentrations greater than this are not likely to be substantially 

compromised by contamination. Similarly, the maximum 

affected concentrations for other analytes are 1 mg/L for 

magnesium, 4.9 mg/L for sodium, 2.4 mg/L for potassium, 

3 mg/L for chloride, 3.1 mg/L for sulfate, 2 mg/L for fluoride, 

14.98 mg/L for silica, and 120 mg/L for total dissolved solids. 

For magnesium, potassium, chloride, sulfate, and fluoride, the 

potential contamination was no more than the common maximum reporting level in at least 95 percent of all groundwater 

samples (table 2), which means that any measured concentration in excess of 10 times that reporting level is not likely to 

be affected.

Potential Effects of Sampling Variability

Sampling variability can be used to (1) evaluate the 

confidence interval for an individual water-quality measurement or for multiple water-quality measurements, (2) determine whether a defined water-quality threshold or standard has 

been exceeded, and (3) determine whether two water-quality 

measurements are different (Apodaca and others, 2006). Uses 

of sampling variability are explained in more detail below. 

Sampling variability estimates associated with concentration 

examples were calculated using the replicate-analysis results 

found in table 7.

When interpreting sampling variability of groundwaterquality data, potential error in an individual measurement and 

the minimum difference likely to be identified as significant 

can be determined. Results of environmental samples are 

evaluated using confidence intervals calculated from estimates 

of sampling variability. For example, the Secondary Maximum Contaminant Level (SMCL) established by the U.S. 

Environmental Protection Agency (USEPA) for chloride is 

250 mg/L (U.S. Environmental Protection Agency, 1992). The 

USEPA establishes nonenforcable SMCLs for some analytes 

in order to provide standard water-quality guidelines that 

are meant to assist in management of aesthetic standards for 

drinking water (U.S. Environmental Protection Agency, 1992). 

At the SMCL of 250 mg/L, the sampling variability of chloride is estimated to be approximately 1.5 mg/L (table 7). The 

range of the 95-percent confidence interval for an individual 

measurement of 250 mg/L is 242.65 to 257.35 mg/L using 

equation 4. This means that measured concentrations as high 

as 257.35 mg/L do not necessarily indicate exceedance of the 

SMCL, while measured concentrations as low as 242.65 do 

not necessarily indicate compliance. Also, rounding of laboratory results can indicate an exceedance of a standard. When 

rounded to three significant figures, a reported concentration 

of at least 258 would indicate an exceedance of the SMCL 

with 95-percent confidence. 

Measurement errors resulting from sampling variability 

can impact the identification of significant differences between 

two measurements or means. If a true difference falls within 

the inherent sampling variability, it is not likely to be distinguished, and this can be determined by the size of the confidence intervals for the two measurements. If the confidence 

intervals overlap, the measured difference is not significant, 

but if the confidence intervals do not overlap, the difference 

is considered to be significant. For example, if chloride in 

groundwater has a concentration of 237 mg/L, the 95-percent confidence interval would be 230.03 to 243.97 mg/L. 

As calculated earlier, the 95-percent confidence interval for 

an individual chloride measurement of 250 mg/L is 242.65 to 

257.35 mg/L. Since the confidence intervals for chloride measurements between 237 and 250 mg/L overlap, these measurements are not considered significantly different. A measurement of 235 mg/L would have a confidence interval of 228.09 

to 241.91 mg/L and would be significantly different from a 

chloride measurement of 250 mg/L because the confidence 

intervals do not overlap. 

The potential errors due to sampling variability for 

two mean values will be less than those for two individual 

measurements becaues the effect of sampling variability is 

moderated by the number of groundwater samples. This also 

means that the confidence intervals for two mean values will 

be smaller than those for two individual values. For a mean of 

10 estimates, the 95-percent confidence interval is calculated 

for chloride in groundwater at a concentration of 250 mg/L 

using equation 5, and ranges from 249.07 to 250.93 mg/L. 

The 95-percent confidence interval for a mean concentration of 237 mg/L is 236.07 to 237.93 mg/L. The difference 

between the two means of 237 and 250 mg/L is significant 

because these confidence intervals do not overlap. Smaller 

confidence intervals indicate less of a chance of overlap and 

more of a chance of the values being significantly different, 

whereas larger confidence intervals have more of a chance 

of overlapping and less of a chance for the values to be 

significantly different.
References Cited 25

Summary

Concentrations of major ions and dissolved solids in field 

blank and replicate samples collected by the U.S. Geological Survey’s National Water-Quality Assessment (NAWQA) 

Program during 1992–2010 were used to assess contamination 

bias and sampling variability associated with environmental 

concentrations in groundwater.

Field blanks are quality-control (QC) samples used to 

estimate contamination associated with environmental waterquality samples. Based on the upper 99-percent confidence 

limit for the 95th percentile of measurements in field blanks, 

contamination bias has little effect on measured concentrations greater than 4.74 mg/L (milligrams per liter) for calcium, 

1 mg/L for magnesium, 4.9 mg/L for sodium, 2.4 mg/L for 

potassium, 3 mg/L for chloride, 3.1 mg/L for sulfate, 2 mg/L 

for fluoride, 14.98 mg/L for silica, and 120 mg/L for total 

dissolved solids. For magnesium, potassium, chloride, sulfate, 

and fluoride, the potential contamination in at least 95 percent 

of all groundwater samples is the same as or less than the common maximum reporting level of each analyte.

