78 80 82 84 86 88 90 92 94 96

120

122

124

126

128

130

132

134

136

138

140

142

144

146

148

150

URANIUM SERIES

A

B

238U4.5x109

 yr

234Th 24.1 d 234Pa 1.18 m, 6.7 h

234U 2.46x105

 yr

230Th 8x10 yr

226Ra 1,602 yr

222Rn

218Po 3.05 m

214Pb 26.8 m

210Tl 1.32 m

206Tl 4.2 m

206Pb stable

210Po 138.4 d 

210Pb 22 yr

210Bi 4.85 d

214Bi 19.7 m 214Po 1.64x10 s

218At 1.5-2.0 s

218Rn 0.035 s

ATOMIC NUMBER

NEUTRON NUMBER

 3.82 d

4

-4

U.S. Department of the Interior

U.S. Geological Survey

Interpreting and Reporting Radiological

Water-Quality Data

Techniques and Methods 5–B6

Prepared by the U.S. Geological Survey Office of Water Quality, National Water Quality Laboratory

Book 5, Laboratory Analysis

Section B, Methods of the National Water Quality Laboratory

Chapter 6

Interpreting and Reporting Radiological 

Water-Quality Data

By David E. McCurdy, John R. Garbarino, and Ann H. Mullin

Book 5, Laboratory Analysis 

Section B, Methods of the National Water Quality Laboratory

Chapter 6

Techniques and Methods 5–B6

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2008

For product and ordering information:

World Wide Web: http://www.usgs.gov/pubprod

Telephone: 1-888-ASK-USGS

For more information on the USGS—the Federal source for science about the Earth,

its natural and living resources, natural hazards, and the environment:

World Wide Web: http://www.usgs.gov

Telephone: 1-888-ASK-USGS

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

McCurdy, D.E., Garbarino, J.R., and Mullin, A.H., 2008, Interpreting and reporting radiological water-quality data: 

U.S. Geological Survey Techniques and Methods, book 5, chap. B6, 33 p.
iii

Contents

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

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

1. Analytical Information Reported by the Contract Laboratory.........................................................3

2. Definitions of Important Analytical Parameters................................................................................3

2.1 Combined Standard Uncertainty ..............................................................................................3

2.2 Sample-Specific Critical Level (ssLC).......................................................................................4

2.3 Minimum Detectable Concentration........................................................................................4

2.3.1 a priori Minimum Detectable Concentration (a priori MDC)....................................4

2.3.2 Sample-Specific Minimum Detectable Concentration (ssMDC).............................5

2.4 Comparison of Radiological, Inorganic, and Organic Detection Levels ............................5

3. National Water Quality Laboratory Evaluations of Contract Laboratory Results ........................6

3.1 Initial Evaluation Criteria............................................................................................................6

3.2 Rounding Results.........................................................................................................................6

3.3 Review of Negative Results.....................................................................................................10

3.4 Assigning Remark and Value-Qualifier Codes......................................................................10

3.5 Information Sent to the National Water Information System (NWIS) Database............10

3.6 Information in Detailed Data Packages.................................................................................11

4. Water Science Center Reviews of National Water Information System (NWIS) 

Database Results............................................................................................................................11

5. Publishing Results................................................................................................................................12

5.1 Technical Reports......................................................................................................................12

5.2 Nontechnical Reports...............................................................................................................12

6. Interpretation and Reporting of Results from an Aggregated Dataset.......................................14

Acknowledgments..............................................................................................................................16

References Cited..........................................................................................................................................16

Glossary.........................................................................................................................................................18

Appendix: Typical Equations for Calculating Radiological Parameters..............................................22

A1. Calculating the Concentration.........................................................................................................23

A2. Calculating the Combined Standard Uncertainty.........................................................................24

A3. Calculating the Critical Level...........................................................................................................24

A3.1 General Principles..................................................................................................................24

A3.2 Calculating the Sample-Specific Critical Level (ssLC) ......................................................25

A3.3 Practical Approach for Verifying the Reported Sample-Specific Critical Level ..........26

A4. Calculating the Minimum Detectable Concentration ..................................................................26

A4.1 General Principles..................................................................................................................26

A4.2 Calculating the Sample-Specific Minimum Detectable Concentration (ssMDC)........28

A4.3 Practical Approach for Verifying the Reported Sample-Specific Minimum 

Detectable Concentration....................................................................................................29

A4.4 The Effect of Sample Size and Counting Time on the Reported 

Sample-Specific Minimum Detectable Concentration (ssMDC)...................................29

A4.5 The Relation between the Combined Standard Uncertainty and the 

Calculated Activity in a Sample for Two Radioanalytical 

Measurement Techniques ...................................................................................................29
iv

Figures

1. Graphical interpretation of radiological results ....................................................................15

2. Graphical presentation of radiological results with pertinent supporting information ..16

A1. The curve representing the critical level concept by using a theoretical distribution 

of the net instrument signal (concentration) obtained when analyzing 

an analyte-free sample..............................................................................................................25

A2. Graphical representation of the a priori Minimum Detectable Concentration 

concept.........................................................................................................................................27

A3. The sample-specific Minimum Detectable Concentration (ssMDC) as a 

function of analysis sample volume ........................................................................................30

A4. The sample-specific Minimum Detectable Concentration (ssMDC) as a 

function of analysis counting time...........................................................................................30

A5a. Typical Combined Standard Uncertainty (CSU) as a function of gross beta 

concentration ..............................................................................................................................31

A5b. Typical relative Combined Standard Uncertainty (CSU) as a function 

of gross beta concentration......................................................................................................31

A6a. Typical Combined Standard Uncertainty (CSU) as a function of 

Uranium-238 concentration ......................................................................................................32

A6b. Typical relative Combined Standard Uncertainty (CSU) as a function of 

Uranium-238 concentration ......................................................................................................32

Tables

1. Equations and error rates used for calculating the critical level and 

long-term method detection level..............................................................................................6

2. Basic assumptions, detection decisions, and results reporting for 

radiological, organic, and inorganic methods .........................................................................7

3. Examples showing the processes that are used by the National Water

Quality Laboratory to review radiological results ...................................................................8

4. An example of typical information that should be provided when 

publishing radiological results .................................................................................................13

5. An example of typical information that could be provided when 

publishing radiological results in a nontechnical report .....................................................14
v

Conversion Factors

To 

Convert To Multiply by

To 

Convert To Multiply by

years (y)

seconds (s)

minutes (min)

hours (h)

3.16 × 107

5.26 × 105

8.77 × 103

s

min

h

y

3.17 × 10–8

1.90 × 10–6

1.14 × 10–4

disintegrations per second (dps) becquerels (Bq) 1.0 Bq dps 1.0

Bq

Bq/kg

Bq/m3

Bq/m3

picocuries (pCi)

pCi/g

pCi/L

Bq/L

27.0

2.70 × 10–2

2.70 × 10–2

103

pCi

pCi/g

pCi/L

Bq/L

Bq

Bq/kg

Bq/m3

Bq/m3

3.7 × 10–2

37

37

10–3

microcuries per milliliter (μCi/mL) pCi/L 109 pCi/L μCi/mL 10–9

disintegrations per minute (dpm) μCi

pCi

4.50 × 10–7

4.50 × 10–1

mCi

pCi dpm 2.22 ×1062.22

Tritium Unit (TU)

Bq/L

dpm/L

pCi/L

0.118

7.08

3.19

Bq/L

dpm/L

pCi/L

TU

8.47

0.141

0.313

cubic feet (ft3) cubic meters (m3) 2.832 × 10–2 cubic meters (m3) cubic feet (ft3) 35.31

gallons (gal) liters (L) 3.78 liters gallons 0.265

gram (g) ounce, avoirdupois (oz) 0.03527 ounce, avoirdupois (oz) gram (g) 28.35

kilogram (kg) pound (lb) 2.205 pound (lb) kilogram (kg) 0.454
vi

Acronyms and Abbreviations

α probability of a Type I error

β probability of a Type II error

λ decay constant

CSU combined standard uncertainty (1-sigma)

DQO data quality objective

USEPA U.S. Environmental Protection Agency

L liter

LC critical level

MARLAP Multi-Agency Radiological Laboratory Analytical Protocols Manual

MDC minimum detectable concentration

MQO measurement quality objective

NWIS National Water Information System

NWQL National Water Quality Laboratory

pCi picocurie

PWS performance work statement

QC quality control

SI International System of units

ssLC sample-specific critical level

ssMDC sample-specific minimum detectable concentration

USGS U.S. Geological Survey

WSC Water Science Center
Abstract

This document provides information to U.S. Geological 

Survey (USGS) Water Science Centers on interpreting and 

reporting radiological results for samples of environmental 

matrices, most notably water. The information provided is 

intended to be broadly useful throughout the United States, but 

it is recommended that scientists who work at sites containing 

radioactive hazardous wastes need to consult additional 

sources for more detailed information. The document is 

largely based on recognized national standards and guidance 

documents for radioanalytical sample processing, most 

notably the Multi-Agency Radiological Laboratory Analytical 

Protocols Manual (MARLAP), and on documents published 

by the U.S. Environmental Protection Agency and the 

American National Standards Institute. It does not include 

discussion of standard USGS practices including field qualitycontrol sample analysis, interpretive report policies, and 

related issues, all of which shall always be included in any 

effort by the Water Science Centers. The use of “shall” in this 

report signifies a policy requirement of the USGS Office of 

Water Quality.

Introduction

Interpreting and reporting radiological results requires 

a full understanding of the concepts of detectability and 

quantification unique to radiochemistry and radiation emissions. Radioactivity describes a group of processes by which 

matter and energy are released from the nucleus of atoms as 

an alpha particle (4He+ nucleus), a beta particle (equivalent 

to an electron), or a gamma ray (photon or energy wave). The 

residual nucleus usually is transformed to a different element, 

and for alpha- and gamma-emitting nuclides, the energy of the 

emission(s) can be measured to identify the source radionuclide. Natural and anthropogenic radionuclides occur widely in 

the hydrologic environment (Hem, 1985, p. 146–151; Drever, 

1988, p. 379–381; Lieser, 2001). The rate of decay of a given 

Interpreting and Reporting Radiological 

Water-Quality Data

By David E. McCurdy,1 John R. Garbarino,2 and Ann H. Mullin2

1

McCurdy Associates, Northboro, Mass.

2

U.S. Geological Survey National Water Quality Laboratory, Denver, Colo.

quantity of radioactive atoms (–dN/dt) is proportional to the 

amount of atoms present (N) as shown in equation 1 where λ

is the decay constant.

 

The USGS currently (2008) reports the activity of a 

radionuclide in curies (Ci). The corresponding International 

System (SI) unit is the becquerel (Bq), and one curie equals 

3.7×1010 Bq. The rate of decay for environmental samples 

is commonly measured in picocuries (pCi = 10–12 Ci). One 

curie is defined as 3.7×1010 disintegrations per second, the 

approximate rate of alpha radiation from one gram of radium. 