Field replicate samples can provide information on 

sampling variability. Estimates of average sampling variability 

were developed for high and low ranges of concentration for 

calcium, magnesium, sodium, potassium, chloride, sulfate, 

fluoride, silica, and total dissolved solids. Average sampling 

variabilities for low concentrations ranged from 0.012 mg/L 

for fluoride to 7.052 mg/L for total dissolved solids. Average 

sampling variabilities for high concentrations ranged from 

0.7 percent for sulfate and silica to 3.3 percent for fluoride.

Sampling variabilities calculated for each of these analytes can be used to evaluate confidence intervals for single or 

multiple water-quality measurements, determine if a waterquality standard has been exceeded, or determine whether 

two measurements are significantly different. Examples 

presented in this report show how to calculate potential error, 

relative error, and confidence intervals, and how to evaluate distinguishable exceedance of standards and differences 

between measurements. Confidence intervals, potential error, 

and relative error calculated for individual measurements are 

greater than those calculated for a mean of 10 measurements. 

Confidence intervals for individual measurements can be used 

to determine the likelihood that a standard has been exceeded. 

In addition, overlapping confidence intervals indicate that 

two water samples are not truly different, whereas confidence intervals that do not overlap indicate that the two water 

samples are significantly different. 

These findings are applicable to interpretation of the 

groundwater-quality environmental samples collected during 

1992–2010 in 48 of 52 NAWQA study units. Contamination 

bias and sampling variability were assumed to be the same or 

similar in all 48 NAWQA study units even though this may 

not necessarily always be the case. These results also provide 

a basis for comparison with the QC results for groundwater 

samples collected in subsequent years.

Acknowledgments

The authors would like to acknowledge the assistance and information provided by David K. Mueller 

of the U.S. Geological Survey. The tasks performed by 

the Cycle I and II NAWQA study-unit hydrologists and 

hydrologic technicians in collecting the major ion and 

total dissolved solids quality-control data are greatly 

appreciated. Without their efforts, analysis of these data 

would not have been possible.

References Cited

Apodaca, L.E., Mueller, D.K., and Koterba, M.T., 2006, 

Review of trace element blank and replicate data collected in ground and surface water for the National 

Water-Quality Assessment Program, 1991–2002: U.S. 

Geological Survey Scientific Investigations Report 

2006–5093, 32 p., available online at http://pubs.usgs.

gov/sir/2006/5093/.

Anderson, R.L., 1987, Practical statistics for analytical 

chemists: New York, Van Nostrand Reinhold, 316 p.

Hahn, G.J., and Meeker, W.Q., 1991, Statistical intervals—A guide to practitioners: New York, John Wiley 

and Sons, 392 p.

Koterba, M.T., Wilde, F.D., and Lapham, W.M., 1996, 

Ground-water data-collection protocols and procedures 

for the National Water-Quality Assessment Program: 

Collection and documentation of water-quality samples 

and related data: U.S. Geological Survey Open-File 

Report 95–399, 113 p., available online at http://pubs.

usgs.gov/of/1995/ofr-95-399/.

Martin, J.D., 2002, Variability of pesticide detections and 

concentrations in field replicate water samples collected 

for the National Water-Quality Assessment Program, 

1992–97: U.S. Geological Survey Water-Resources 

Investigations Report 01–4178, 64 p.

Mueller, D.K., 1998, Quality of nutrient data from streams 

and ground water sampled during 1993–95—National 

Water-Quality Assessment Program: U.S. Geological 

Survey Open-File Report 98–276, 25 p. 

Mueller, D.K., and Titus, C.J., 2005, Quality of nutrient 

data from streams and ground water sampled during 

water years 1992–2001: U.S. Geological Survey Scientific Investigations Report 2005–5106, 27 p., available 

online at http://pubs.usgs.gov/sir/2005/5106/.

SAS Institute Inc., 1990, SAS/Graph software—version 

8.1: Cary, North Carolina, SAS Institute Inc., 705 p.
26 Quality of Data from Groundwater Sampled by the National Water-Quality Assessment Program, 1992–2010

Shelton, L.R., 1994, Field guide for collecting and processing stream-water samples for the National Water-Quality 

Assessment Program: U.S. Geological Survey Open-File 

Report 94–455, 42 p.

S-Plus, 2002, S-Plus 6.1 for Windows Professional Edition, 

version 6.1, release 1: Seattle, Washington, Insightful Corporation, 698 p.

U.S. Environmental Protection Agency, 1992, Secondary 

drinking water regulations–Guidance for nuisance chemicals: Washington, D.C., Office of Water, Groundwater and 

Drinking Water, EPA 810/K-92-00, 3 p.

U.S. Geological Survey, variously dated, National field 

manual for the collection of water-quality data: U.S. 

Geological Survey Techniques of Water-Resources Investigations, book 9, chaps. A1–A9, available online at 

http://pubs.water.usgs.gov/twri9A.
For additional information:

Director

U.S. Geological Survey

215 Limekiln Road

New Cumberland, PA 17070

http://pa.water.usgs.gov/

Document prepared by the West Trenton Publishing Service Center
Gross and others—Quality of Data from Groundwater Sampled by the National Water-Quality Assessment Program, 1992–2010—Scientific Investigations Report 2011–5153