One pCi is thus 0.037 disintegration per second or 2.22 

disintegrations per minute (dpm). Radiological analysis in 

essence involves detecting and counting individual decayproduct emissions from a sample for enough time to compute 

an average rate. The decay constant λ is inversely proportional 

to the half-life of the radionuclide (T1/2), which is the time 

required for half of the original amount to decay as shown in 

equation 2.

 

A radionuclide concentration reported in picocuries per 

unit of measure can be converted to specific activity (SA) per 

moles or grams by using the half-life of the radionuclide and 

Avogradro’s number using equation 3.

 

 

where No is Avogradro’s number of atoms (6.023×1023) per 

gram mole of the radionuclide, λ is the decay constant (unit 

of 1 per second), and T1⁄2 is half-life of the radionuclide in 

units of seconds. By incorporating Avogradro’s number into 

equation 3, a simpler equation 4 can be derived:

 

where AW is the atomic weight of the radionuclide. The 

following table provides similar equations for a specific 

activity (but in units of picocuries per gram, pCi/g) for 

radionuclides that have half-lives in years, days, hours, 


  dN

dt

N (1)

  ln / 1/2 2 T (2)

SA  s  	 N N s  s T 
  / . ( . ) / /3 7 10 18 73 2

1 2 o o (3)

SA  s ( . ) /( ) AW sT / 1 13 1025

1 2

(4)
2 Interpreting and Reporting Radiological Water-Quality Data

National Water Information System (NWIS) database through 

which they are provided to WSCs for further analysis, 

interpretation, and publication. The ancillary data stored in 

NWIS include all the parameters needed to publish the data in 

a report or on NWISWeb including the result, its associated 

combined standard uncertainty, the sample-specific critical 

level, and appropriate remark and value-qualifier codes. An 

additional data package sent by the NWQL to the WSCs 

provides radiological results with their associated combined 

standard uncertainty and other parameters and data, which 

provide ancillary measurement information including qualitycontrol sample results. These ancillary data are used by 

NWQL to make decisions about detection, uncertainty of 

results, and reporting of data. Definitions and use of these 

ancillary data and information are detailed elsewhere in this 

document.

The laboratories used by NWQL analyze environmental 

samples according to the PWS, including the measurement 

quality objective of the a priori minimum detectable 

concentration (a priori MDC) for a radiological constituent 

and sample matrix combination. Unacceptable Type II errors 

(false nondetection) are avoided through the establishment of 

the a priori MDC and the method selected by the laboratory.

Limiting unacceptable Type I errors (false detection) is 

assured by verifying that each reported result exceeds its 

respective sample-specific critical level (ssLC). Specifications 

for the Data Quality Objective (DQO) required detection 

levels for certain radiological constituents relative to the 

USEPA Safe Drinking Water Act (SDWA) also are included 

in the PWS. In this report, DQO is used in the same manner as 

the term Measurement Quality Objective used in the MultiAgency Radiological Laboratory Analytical Protocols Manual 

(MARLAP). The a priori MDC is the only DQO specified by 

NWQL in the PWS. The PWS also will specify the approved 

radiological method that must be used for the analysis (U.S. 

Environmental Protection Agency, 1980a). Other important 

information specified in the PWS include the calculation of 

the ssLC, sample-specific Minimum Detectable Concentration 

(ssMDC), and Combined Standard Uncertainty (CSU) of 

the measured result. The reported laboratory values for these 

measurement parameters are used by NWQL personnel to 

verify contractual compliance with PWS specifications, to 

determine detection of radiological constituents, to interpret 

the quality of the result, and to support decisions related to 

data usability and reporting of data in reports.

Appendix sections A3 and A4 contain the technical basis 

for the ssLC and the ssMDC as defined in chapter 20 of the 

Multi-Agency Radiological Laboratory Analytical Protocols 

Manual (MARLAP, 2004) and a discussion on the effect of 

sample size and instrument sample processing time on achieving a specified minimum detectable concentration. Terms are 

defined in a Glossary at the back of the report.

T1/2 Equation (pCi/g) Equation (g/pCi)

Years SA = (3.58 × 1017)/(AW×T1/2) AW × T1/2×2.80 × 10–18

Days SA = (1.31 × 1020)/(AW×T1/2) AW × T1/2×7.63 × 10–21

Hours SA = (3.14 × 1021)/(AW×T1/2) AW × T1/2×3.18 × 10–22

Minutes SA = (1.88 × 1023)/(AW×T1/2) AW × T1/2×5.32 × 10–24

Seconds SA = (1.13 × 1025)/(AW×T1/2) AW × T1/2×8.85 × 10–26

minutes, and seconds. For example, by using the equation 

above corresponding to T1/2 in years, 1 pCi of 238U with a 

half-life of 4.46×109 years corresponds to a mass of 2.97×10–6

grams (238 × 4.46×109 years × 2.80×10–18). A more complete 

introduction to environmental radiochemistry can be found in 

Eisenbud and Gesell (1997).

Some radiochemical analyses involve separation or isolation steps followed by a quantitation step typically based on 

some radiation emission measurement. The uncertainty of a 

radiological result is affected by the activity in the sample, the 

duration of the measurement, and other various factors that 

can be controlled for that single measurement. Supplemental 

information and guidance relative to these concepts have been 

provided in an Appendix.

Analytical laboratories that provide chemical, radiochemical, and biological analyses to the U.S. Geological 

Survey (USGS) shall be evaluated relative to the objectives 

of a project requiring analyses and approved for use for that 

specific project. Analysis of performance-testing samples 

will provide the basis for the initial laboratory approval, and 

an approved laboratory must continue to provide acceptable 

performance-testing sample results during the life of the 

project. The National Water Quality Laboratory (NWQL) 

submits performance-testing samples before the award of all 

radioanalytical contracts it administers. Review the Policy for 

the Evaluation and Approval of Analytical Laboratories before 

submitting samples for analysis (U.S. Geological Survey 

Office of Water Quality Technical Memorandum No. 2007.01, 

2007). Additional information on the laboratory evaluation 

process can be found at http://qadata.cr.usgs.gov/lep (accessed 

2008).

USGS National Programs and Water Science Centers 

(WSCs) conduct research studies and monitoring programs 

that focus on the detection and quantification of radiological 

constituents in various environmental matrices, most notably 

water. In order to support these studies and programs, the 

USGS NWQL maintains memoranda of understanding and 

contracts with various USGS and commercial laboratories 

to process and analyze samples collected by the WSCs. 

Within the memoranda of understanding and contracts are 

generic performance work statements (PWS) that apply to 

all USGS projects. Once the analyses have been completed, 

the contract laboratories provide NWQL with the results for 

each radiological constituent and sample matrix combination. 

The NWQL staff evaluates the reported data and information 

for technical issues and compliance to specifications stated 

in the PWS. The acceptable data are transferred to the USGS 
2. Definitions of Important Analytical Parameters 3

1. Analytical Information Reported by 

the Contract Laboratory

Various information related to the sampling and radioanalytical processes are reported by the contract laboratories 

to NWQL and subsequently to USGS WSCs. An Electronic 

Data Deliverable (EDD) is provided to NWQL by the contract 

laboratory that contains the unrounded result, CSU, ssLC, and 

ssMDC. The information to be reported by the contract laboratory is defined within the PWS and includes sampling and 

laboratory processing parameters. The analytical information 

includes:

•	 client sample identification (ID) code

•	 sample collection date

•	 sample matrix

•	 sample size received

•	 special instructions

The contract laboratory also reports the following information 

with the analytical results:

•	 laboratory identification number cross-referenced to 

client sample ID

•	 sample receipt date

•	 analyte (radiological constituent)

•	 analysis date

•	 result value (positive, negative, or zero)

•	 combined standard uncertainty (CSU; 1-sigma 

uncertainty)

•	 sample-specific minimum detectable concentration 

(ssMDC; a posteriori MDC)

•	 contract required minimum detectable concentration 

(MDC; a priori MDC)

•	 sample-specific critical level (ssLC)

•	 chemical yield (percent) for radiochemical processing

•	 aliquant size processed

•	 tracer used

The contract laboratory provides additional information 

in the form of narrative comments for use in evaluating results 

for data usability. Also, the method used and its reference 

designation are provided. All of this information is included 

on the compact disk data package that is sent to the contact 

person listed on the Analytical Services Request form (see 

section 3.6).

2. Definitions of Important Analytical 

Parameters

2.1 Combined Standard Uncertainty

The Combined Standard Uncertainty (CSU) can be 

viewed as the statistical standard deviation of an individual 

radiological result. The concentration of a radiological 

constituent in a sample is typically calculated using a 

mathematical equation that includes such parameters as the 

measured signal response of a radiation detector (events 

per time unit), the detector background signal response, the 

detector efficiency for the radiation emission producing the 

response, sample aliquant size processed, chemical yield of the 

radiochemical process, and decay and ingrowth factors based 

on the half-life of the radionuclide or its decay product. Each 

measurement parameter in the equation has its own uncertainty 

defined as a standard uncertainty. The CSU of the final result 

is determined using the common statistical approach that the 

variance (squared CSU) of a function of several variables can 

be approximated by applying the function to the variance of 

each variable component (for example, Benjamin and Cornell, 

1970, p. 180–186; MARLAP, 2004, chapter 19). Using this 

logic, the CSU of a radiological result is the square root of 

a sum of variances. The Appendix provides an example of a 

generic equation for calculating concentration (section A1) 

and the propagation of the standard uncertainties to derive the 

combined standard uncertainty (section A2).

The statistical normal distribution describes the uncertainty of most contributing variables in a radiological analysis, 

but the measured number of counts for an analysis follows the 

Poisson distribution. Poisson variables have a lower bound 

(zero for radiation counts) and thus have a positive skew. For 

sufficiently large counts, however, the Poisson distribution can 

reasonably be approximated as a normal distribution. All the 

statistical calculations in this report treat the uncertainty of a 

radiological result as a normal distribution.

When a concentration and its associated CSU are 

reported, a confidence interval can be calculated that defines 

the range of concentration (the lower and upper concentration) 

for the “true concentration” with a certain confidence. 

Contract laboratories calculate and report the CSU at the 

68-percent or 1-sigma (1σ) confidence level (analogous to the 

standard confidence level used when reporting the standard 

deviation for other water-quality results). The confidence 

level that is used when interpreting or publishing radiological 

results is dependent on the DQOs of the project. Reporting 

the concentration with its corresponding CSU (as provided 

in the NWIS database) provides the 68-percent confidence 

interval. The WSC shall always state the level of confidence of 

the CSU that is reported; for example, 1.25 ± 0.25 picocuries 

per liter (pCi/L) at 1σ or 1.25 ± 0.25 pCi/L at the 68-percent 

confidence level. The corresponding 68-percent confidence 

interval would be 1.00 to 1.50 pCi/L; or in other words, there 
4 Interpreting and Reporting Radiological Water-Quality Data

is a 68-percent chance that the true value is between 1.00 and 

1.50 pCi/L.

For most radionuclide concentrations reported by NWQL, 

the principal contributor to the CSU is the standard uncertainty 

of the net count rate. The relation between the CSU and 

the calculated activity for two radioanalytical measurement 

techniques is shown in figures A5a, A5b, A6a, and A6b in 

section A4.5 of the Appendix.

2.2 Sample-Specific Critical Level (ssLC)

The critical level (LC) is the smallest measured 

concentration that is statistically different from the instrument 

background or analytical blank, and it serves as the detection 

threshold for deciding whether the radionuclide is present in 

a sample. The LC is calculated from measurements obtained 

using nominal or typical analytical parameter values, whereas 

the sample-specific critical level (ssLC) is calculated from 

measurements obtained using the same analytical parameter 

values that were used during the analysis of a sample. USGS 

PWSs require the routine calculation of the ssLC for each 

sample, using parameter values that were actually measured 

during the generation of the sample result. The null hypothesis 

for establishing the critical level is that “the sample activity 

level is the same as the measured instrument background or 

blank sample value.” The maximum acceptable probability 

α of false detection (significance level), together with the 

standard deviation of the net blank sample distribution having 

a mean value of zero, forms the basis for the critical level upon 

which detection decisions may be made (Currie, 1968). For 

analysis of USGS radiological samples, a false detection rate 

of 5 percent (α0=0.05) is used. This hypothesis test strives 

to limit false detection (known as Type I error). Figure A1, 

section A3.1 in the Appendix graphically illustrates the critical 

level concept. Note that the critical level concept as applied to 

radionuclide detection is based on a “one-sided” hypothesis 

test that considers only the upper-tail probabilities of the null 

distribution and is different from a two-sided test that would 

consider both the upper- and lower-tail probabilities.

A detection decision is based on comparison of the 

sample result with the ssLC. Because the ssLC is a hypothesistesting concept based on a preestablished probability of false 

detection and the standard deviation of the net background 

distribution, the combination of the result and the ssLC and not 

the measurement CSU (and resultant symmetrical confidence 

interval) is used for detection decisions. Whenever the concentration of a radiological constituent is greater than the ssLC, it 

shall be considered detected; that is, the reported concentration is positive and greater than the measurement (instrument) 

background or the radiological constituent’s concentration in a 

blank sample. When the concentration is greater than the ssLC, 

the decision “detected” shall be reported, and a symmetrical 

confidence interval shall be given “after the detection decision 

is made” (Currie, 1968).

Scientists can evaluate the reported sample data set to 

determine if the reported ssLC has been calculated properly. 

Section A3.3 of the Appendix provides a practical approach 

for verifying the ssLC for most radioanalytical methods using 

the reported CSU. This guidance is not definitive but may be 

used to determine whether or not the relation of reported ssLC

and its uncertainty is reasonable.

2.3 Minimum Detectable Concentration

The critical level concept discussed in section 2.2 

addresses Type I error (false detection), but it does not consider Type II error (false nondetection). If the true concentration of a radionuclide were exactly equal to the critical level, 

the inherent uncertainty of the measurement would produce 

larger (detected) results for some samples and smaller (not 

detected) results for others. The Minimum Detectable Concentration (MDC) concept addresses Type II error. The MDC 

can be calculated a priori, using nominal or typical analytical 

parameter values, or a posteriori for a specific sample, using 

the ssLC and parameter values for an individual sample.

2.3.1 a priori Minimum Detectable 

Concentration (a priori MDC)

Consideration of both Type I and II errors is the basis 

of the a priori MDC concept. The critical level incorporated 

in the expression for the a priori MDC (see equation A9 

of section A4.1 of the Appendix) is typically calculated 

using nominal or typical parameter values such as detector 

efficiency, chemical yield, and sample aliquant processed. 

The a priori MDC for a radioanalytical method is a laboratory 

analytical-method performance characteristic.

The a priori MDC is an a priori (before the sample 

measurement) concept that is only used to facilitate comparisons of the relative detection capabilities of measurement 

systems or radiological methods. It is defined as the lowest 

true concentration that gives a specified probability that the 

measured concentration will exceed its critical level concentration (Currie, 1968; MARLAP, 2004, chapter 20). The a priori

MDC satisfies the hypothesis testing the probability (β) at 

the 0.05 or 95-percent confidence level that the true result is 

greater than the LC, given that the analytical result equals the 

a priori MDC and assuming a normal distribution. As such, 

its definition may be restated as the lowest concentration for 

which there is a 95-percent probability of producing a result 

greater than the critical level and a 5-percent probability of 

falsely concluding that a blank measurement represents a positive measurement (above the critical level). Figure A2, section 

A4.1 in the Appendix, graphically illustrates the a priori MDC 

concept and shows a distribution of measurement results from 

a set of samples having a radiological constituent concentration at the MDC.

Based on USGS program needs and state-of-the art 

radioanalytical methods, standardized a priori MDC DQOs 
2. Definitions of Important Analytical Parameters 5

for various radiological constituent/matrix combinations have 

been established by NWQL. The a priori MDC for a radiological analyte is in the NWQL Catalog (see the reporting 

level entry at http://nwql.cr.usgs.gov/usgs/catalog/index.cfm). 

The established a priori MDC DQO specification is based 

on need or the expected detection capability of a method, or 

both. For example, an a priori MDC contractual specification 

of 1 pCi/L for tritium (3H) in water has been chosen for 

certain research studies. These standardized a priori MDC 

concentrations and matrix combinations become laboratory 

contract specifications as defined in the PWS. By establishing 

the a priori MDC, an acceptable Type II error is defined. 

When the laboratory selects a method to meet the a priori

MDC, unacceptable Type II errors are limited.

The contract laboratory uses the a priori MDC 

requirements to select appropriate methods and method 

parameters to meet the contract specifications. Nominal or 

typical parameter values (detector efficiency, chemical yield, 

sample aliquant processed, and so forth) of the radioanalytical 

method are generally chosen by the contract laboratory 

when calculating the a priori MDC for a given method and 

radiological constituent.

2.3.2 Sample-Specific Minimum Detectable 

Concentration (ssMDC)

NWQL contracts also require calculation and reporting 

of an a posteriori (after the measurement) or sample-specific 

Minimum Detectable Concentration (ssMDC) in association 

with each radiological result reported. The contract laboratory uses the ssLC as the basis for establishing the ssMDC as 

evaluated in context with the a priori MDC on each individual 

measurement to establish the Type II error. The ssMDC is 

used by the NWQL to verify that the a priori MDC DQO has 

been met. Because the ssMDC is calculated with actual parameter values used during the analysis of the sample in question, 

the ssMDC, in most cases, may tend to be below the a priori

MDC, which uses more conservative nominal method parameter values. In most cases, the actual method parameter values 

used for the ssMDC calculation do not substantially change 

from the nominal values used in the a priori MDC calculation unless certain circumstances have occurred; for example, 

smaller sample size processed or lower chemical yields may 

lead to longer counting times. Occasionally, if the laboratory 

does not adjust certain method parameters, the a priori MDC 

DQO may not be met because of possible unexpected chemical and instrumental interferences and small sample sizes. In 

such cases, the ssMDC will be greater than the a priori MDC 

DQO.

The MDC (a priori MDC or a posteriori ssMDC) 

shall never be applied to make decisions about whether a 

radiological constituent has been detected in a sample; rather, 

the ssLC shall be used for defining when a concentration is 

different from zero with a specified probability (5 percent for 

most cases) of false detection. Section A4.2 of the Appendix 

provides additional information and the typical equations used 

by a laboratory to calculate the ssMDC. Practical approaches 

for determining whether a reported ssMDC has been 

calculated properly (section A4.3), and the effects of sample 

volume and counting time on the magnitude of the ssMDC 

(section A4.4) are provided in the Appendix.

2.4 Comparison of Radiological, Inorganic, and 

Organic Detection Levels

The concepts on radiological detectability as presented in 

section 2.2 on the ssLC and section 2.3.2 on the ssMDC (also 

sections A3 and A4 in the Appendix) are similar to those presented for organic and inorganic analytes in the U.S. Geological Survey Open-File Report 99–193 (Childress and others, 

1999) for the long-term method detection level (LT–MDL) and 

the laboratory reporting level (LRL), respectively. The LT–

MDL is based on a modification of the U.S. Environmental 

Protection Agency’s method detection limit (MDL) procedure 

and relies on several of its key assumptions (Childress and 

others, 1999). The primary difference between the MDL and 

the LT–MDL is that the LT–MDL is designed to measure more 

sources of variability and therefore is expected to be higher 

than the MDL. The MDL uses the standard deviation of spiked 

samples based on a minimum number of seven spiked samples 

(a snapshot or single set of measurements made at between 1 

and 5 times the estimated MDL concentration), whereas the 

LT–MDL uses the standard deviation based on a much larger 

set of spiked samples (at least 24 per year) collected over an 

extended period of time, typically 6 to 12 months.

The basic concepts presented for radiological, organic, 

and inorganic analytes assume a normal distribution for the 

blank and spike sample measurements and use the standard 

deviations of these distributions and defined error rates for 

false detection and false nondetection. The equations for the 

critical level (LC and ssLC) and the long-term method detection level (LT–MDL) are basically identical except that the 

critical level equations use a 5-percent α error rate for false 

detection compared with 1-percent α error rate for false detection used to calculate the long-term method detection level. 

For both applications, the critical level and LT–MDL are 

incorporated into the determination of the MDC and the LRL, 

respectively. Similar to the LC and the LT–MDL, the error 

rates for the MDC and LRL differ; the MDC equation uses a 

5-percent β error rate for false nondetection, whereas a 

1-percent β error rate for false nondetection is used for the 

LRL.

Another basic difference in calculating the LC and 

the LT–MDL is that the LC uses a standard deviation for 

a distribution of blank sample results whereas, for organic 

analytes and some inorganic analytes, the LT–MDL uses a 

standard deviation of a distribution of results from samples 

spiked near the estimated detection level. In both cases, the 

calculations assume the standard deviation in blanks and the 

standard deviation near the critical or detection level are 
6 Interpreting and Reporting Radiological Water-Quality Data

equal. A comparison of the basic differences between 

detection-level terms and error rates and basic assumptions, 

detection decisions, and results reporting for radiological, 

organic, and inorganic constituents is presented in tables 1 and 

2, respectively.

3. National Water Quality Laboratory 

Evaluations of Contract Laboratory 

Results

Initial evaluation of the quality of contract laboratory radiological data is conducted by NWQL before the 

data are sent to the NWIS database. This initial evaluation 

is done largely to determine contractual compliance and 

overall quality of the data. The data are then transferred to 

the NWIS database through which they can be accessed by 

USGS WSCs.

3.1 Initial Evaluation Criteria

As a standard practice, NWQL evaluates a contract laboratory’s reported radiological data for each sample for contractual compliance for technical items such as, but not limited to:

•	 reporting of sample parameters and information 

according to specifications (see section 1);

•	 contractual MDC specification (by comparing the 

ssMDC value to the contractual a priori MDC);

•	 radiological hold time (by comparing sample collection 

and analysis dates);

Table 1. Equations and error rates used for calculating the critical level and long-term method detection level.

[LC, critical level; LT–MDL, long-term method detection level; MDC, minimum detectable concentration; LRL, laboratory reporting level; NA, 

not applicable; sblanks, standard deviation for blanks; sLT–MDL, standard deviation for spikes at 1 to 5 times the estimated detection level; kβ, 

statistical factor; t(n–1,1–α=0.99), statistical factor; n, number of samples; α, probability of false detection; β, probability of false nondetection]

LC

a LT–MDLb a priori MDCc LRL

Basic practical equation sblanks × kα sLT–MDL × t

(n–1,1–α=0.99) LC + kβ × sblanks 2 × sLT–MDL × t

(n–1,1–α=0.99)

Specific equation sblanks × 1.645 sLT–MDL × 2.50 2.71 + 3.29 × sblanks 2 × LT–MDL

False detection error rate 0.05 0.01 0.05 0.01

False nondetection error rate NA NA 0.05 0.01

aWhen α = 0.05, kα = z(

1–α) = 1.645; where z(1–α)

 denotes the (1–α) quantile of the standard normal distribution.

bThe basic equation is described by Childress and others (1999). The Student’s t statistic for 23 degrees of freedom is equal to 2.50 for α = 0.01.

cFor practical purposes, the basic assumption is that sblanksis approximately equal to sspikes–MDC (the standard deviation of the distribution of a sample 

spiked at the MDC). The equation simplifies by assuming β = 0.05 and kαβ = z(1–β) = 1.645; where z(1–β) denotes the (1–β) quantile of the standard normal 

distribution.

•	 processing turnaround time (by comparing sample 

receipt and analysis report dates);

•	 insufficient sample size for analysis;

•	 yield for certain radiological constituents; and

•	 batch Quality Control (QC) sample results related 

to method bias (laboratory control and matrix spike 

samples), excess uncertainty or imprecision (split or 

duplicate sample analyses), and false positive and 

negative (blank samples).

The typical processes that NWQL uses to evaluate contract 

laboratory results are listed in table 3. Several examples of 

the most common and relatively unambiguous situations and 

those that occur less frequently and require deeper scrutiny are 

discussed.

3.2 Rounding Results

The NWQL Laboratory Information Management System 

(LIMS) rounds contract laboratory results received through 

the EDD by using the American National Standards Institute 

procedure N42.23 (American National Standards Institute, 

2003). The CSU shall be rounded to two significant figures, 

and both the radiological concentration and CSU shall be 

reported to the same number of decimal places. Proper rounding conventions notwithstanding, one must always remember 

that the CSU reported in association with the sample concentration, and not the base-10 rounding of results, establishes the 

number of significant digits in a radiological result. Examples 

are provided in table 3 showing how contract laboratory radionuclide concentrations and their CSUs are rounded before they 

are sent to the NWIS database.
3. National Water Quality Laboratory Evaluations of Contract Laboratory Results 7

Table 2. Basic assumptions, detection decisions, and results reporting for radiological, organic, and inorganic methods.

[LC, critical level; ssLC, sample-specific critical level; a priori MDC, method-specific a priori minimum detectable concentration; ssMDC, samplespecific MDC; LT–MDL, long-term method detection level; LRL, laboratory reporting level; PWS, performance work statement for contract laboratory; 

NA, not applicable; lc std, lowest calibration standard; ≥, greater than or equal to; <, less than]

Radiological methods LC ssLC

Basic assumptions Typical blank or instrument background distribution and sample 

parameters; can be instrument specific or average value for 

all instruments using method

Instrument-specific background 

distribution and sample-specific 

parameters

Detection decisions Not used Result ≥ ssLC

Reporting results Not reported Is always reported with the result 

(negative, zero, or positive) and the 

combined standard uncertainty (CSU)

Organic and inorganic 

methods LT–MDL No corresponding term

Basic assumptions Multiple instrument and multiple analysts; analysis of samples 

spiked at 1 to 5 times the estimated detection level; spike distribution of ≥ 24 samples over 6 to 12 months; and constant 

sample parameters used

NA

Detection decisions Result ≥ LT–MDL NA

Reporting results Result concentrations ≥ LT–MDL are reported with a qualifier 

when the concentration is less than the LRL or lc std, whichever is greater (ideally, the lc std is equal to the LRL); when 

the result < LT–MDL, then < LRL is reported; for information-rich organic methods, qualitative results are reported 

with a qualifier when a result is < LT–MDLb

NA

Radiological methods a priori MDC ssMDC

Basic assumptions Typical blank or instrument background distribution and sample 

parameters; can be instrument specific or average value for 

all instruments using method

Instrument-specific background 

distribution and sample-specific 

parameters

Detection decisions Not used Not used

Reporting results Available from NWQL Cataloga Not generally reported; it is used only 

to evaluate contractual requirements 

of the PWS

Organic and inorganic 

methods LRL No corresponding term

Basic assumptions Multiple instrument and multiple analysts; analysis of samples 

spiked at 1 to 5 times the estimated detection level; spike distribution of ≥ 24 samples over 6 to 12 months; and constant 

sample parameters used

NA

Detection decisions Not used NA

Reporting results All results greater than the LRL or lc std, whichever is greater, 

are reported without a qualifierb

NA

aThe a priori MDC is listed in the NWQL Catalog under the reporting level entry; see http://nwql.cr.usgs.gov/usgs/catalog/index.cfm.

bRefer to figure 10 in U.S Geological Survey Open-File Report 99–193 (Childress and others, 1999) for details.
Table 3. Examples showing the processes that are used by the National Water Quality Laboratory to review radiological results. [All numbers are in units of picocuries per liter; CSU, 1-sigma Combined Standard Uncertainty; ssLC, sample-specific critical level sent to the National Water Informtion System (NWIS) database; a priori MDC, contractual a priori Minimum Detectable Concentration; ssMDC, sample-specific Minimum Detectable ConcentrationCode, remark or value-qualifier code(s) sent to the NWIS database; R, nondetect, result less than sample-specific critical level; ), ssMDC exceeded the a priori MDC=, negative result may indicate potential negative bias; NWQL, National Water Quality Laboratory; ±, plus or minus; <, less than; >, greater than; WSC, Water ScienCenter] Unrounded concentra- tion Unrounded CSU ssLC ssMDC a priori MDC Code Decision processes Rounded concentration and (CSU) sent to the NWIS database 2.346 0.542 0.93 2.3 3.0 Result > ssLC; reasonable relation between CSU, ssLC, and ssMDC; ssMDC < a priori MDC. 2.35 (0.54) 0.534 0.542 0.93 2.3 3.0 R Result < ssLC; reasonable relation between CSU, ssLC, and ssMDC; ssMDC < a priori MDC. Remark code sent to NWIS. 0.53 (0.54) 6.636 1.542 3.2 6.5 3.0 ) Result > ssLC, reasonable relation between CSU, ssLC, and ssMDC. However, the ssMDC > contractual a priori MDC. NWQL will try to determine the cause by looking at other data and information and consulting with the contract laboratory. Reanalysis may be requested. Value-qualifier code sent to 

NWIS.

6.6 (1.5)

0.534 0.742 1.6 3.2 3.0 R ) Result < ssLC; reasonable relation between 

CSU, ssLC, and ssMDC. However, the ssMDC > contractual a priori MDC. NWQL will try to determine the cause by looking at other data and information and consulting with the contract laboratory. Reanalysis may be requested. Remark and value-qualifier codes sent to NWIS.

0.53 (0.74)

–1.525 0.972 0.93 2.7 3.0 R Result < ssLC; reasonable relation between 

CSU, ssLC, and ssMDC; ssMDC < a prioriMDC; and no negative bias (negative concentration < 1.65 × CSU). Remark code sent to NWIS.

–1.52 (0.97)

–0.504 0.735 0.22 0.70 0.90 The ssMDC < a priori MDC and there is no 

negative bias (negative concentration < 1.65 CSU). However, the result is unacceptable because the ssLC and ssMDC are too small relative to the CSU. NWQL may request a recalculation or reanalysis.

Results are not sent to the NWIS d

base unless the problem is resol
Table 3. Examples showing the processes that are used by National Water Quality Laboratory to review radiological results.—Continued[All numbers are in units of picocuries per liter; CSU, 1-sigma Combined Standard Uncertainty; ssLC, sample-specific critical level sent to the National Water Informtion System (NWIS) database; a priori MDC, contractual a priori Minimum Detectable Concentration; ssMDC, sample-specific Minimum Detectable ConcentrationCode, remark or value-qualifier code(s) sent to the NWIS database; R, nondetect, result less than sample-specific critical level; ), ssMDC exceeded the a priori MDC=, negative result may indicate potential negative bias; NWQL, National Water Quality Laboratory; D, detection; ±, plus or minus; <, less than; >, greater than; WSCWater Science Center]

Unrounded concentration Unrounded CSU ssLC ssMDC a priori MDC Code Decision processes Rounded concentration and (CSU) sent to the NWIS database

–2.523 0.731 0.93 2.7 3.0 R = Result < ssLC; reasonable relation between 

CSU, ssLC, and ssMDC; ssMDC < a prioriMDC. However, the result is unacceptable or requires careful qualification because the negative concentration > 1.65 × CSU. Remark and value-qualifier codes sent to NWIS. WSC scientists should search for patterns among any samples in this category. 

–2.52 (0.73)

0.636 2.542 3.2 2.7 3.0 Result < ssLCC and ssMDC < a priori MDC. 

However, the result is unacceptable because of the unusually high CSU and because the ssLC and ssMDC are too small relative to the CSU. NWQL may not accept this result for technical reasons and may request a reanalysis of this sample. NWQL will try to determine the cause of error by looking at other data and information.

Results are not sent to the NWI

database unless the problem 

resolved

1.005 0.544 0.53 2.7 3.0 Result > ssLC and ssMDC < a priori MDC. 

However, the result is unacceptable because the ssLC is too small relative to the CSU. NWQL may not accept this result for technical reasons and may request a reanalysis of this sample. NWQL will try to determine the cause of error by looking at other data and information.

Results are not sent to the NWI

database unless the problem 

resolved

10.783 4.204 8.9 19.7 1.0 ) Result > ssLC and there is a reasonable relation 

between CSU, ssLC, and ssMDC. However, the ssMDC > a priori MDC. Upon further review, NWQL determined that a small sample volume was used. Therefore, because the result is positive and reasonable for sample size and reanalysis is not possible because of the lack of sample, the result is recorded in the NWIS database. Value-qualifier code sent to NWIS.

10.8 (4.2)
10 Interpreting and Reporting Radiological Water-Quality Data

3.3 Review of Negative Results

Analysis of a radiological sample produces a gross signal 

response that is related to the quantity of the radionuclide 

present. However, random measurement uncertainties will 

cause this signal to vary somewhat if the measurement is 

repeated. A nonzero signal may be produced even when no 

radionuclide is present. For this reason, the contract laboratory 

analyzes an instrument background or a blank sample (discrete 

from the blank used for quality-control purposes) and subtracts 

its signal from the gross signal to obtain the net signal. If the 

measurement process is under control (free from systematic 

bias) and a series of blanks were analyzed and the background 

signal subtracted from each measurement, the results should 

be evenly distributed above and below a zero concentration, 

with negative values in approximately one-half of the blanks 

(see fig. A1 in the Appendix). Therefore, negative results are 

possible due to the randomness of the measurement process. 

Nevertheless, this does not imply that there is negative 

radioactivity. Each calculated result will have an associated 

CSU, and thus a confidence interval can be calculated and 

interpreted. Sometimes the lower end of the confidence 

interval may be negative, meaning that the true concentration 

may not be different from zero.

In order to determine if a negative result is valid, it 

is compared to the lower 95 percent one-sided confidence 

interval. A negative result is considered valid if the magnitude 

of the negative result is ≤ 1.65 times the reported CSU (1.65 

is the 95th percentile of the standard normal distribution). 

When the magnitude of the negative result is greater than 1.65 

times the reported CSU, the result may be considered invalid 

because there is less than 5-percent probability that the result 

is from a blank or instrument background distribution (for 

example, with a zero mean value), indicating that the measurement process may not be in control (see examples in table 3). 

Typical reasons for invalid negative results include a nonrepresentative background or blank signal or an inaccurate determination of radionuclide interferences. An invalid negative result 

can be reported with the corresponding value-qualifier code 

(see section 3.4). A valid negative result can be reported as a 

nondetect concentration.

3.4 Assigning Remark and Value-Qualifier 

Codes

Remark and value-qualifier codes are assigned by NWQL 

and are included with results whenever additional information 

is needed for interpretation. The following remark and valuequalifier codes with their explanations can be used with radiological results. Only one remark code can be included with a 

radiological result, whereas up to three value-qualifier codes 

can be used. Remark and value-qualifier codes are assigned 

to the results during evaluation by the NWQL (see examples 

in table 3). Contractual acceptance criteria associated with the 

remark and value-qualifier codes can be found at 

http://wwwnwql.cr.usgs.gov/USGS/acu_contracts.html.

Remark code Explanation

R Nondetect, result below sample- 

 specific critical level (ssLC)

Value-qualifier Explanation

( Blank greater than the samplespecific critical level (ssLC)

) Sample-specific Minimum 

Detectable Concentration (ssMDC) 

is above the contractual a priori

MDC

/ Matrix Spike (MS) recovery is 

outside of contractual acceptable 

range (see Glossary for definition 

of recovery)

@ Exceeded sample holding time

\ Laboratory Control Sample (LCS) 

recovery is outside of contractual 

acceptable range

∼ Duplicates are not within the 

contractual acceptance limits

= Negative result may indicate 

potential negative bias

∧ Yield is outside of contractual 

acceptable range (see glossary for 

definition of yield)

3.5 Information Sent to the National Water 

Information System (NWIS) Database

The following information is sent to the NWIS database. 

The concentration, CSU, and ssLC are reported in either pCi/L 

or pCi/g.

•	 Site-agency code

•	 Station-identification number

•	 Sample-collection date

•	 Sample-collection time

•	 Sample-collection end date

•	 Sample-collection end time

•	 Sample-medium code

•	 Parameter Code

•	 Rounded concentration

•	 Remark and value-qualifier code(s)

•	 Rounded Combined Standard Uncertainty (1-sigma)
4. Water Science Center Reviews of National Water Information System (NWIS) Database Results 11

•	 Sample-specific critical level

The NWIS database information also is transferred to 

NWISWeb to provide electronic access to radiological and 

other water-quality information through website http://waterdata.usgs.gov/nwis.

3.6 Information in Detailed Data Packages

Additional information associated with the sample 

analysis is provided in a compact disk data package sent to the 

WSC to assist with the review of the laboratory and field QA 

sample results. Some of the information in the data package is 

not recorded in the NWIS database. The data package includes 

a narrative, data, sample information, and laboratory information sections as shown in the following list. The data section 

provides the result, CSU (1-sigma), ssMDC, a priori MDC, 

ssLC, percent yield, aliquant size, and results for laboratory 

quality-control samples.

•	 Data report narrative (additional details specific to the 

analyses; for example, relative percent difference for 

duplicate samples)

•	 Data section

– Sample summaries (client sample ID, location,

 matrix, laboratory sample ID, chain of custody,

 sample date and time, amount of sample

 received, and the WSC contact

– Sample batch QC summary (number of blanks,

 laboratory control samples, and duplicates)

– Work summary (date collected, date received, 

 date analyzed, date reviewed)

– Method blank results

– Laboratory control sample results

– Matrix spike results

– Duplicate results

– Results by sample and method

•	 Analytical Services Request (ASR) form for each 

sample

•	 Radiological login sheet

4. Water Science Center Reviews 

of National Water Information System 

(NWIS) Database Results

Specific information from NWIS is needed to complete 

a thorough review of radiological results. For the radiological 

data corresponding to samples analyzed after March 1, 2003, 

the following list of alpha parameters should be retrieved from 

NWIS into a “by-result” table for review.

PCODE – Parameter code

PSNAM – Parameter abbreviated name

REMRK – Remark code; this will include any remark

 code stored with the result

VALUE – Result value; if retrieved with the no-rounding 

option, this will be the laboratory result

UNITS – Result unit of measure

QUAL1 – First value-qualifier code stored with the result

QUAL2 – Second value-qualifier code stored with the

 result

QUAL3 – Third value-qualifier code stored with the

 result

LSDEV – Laboratory standard deviation; this field is 

where the Combined Standard Uncertainty 

(1σ CSU) for the result is stored

RLTYP – Report level type; for radiological samples 

analyzed after March 1, 2003, this field 

always equals “ssLC”

RPLEV – Report level; this field is where the samplespecific critical level (ssLC) for the result is 

stored

RCMLB – Result-level laboratory comment; this field 

will provide any additional information 

stored with the result

Results should be retrieved using the unrounded option 

because radiological results stored in NWIS are already 

rounded. The VALUE, LSDEV, and RPLEV are reported in 

the same UNITS.

For radiological samples analyzed before March 1, 2003, 

sample-specific critical levels (ssLC) were not reported, and 

2-sigma precision estimates or 2SPE (equivalent to 2 sigma 

Combined Standard Uncertainty) were reported under separate 

parameter codes. For tritium and radon samples analyzed 

prior to August 1, 2008, the ssLC was not reported and the 

2SPE was reported under a separate parameter code. For 

tritium and radon samples submitted after August 1, 2008, 

the ssLC and 1σ CSU will be reported. More details about 

the retrieving results from the NWIS database can be found 

at http://wwwnwql.cr.usgs.gov/USGS/rapi-note/05-019.html

and in section 3.4.6 of Web page http://wwwnwis.er.usgs.gov/

currentdocs/qw/QW.user.book.html.

Much of the review by the WSC is focused on data 

interpretation. The WSC shall review the radiological results 

with respect to historical data from the collection site. Results 

obtained for QC samples, such as matrix-spike samples, 

can be reviewed to identify quality problems in laboratory 

analytical performance, sample matrix effects, and field 

sample collection. Matrix spike results can be used to establish 

bias, whereas laboratory-duplicate results can be used to 

establish subsampling and method variability. Duplicate field 

samples can be used to establish sample-collection variability. 

Remark and value-qualifier codes should be reviewed in order 
12 Interpreting and Reporting Radiological Water-Quality Data

to evaluate their effect on interpretation and for providing 

descriptive information presented in publications.

5. Publishing Results

5.1 Technical Reports

The USGS conventions for publishing radiological 

results as outlined in this report follow the practices of the 

U.S. Environmental Protection Agency (U.S. Environmental 

Protection Agency, 1980b), American National Standards 

Institute N42.23 (American National Standards Institute, 

2003), and Multi-Agency Radiological Laboratory Analytical 

Protocols (MARLAP, 2004, chapter 16). These national standards and guidance documents state that reported radiological data should always consist of two numbers, the measured 

concentration (or activity) and the associated measurement 

uncertainty (CSU at a stated level of confidence). Therefore, 

after radiological results have been reviewed by the WSC, the 

minimal acceptable information to be published shall include 

the:

•	 Result (positive, negative, or zero)

•	 CSU (1σ)

•	 Reference radionuclide for gross alpha and 

 beta analyses

The concentration (or activity) and CSU should not be 

interpreted as a single point, but as a confidence interval about 

the measured concentration in which one has a high statistical probability of finding the true concentration of the sample 

(approximately 68 percent at 1-sigma). The practice of not 

including the CSU is ill advised as it withholds critical information associated with the result that could lead to misinterpretation or even critical misapplication of the data. Although 

the measurement uncertainty is not used in determining 

compliance with the Safe Drinking Water Act (SDWA), it will 

be needed for data evaluation of other studies.

The concentration, including zero and negative results, 

and the CSU shall be recorded in the same units (for example, 

picocuries per liter). In addition, the CSU shall never be stated 

as a relative percentage or fraction of the result because as 

a result approaches zero the relative uncertainty becomes 

exceedingly large and does not lend itself to meaningful interpretation. When nondetect results are published, it is strongly 

recommended that the report include a “detection indicator” 

for clarification. For example, the result and CSU are reported 

and flagged with a nondetect identifier whose definition is 

provided. Results shall not be reported as <ssMDC or <ssLC. 

Radiological results should be reported according to 

conventions that establish and preserve their technical defensibility. Results should be identified in a manner that permits 

them to be connected unambiguously to a sampling event 

and to the radioanalytical measurements used to generate the 

results. Individual results are best reported in association with 

a unique identifier that is, or can be, associated with a project, location, date, time, and record of collection. If groups of 

data are being averaged, it may not be feasible to reference 

each unique identifier, but the descriptor associated with the 

averaged data point should always accurately and unambiguously characterize the group of data in question. Results 

should always be presented in association with the name of 

the analyte, the measured concentration (inclusive of all positive, zero, or negative values) and associated CSU, the level 

of significance for the confidence interval reported, the ssLC, 

and an activity reference date for shorter lived radionuclides 

or mixtures of radionuclides. In the case of nonradionuclidespecific measurements, one should include the measurement 

parameter, such as gross alpha or total uranium, as well as any 

applicable assumptions underlying the gross measurement. 

For example, for gross alpha, the WSC should specify the 

reference nuclide used for calibration of the instrument that is 

“gross alpha (referenced to 230Th).”

Oftentimes, the activity reference date and time are 

overlooked by investigators who are unfamiliar with radioanalytical measurements. The measured activity reported for 

a sample is only valid for a specified point in time because the 

radioactivity of a sample changes over time, depending on the 

half-life of the supporting radionuclide. Failure to specify the 

activity reference date and time, especially with short-lived 

radionuclides, can render published results useless. If the holding time for a sample analyzed for a short-lived radionuclide 

is exceeded, the published result shall include a statement that 

the holding time was exceeded with the specific time interval 

beyond the holding-time limit.

Table 4 shows an example of the types of information that 

should be included when publishing radiological results, such 

as those discussed in table 3. NWIS remark and value-qualifier 

codes can be translated to convey additional interpretive information for the data presented.

5.2 Nontechnical Reports

Presenting radiological data in a technically defensible, 

yet understandable manner is a challenge to any investigator who prepares reports for issuance to the general public. 

Clearly, WSCs must always ensure that data are presented in a 

manner that addresses the subject clearly without compromising technical accuracy or validity. While attempting to prevent 

or minimize confusion among the lay reader, the WSC may 

decrease the level of detail of the data provided or simplify 

the complexity of concepts presented to a level appropriate 

for the purpose and the perceived background of the audience. 

The WSC shall ensure that reports are presented clearly and 

that the depth and limitations of the presentation are clear to 

any reader, ranging from the layperson to the expert. Although 

authors cannot foresee every use or interpretation of their 

published data, it is important that they remain mindful that 
Table 4. An example of typical information that should be provided when publishing radiological results.[Result, radiological concentration plus or minus the 1-sigma combined standard uncertainty; ssLC, sample-specific critical level; GA, gross alpha; 72h, sample analyzed for GA concentration at approximately 72 hours after sample collection as referenced to a detector calibrated using 230Th; 30d, sample used for the 72-hour GA analysis is counted a second time approximately 30 days after the initial count as referenced to a detector calibrated using 230Th; pCi/L; picocurie per liter; D, analyte detected; ND, analyte not detected, concentration is less than the sample-specific critical level; a, 72-hour sample holding time was exceeded; b, negative result may indicate potential negative bias; c, sample-specific Method Detectable Concentration (ssMDC) exceeded the a priori MDC; d, ssMDC exceeded the a priori MDC but was reasonable for the sample volume processed; ±, plus or minus; EPA, U.S. Environmental Protection Agency]

Sampling 

site

Sample 

collection date 

and time

Analysis date and 

time

Radiological 

constituent Result ssLC Remark Units Sample type Analytical method

Well 5 9/18/2006 14:10 9/25/2006 8:35 GA (72h) 17 ± 12 23 ND, a pCi/L Unfiltered EPA 900.0Well 6 9/21/2006 8:37 9/23/2006 9:40 GA (72h) 5.1 ± 1.9 2.5 D pCi/L Filtered EPA 900.0Well 5 9/18/2006 14:10 10/20/2006 15:11 GA (30d) 23 ± 14 28 ND pCi/L Unfiltered EPA 900.0Well 6 9/21/2006 8:37 10/27/2006 8:25 GA (30d) 5.8 ± 2.7 4.2 D pCi/L Filtered EPA 900.0Well 5 10/7/2006 9:11 10/9/2006 8:11 228Ra 2.35 ± 0.54 0.93 D pCi/L Filtered EPA 904.0Well 5 10/14/2006 9:15 11/16/2006 13:25 228Ra 0.53 ± 0.54 0.93 ND pCi/L Filtered EPA 904.0Well 5 11/20/2006 9:04 11/25/2006 10:04 228Ra –2.52 ± 0.73 0.93 ND, b pCi/L Filtered EPA 904.0Well 6 10/22/2006 9:45 10/25/2006 14:45 228Ra 6.6 ± 1.5 3.2 D, c pCi/L Filtered EPA 904.0Well 6 10/31/2006 9:30 11/2/2006 10:30 228Ra 0.53 ± 0.74 1.6 ND, c pCi/L Filtered EPA 904.0Well 6 11/20/2006 9:10 11/25/2007 11:04 228Ra 7.8 ± 2.2 3.9 D, d pCi/L Filtered EPA 904.0
14 Interpreting and Reporting Radiological Water-Quality Data

Table 5. An example of typical information that could be provided when publishing radiological results in a nontechnical 

report.

[Filtered water samples were collected from wells and analyzed for gross alpha, radium-226, and radium-228 using U.S. Environmental Protection Agency methods EPA 900.0, EPA 903.1 and EPA 904.0, respectively; gross alpha analysis is referenced to a detector calibrated using 230Th]

Sampling 

site

Contaminant, 

units1 MCL1

Number 

of 

samples1

Average 

concentration1

Number of results 

greater than the 

critical level1

Range 

of 

concentrations1

Well 5 Gross alpha, pCi/L 15 5 5.86 4 ND to 9.71

Well 6 Gross alpha, pCi/L 15 7 9.2 7 6.5 to 11

Well 5 226Ra + 228Ra, pCi/L 5 5 2.97 5 2.63 to 3.31

Well 6 226Ra + 228Ra, pCi/L 5 7 0.65 3 ND to 1.05

1

Definitions:

The average contaminant concentration, uncertainty, and critical level for a radiological constituent(s) is given in picocuries per liter (pCi/L).

The average is calculated by adding together all the individual results from a sampling site and dividing the sum by the number of individual 

results.

The Safe Drinking Water Act’s Maximum Contaminant Level (MCL) is the highest concentration of a contaminant that is allowed in drinking 

water.

The number of samples corresponds to the number of samples analyzed from the location.

The uncertainty characterizes the range of the concentrations, low to high limit, which could reasonably be attributed to the radiological measurement.

The critical level is the concentration below which results are considered to be nondetections with a 5-percent probability of false detection.

A radiological contaminant is not detected (ND) when its concentration is less than the critical level.

data may lose validity when it is taken out of the context or 

presented in an otherwise incomplete manner. WSCs shall 

always attempt to minimize the probability that results could 

be misinterpreted or misconstrued.

USGS WSCs conduct research studies and monitoring 

programs that focus on the detection and quantification of 

radiological constituents in various environmental matrices 

at substantially lower concentrations than those associated 

with regulatory action levels (AL), Safe Drinking Water 

Act Maximum Contaminant Levels (MCL), or other health 

benchmark levels. Surface water and ground water may 

reasonably be expected to have at least small amounts of some 

radionuclides. However, their presence does not necessarily 

indicate the water poses a health risk. Therefore, providing 

a comparison of WSC results to AL or MCL should be 

considered to ensure the lay public interprets the radiological 

concentrations from a relevant perspective. In addition, it 

also should be emphasized that nondetection does not imply 

that the radiological constituent is not present; rather, its 

concentration is below the level that can be measured. Table 5 

shows an example of the types of information that should be 

included when publishing radiological results in nontechnical 

reports.

6. Interpretation and Reporting of 

Results from an Aggregated Dataset

As discussed in section 5, reporting of radiological results 

can be either simple and straightforward or challenging. 

Therefore, the aggregation of individual results into a single 

dataset for graphical presentation, summarization, or other 

purposes must be considered carefully within the limitations 

of individual results. For example, it is not uncommon to have 

an aggregated dataset that includes positive, negative, and zero 

results. The WSC should exercise caution when summarizing 

large-scale multisite, single-measurement datasets that have 

a large percentage of data below detection because such data 

could impart substantial weight to the overall statistical computation, depending on the treatment used. Appropriate statistical tools for the analysis of such datasets are presented by 

Helsel (2005) and Taylor (1990). Many of the same treatments 

that are used with other aggregated water-quality datasets are 

appropriate for aggregated radiological data as long as the 

implications and limitations cited in this document are clearly 

accounted for.
6. Interpretation and Reporting of Results from an Aggregated Dataset 15

Figure 1. Graphical interpretation of radiological results. 

The detection (D) and nondetection (ND) values are shown, 

and the 68-percent confidence level or 1-sigma Combined 

Standard Uncertainty (1σ CSU) are identified by the shaded 

areas. Units are picocuries per liter (pCi/L).

0 0.2 0.4 0.6 0.8 1.0 1.2

PICOCURIESPERLITER

Sample 1: 0.98 ±0.15 pCi/LD

Sample 2: 0.65 ±0.10 pCi/LD

Sample 3: 0.87 ±0.20 pCi/LD

Sample 4: 0.53 ±0.40 pCi/LND

The combined standard uncertainty (CSU) may be 

used when interpreting radiological results. For example, a 

graphic display of the sample result and CSU for four samples 

collected from the same location is provided in figure 1. The 

collected from the same location at different times or from 

samples collected at different locations. Results obtained 

from the NWIS database should be reviewed and noted for 

acceptability before aggregating the data. When results are 

determined to be acceptable, the statistical analysis shall 

include the concentration and CSU (include the ssLC for 

graphical representations) no matter if the result is negative, 

zero, or determined to be detected or nondetected. Excluding 

any positive, negative, or zero result from a dataset will 

bias the statistical evaluation and lead to possible erroneous 

conclusions.

Basic statistical terms such as the mean and standard 

error of the mean can be used to summarize aggregated measurements and are presented here. Other statistical approaches 

also can be used, but their description and use are beyond the 

scope of this report. Information on other statistical treatments 

can be found in Bevington and Robinson (1992). The average 

(x) of multiple laboratory measurements x1, x2, ..., xN of the 

same sample or of samples collected at the same location at 

the same time can be calculated using equation 6, where N is 

the number of measurements.

 (6)

The corresponding standard uncertainty of , based on 

the variance of the measurement , can be calculated 

using either equation 7 or 8, depending on how strongly correlated the measurements are with each other.

 

 

If all the measurement errors are essentially independent, the standard uncertainty is calculated using equation 7. 

If all the measurement errors are very strongly correlated, the 

standard uncertainty is calculated using equation 8. Equation 7 

reduces the uncertainty roughly by a factor of , whereas 

equation 8 does not reduce the uncertainty at all.

For single measurements on samples collected at different 

locations and (or) times, it is not appropriate to propagate 

the uncertainties for the individual measurements when 

calculating the average because of the variability in sample 

collection. Sampling variability is usually assumed to be much 

larger than laboratory measurement variability. Therefore, in 

this case, the standard error of the mean is the best estimate 

of uncertainty for the average measurement and is calculated 

using equation 9.

 

x

x x x

N

N  1 2   ... 

x

u xN

2

( )

1 2

1

2

N

u x u xN ( )   ( ) ... (7)

u x u x

N

N ( ) ( ) 1   ... (8)

1/ N

s x

N N

x x i

i

N

( ) ( )  ( ) 
 
 

¤ 1

1

2

1

(9)

CSU provides an upper and lower limit to the range in which 

the true sample result lies; the bar chart shows the relation 

between the activities measured in individual samples.

The results and associated CSUs from two samples 

collected at the same site and time (or duplicate samples in a 

laboratory’s batch QC) can be evaluated to determine whether 

they are statistically the same or different. An example of a 

simple equation that may be used to determine if two results 

(R1 and R2) with their associated CSUs (CSU1 and CSU2) 

are different is provided in equation 5. This equation is taken 

from the concept of normalized absolute difference (Paar 

and Porterfield, 1997), which tests the null hypothesis that 

the results do not differ significantly when compared to their 

respective CSUs. When the normalized absolute difference 

expression exceeds the z value, the results may be considered 

to be different on the basis of a defined significance level. It 

is common to use a z value of 2 or 3 (corresponding to 5 and 

about 0.3 percent significance levels, respectively).

 (5)

Other possible approaches for interpreting or presenting 

aggregated radiological results, such as a statistical summary 

or graphical illustration, are provided herein as examples. 

These examples are not meant to be all-inclusive nor are they 

the only viable approaches. However, they serve to provide 

a perspective on aggregating and displaying radiological

data. As with any interpretation or presentation of data, any 

approach should be reproducible and documented.

For certain projects, a WSC may want to use statistical 

analysis to summarize radiological results from samples 

| R - R | / CSU +CSU > z 1 2 1

2

2

2  	
16 Interpreting and Reporting Radiological Water-Quality Data

All the required radiological parameters also can be 

presented graphically. Figure 2 illustrates 226Ra results for 120 

water samples. The figure includes reported results, their 

corresponding CSU and ssLC, and nondetections. The dataset 

also included a few negative results that could be presented 

as reported and without manipulation or substitution. This 

simple illustration provides perspective on the overall dataset, 

including the range of detections and their concentrations. 

Using a graphical approach to presentation of data may 

facilitate interpretations not immediately evident in a data 

table by expanding the perspective on a large radiological

dataset without censoring or manipulating the data.

Many USGS water-quality projects transcend the basic 

reporting of occurrence data described previously and require 

more detailed assessments of fate and transport or other 

process-oriented interpretations, such as comparisons of 

aggregated datasets between different environmental sites. It 

is beyond the scope of this report to provide details on all such 

activities. However, the WSC may build on the basic concepts 

of data reporting described in this report to reliably design and 

carry out its technically sound projects. Most of the potentially 

limiting factors are centered on the pitfalls that could arise if 

interpretations are made without consideration of the uncertainties in each individual result or aggregate of results. For 

example, in order to assess the fate of a naturally occurring 

radiological constituent, the WSC may need to distinguish 

between low levels of true environmental concentrations and 

the uncertainties due to laboratory analyses. In some cases, 

the uncertainties will be large, thereby making calculations of 

concentration gradients or differences between sites impossible or unreliable (for example, the data from sample numbers 

1–40 in figure 2 are all of similar magnitude and associated 

uncertainty). On the other hand, in many cases, the differences 

between measurements will exceed the associated uncertainties by large margins and therefore could reliably be compared 

in these types of analyses (for example, in figure 2, the data 

point for sample number 80 could reliably be compared to 

the data point for sample number 100). In addition, statistical 

analysis of individual or aggregated data also should consider 

the associated uncertainties as part of the interpretation.

Acknowledgments

Anita Bhatt (U.S. Department of Energy-Idaho National 

Laboratory Radiological and Environmental Sciences 

Laboratory), Richard Graham (U.S. Environmental Protection 

Agency –Region VIII), John Griggs and Keith McCroan (U.S. 

Environmental Protection Agency –National Air and Radiation 

Environmental Laboratory), Rodney Melgard (Eberline 

Services Analytical Laboratory), Donovan Porterfield (Los 

Alamos National Laboratory), Robert Shannon (Quality 

Radioanalytical Support, LLC), and Myint Thein (U.S. 

Department of Energy, Oak Ridge National Laboratory) are 

thanked for graciously reviewing this report. The authors also 

thank James Eychaner, Michael Focazio, Dorrie Gellenbeck, 

Jeanne Hatcher, Gregory Mohrman, Lisa Olsen, Lisa Senior, 

Sylvia Stork, and Zoltan Szabo of the U.S. Geological Survey 

for their thorough reviews, which greatly improved the report.

References Cited

American National Standards Institute (ANSI), 2003, Measurement and associated instrumentation quality assurance 

for radioassay laboratories: American National Standards 

Institute Report N42.23.

Benjamin, J.R., and Cornell, C.A., 1970, Probability, statistics, 

and decision for civil engineers: New York, McGraw-Hill, 

684 p.

Bevington, P.R., and Robinson, D.K., 1992, Data reduction 

and error analysis for the physical sciences: McGraw-Hill 

College, ISBN-13 978-0079112439.

Childress, C.J.O., Foreman, W.T., Conner, B.F., and Maloney, 

T.J., 1999, New reporting procedures based on long-term 

method detection levels and some considerations for 

interpretations of water-quality data provided by the U.S. 

Geological Survey National Water Quality Laboratory: U.S. 

Geological Survey Open-File Report 99–193, 19 p.

Currie, L.A., 1968, Limits for qualitative detection and 

quantitative determination—Application to radiochemistry: 

Analytical Chemistry, v. 40, p. 586–592.

Figure 2. Graphical presentation of radiological results with 

pertinent supporting information. 

–5

0

5

10

15

20

0 20 40 60 80 100 120

+1SCSU

–1 S CSU

Detected concentration

Nondetect

ssLC

RADIUM-226, IN PICOCURIES PER LITER

SAMPLE NUMBER
References Cited 17

Drever, J.I., 1988, The geochemistry of natural waters, 2d Rucker, T.L., 2001, Calculation of decision levels and miniedition: Englewood Cliffs, New Jersey, Prentice-Hall, 437 p. mum detectable concentrations from method blank and 

sample uncertainty data—Utopian statistics: Journal of 

Eisenbud, M., and Gesell, T.F., 1997, Environmental Radioanalytical and Nuclear Chemistry, v. 248, no. 1, 

radioactivity: Academic Press, 4th edition, ISBN-13, p. 191–196.

978-0122351549.

Taylor, J.K., 1990, Statistical techniques for data analysis: 

Helsel, D.R., 2005, Nondetects and data analysis: Hoboken, Boca Raton, Fla., Lewis Publishers, Inc., ISBN 

New Jersey, John Wiley, 250 p. 0-87371-250-1, 75 p.

Hem, J.D., 1985, Study and interpretation of the chemical U.S. Environmental Protection Agency, 1980a, Prescribed 

procedures for measurement of radioactivity in characteristics of natural water, 3d edition: U.S. Geological 

drinking water: U.S. Environmental Protection Agency, Survey Water-Supply Paper 2254, 263 p. Radiochemical Methods Section, Physical and Chemical 

International Organization for Standardization, 1995, Guide to Methods Branch, Environmental Monitoring and Support 

the expression of uncertainty in measurement: International Laboratory, Cincinnati, Ohio, publication number EPA 

Organization for Standardization, Geneva, Switzerland. 600/4-80-032.

U.S. Environmental Protection Agency, 1980b, Upgrad- International Union of Pure and Applied Chemistry, 1995, ing environmental radiation data: Health Physics Society Nomenclature in evaluation of analytical methods including Committee Report HPSR-1, U.S. Environmental Protec- detection and quantification capabilities: Pure and Applied tion Agency publication number EPA 520/1-80-012, U.S. Chemistry, v. 67, no. 10, p. 1699–1723. Environmental Protection Agency, Office of Radiation 

Lieser, K.H., 2001, Nuclear and radiochemistry—Fundamen- Programs, Washington, D.C.

tals and application: Wiley-VCH, 2d edition, ISBN-13, U.S. Environmental Protection Agency, 2006, Inventory of 978-3527303175. radiological methodologies for sites contaminated with 

radioactive material: Office of Air and Radiation, National MARLAP (Multi-Agency Radiological Laboratory Analyti- Air and Radiation Environmental Laboratory, Montgomery, cal Protocols), NUREG-1576, 2004, U.S. Environmental Ala., U.S. Environmental Protection Agency publication Protection Agency publication number EPA 402-B-04- number EPA 402-R-06-007.

001C: National Technical Information Services publication 

number NTIS PB2004-106421, July edition. U.S. Geological Survey, 2007, Policy for the evaluation and 

approval of analytical laboratories: Office of Water Quality 

Paar, J.G., and Porterfield, D.R., 1997, Evaluation of Technical Memorandum No. 2007.01, accessed July 21, 

radiochemical data usability: U.S. Department of Energy, 2008, at http://water.usgs.gov/admin/memo/QW/qw07.01.

Office of Environmental Management, es/er/ms-5, 30 p. html.
the corresponding known value of a parameter of 

interest. 

combined standard uncertainty (CSU): Standard 

uncertainty of an output estimate calculated by 

combining the standard uncertainties of the input 

estimates. The combined standard uncertainty of y

is denoted by uc(y). The CSU is reported at the 68 

percent or 1-sigma (1σ) confidence level.

critical level (LC): In the context of analyte 

detection, critical level means the minimum 

measured value (for example, of the instrument 

signal or the radionuclide concentration) that 

indicates a positive (nonzero) amount of a 

radionuclide is present in the material within 

a specified probable error. The critical level is 

sometimes called the critical value or decision 

level. The general use of the term “critical level” 

is for a method wherein nominal measurement 

parameters are used in the calculation. Contrast 

this use to the sample-specific critical level (ssLC) 

defined herein.

D

decay factor: The fractional amount of the 

original radionuclide activity in a sample that 

remains after decay in the time interval between 

sample collection and sample analysis.

duplicate sample: Two equal-sized samples 

of the material being analyzed, prepared, and 

analyzed separately as part of the same batch, 

used in the laboratory to measure the overall 

precision of the sample-measurement process 

beginning with laboratory subsampling of the 

field sample.

E

emission probability per decay event: The 

fraction of total decay events for which a 

particular particle or photon is emitted. The 

emission probability per decay event is also 

known as the branching fraction or branching 

ratio.

I

ingrowth factor: The activity of a supported 

radionuclide progeny at a specific time after 

chemical separation, expressed as a fraction of the 

amount of radioactivity at full ingrowth. 

Many of the definitions in the glossary are 

taken from MARLAP (2004).

A

activity: Mean rate of nuclear decay 

occurring in a given quantity of material. The 

“Curie” unit for activity is currently (2008) 

used by the USGS. The SI unit of activity is 

the becquerel (Bq), which equals one nuclear 

transformation per second. One curie equals 

3.7×1010 Bq.

activity reference date: The date that is 

synonymous with the activity (concentration) 

on the day of sample collection.

aliquant: A representative portion of a 

homogeneous sample removed for the purpose 

of analysis or other chemical treatment. The 

quantity removed is not an evenly divisible 

part of the whole sample. By contrast, an 

aliquot is an evenly divisible part of the whole.

B

background (instrument): Radiation detected 

by an instrument when no source is present. 

The background radiation that is detected may 

come from radionuclides in the materials of 

construction of the detector, its housing, its 

electronics, and the building as well as the 

environment and natural radiation.

bias (of a measurement process): A 

persistent deviation of the mean measured 

result from the true or accepted reference 

value of the quantity being measured, which 

does not vary if a measurement is repeated.

blank (analytical or method): A sample 

that is assumed to be essentially free of 

the radionuclide that is carried through the 

radiochemical preparation, analysis, mounting, 

and measurement process in the same manner 

as a routine sample of a given matrix.

C

calibration: The set of operations that 

establish, under specified conditions, the 

relation between values indicated by a 

measuring instrument or measuring system, or 

values represented by a material measure, and 

Glossary

18 Interpreting and Reporting Radiological Water-Quality Data
Glossary 19

L

laboratory control sample: A standard 

material of known composition or an artificial 

sample (created by fortification of a clean 

material similar in nature to the sample), 

which is prepared and analyzed in the same 

manner as the sample. In an ideal situation, the 

result of an analysis of the laboratory control 

sample should be equivalent to (give 100 

percent of) the target analyte concentration or 

activity known to be present in the fortified 

sample or standard material. The result 

normally is expressed as percent recovery.

M

matrix spike sample: An aliquant of a 

sample prepared by adding a known quantity 

of target analytes to a specified amount of 

matrix and subjected to the entire analytical 

procedure to establish if the method or 

procedure is appropriate for the analysis of the 

particular matrix.

maximum contaminant level (MCL): A 

regulatory limit established by the U.S. 

Environmental Protection Agency (USEPA) 

for the concentration of certain radionuclides 

in drinking water. The highest level 

(concentration) of a contaminant that is 

allowed in drinking water distributed to the 

public. MCLs are set as close as feasible 

to the level believed to cause no human 

health effects, while using the best available 

treatment technology and taking cost into 

consideration. MCLs are enforceable 

standards.

measurement quality objective (MQO): The 

analytical data requirements of the dataquality objectives, which are project- or 

program-specific and can be quantitative or 

qualitative. These analytical data requirements 

serve as performance measurement criteria or 

objectives of the analytical process. 

Multi-Agency Radiological Laboratory 

Analytical Protocols (MARLAP) refer to these 

performance objectives as MQOs. Examples 

of quantitative MQOs include statements of 

required radionuclide detectability and the 

uncertainty of the analytical protocol at a 

specified radionuclide concentration, such as 

an action level. Examples of qualitative MQOs 

include statements of the required specificity 

of the analytical protocol (for example, the 

ability to analyze for the radionuclide of 

interest, given the presence of interferences).

method blank: A sample assumed to be 

essentially target analyte-free that is carried 

through the radiochemical preparation, analysis, 

mounting, and measurement process in the same 

manner as a routine sample of a given matrix.

minimum detectable concentration (MDC): The 

minimum detectable concentration of the analyte 

in a sample. The smallest (true) radionuclide 

concentration that gives a specified probability 

(Type II - β) that the value of the measured 

radionuclide will exceed its critical level 

concentration (that is, that the material analyzed 

is not “blank” or free of analyte) (Currie, 1968; 

MARLAP, 2004, chapter 20). The general use 

of the term “MDC” or “a priori MDC” is for a 

method wherein nominal measurement parameters 

are used in the calculation. Contrast this use to the 

sample-specific MDC (ssMDC) defined herein.

N

nominal value: A value related to a designated or 

theoretical size that may vary from the actual.

null hypothesis (H0): One of two mutually 

exclusive statements tested in a statistical 

hypothesis test (compare with alternative 

hypothesis). The null hypothesis is presumed to 

be true unless the test provides sufficient evidence 

to the contrary, in which case the null hypothesis 

is rejected and the alternative hypothesis (Ha) is 

accepted.

P

Poisson distribution: A random variable X has 

the Poisson distribution (Pr) with parameter λ if for 

any nonnegative integer k, Pr[X = k] = (λke–λ)/k!. 

In this case, both the mean and variance of X are 

numerically equal to λ. The Poisson distribution 

is often used as a model for the result of a nuclear 

counting measurement.

precision: The closeness of agreement between 

independent test results obtained by applying 

the experimental procedure under stipulated 

conditions. Precision may be expressed as the 

standard deviation. Conversely, imprecision is 

the variation of the results in a set of replicate 

measurements.

Q

quality control (QC): The overall system of 

technical activities that measures the attributes and 

performance of a process, item, or service against 

defined standards to verify that they meet the 
decreased by the measured amount of analyte 

in the sample that was present before spiking. 

Contrast this to yield defined herein.

relative standard uncertainty: The ratio of the 

standard uncertainty of a measured result to the 

result itself. The relative standard uncertainty of x

may be denoted by ur(x).

S

sample: A portion of material selected from a 

larger quantity of material or a set of individual 

samples or measurements drawn from a 

population whose properties are studied to gain 

information about the entire population.

sample-specific critical level (ssLC): The 

sample-specific critical level is calculated using 

the parameter values measured during the 

generation of the sample result. This is different 

than the critical level for a method wherein 

nominal measurement parameters are used in the 

calculation (see critical level). Concentrations 

below the ssLC are considered nondetections.

sample-specific minimum detectable 

concentration (ssMDC): The sample-specific 

minimum detectable concentration is calculated 

using the parameter values measured during the 

generation of the sample result (see minimum 

detectable concentration).

significance level: The risk (probability) of 

making a Type I error (α) is traditionally called 

the level of significance of the test.

standard uncertainty: The uncertainty of 

a measured value expressed as an estimated 

standard deviation, often call a “1-sigma” (1-σ) 

uncertainty. The standard uncertainty of a value x

is denoted by u(x).

T

Type I decision error: In a hypothesis test, the 

error made by rejecting the null hypothesis when 

it is true. A Type I decision error is sometimes 

called a “false detection” or a “false positive.”

Type II decision error: In a hypothesis test, the 

error made by failing to reject the null hypothesis 

when it is false. A Type II decision error is 

sometimes called a “false nondetection” or a 

“false negative.”

stated requirements established by the project; 

operational techniques and activities that are 

used to fulfill requirements for quality. This 

system of activities and checks is used to ensure 

that measurement systems are maintained 

within prescribed limits, providing protection 

against out-of-control conditions and ensuring 

that the results are of acceptable quality.

quantile: A p-quantile of a random variable X

is any value xp such that the probability that X 

< xp is at most p and the probability that X ≤ xp

is at least p.

R

radioactivity: The property possessed by 

some elements or isotopes of spontaneously 

emitting energetic particles (electrons or alpha 

particles) by the disintegration of their atomic 

nuclei.

radioanalytical analysis: A general term used 

to denote the analysis of a sample for a specific 

radionuclide, group of radionuclides, or gross 

screening of radioactivity. The term may be 

used for a single radionuclide analysis or to 

denote a collection of analyses that may include 

gamma-ray spectrometric analyses, gross alpha 

and beta analyses, and specific radionuclide 

analyses that require chemical separations such 

as isotopic uranium, 226Ra, and 90Sr. 

radiochemical analysis: A term used to 

denote the analysis of a radionuclide in a 

sample that requires chemical processes to 

isolate the radionuclide in the sample. Isotopic 

uranium, 226Ra, and 90Sr in a sample require 

radiochemical analyses.

radiological: An adjective relating to nuclear 

radiation.

radiological hold time: Refers to the time 

differential between the sample collection date 

and the final sample counting (analysis) date.

radionuclide: A nuclide that is radioactive 

(capable of undergoing radioactive decay).

recovery: The ratio of the amount of analyte

measured in a spiked or laboratory control 

sample, to the amount of analyte added, 

usually expressed as a percentage. For a matrix 

spike, the measured amount of analyte is first 

20 Interpreting and Reporting Radiological Water-Quality Data
Glossary 21

U

uncertainty: A parameter, usually associated 

with the result of a measurement, that 

characterizes the dispersion of the values that 

could reasonably be attributed to the measurement 

of interest. Y

yield: The ratio of the amount of radiotracer

or carrier determined in a sample analysis to 

the amount of radiotracer or carrier originally 

added to a sample. The yield is an estimate of 

the analyte during analytical processing. It is 

used as a correction factor to determine the 

amount of radionuclide (analyte) originally 

present in the sample. Yield is typically 

measured gravimetrically (through a carrier) or 

radiometrically (through a radiotracer).
22 Interpreting and Reporting Radiological Water-Quality Data

Appendix: Typical Equations for Calculating Radiological 

Parameters

The information presented in this appendix conforms to the formulations and concepts presented in the Multi-Agency 

Radiological Laboratory Analytical Protocols, commonly referred to as MARLAP (2004), the International Organization for 

Standardization (1995), and International Union of Pure and Applied Chemistry (1995).
A1. Calculating the Concentration 23

A1. Calculating the Concentration

The general equation used to calculate concentration takes on the following form (MARLAP, 2004, chapter 19):

 (A1)

where:

Concentration is in pCi/L;

Gross Instrument Signal is detector response in units of detector events registered per unit time from all 

 constituents in the sample (includes detector and process-related background events);

Blank Signal is detector events registered per unit time from analyzing a blank sample having no target constituent;

Estimated Interferences is detector counts registered per unit time from nontarget constituents in the sample; and

Sensitivity Factor is a combination of multiplicative parameters, such as sample size, detector efficiency for 

 radiation emitted, chemical yield of process, decay factor, ingrowth factor, and unit conversion factor. 

The complexity of the equation used to calculate the concentration varies substantially and usually depends on the type 

of radiation emitted during radioactive decay (α, β, γ) and the radiochemical method chosen. The basic equation that has all 

possible parameters incorporated in a complex equation, such as for 228Ra or 90Sr by the analysis of their decay products 228Ac 

and 90Y, has the form taken from “Inventory of Radiological Methodologies for Sites Contaminated with Radioactive Material”

(U.S. Environmental Protection Agency, 2006).

 (A2)

 

where:

NS is the number of accumulated detector events (counts) for the decay product;

NB is the number of background detector events (counts) for the equivalent sample count interval;

t is the counting interval for sample (t

s) and background (tB);

CF is the factor used for converting to desired reporting units, typically 2.22 disintegrations per 

 picocurie (pCi);

V is the sample size (mass or volume);

B is the branching fraction of the particle emission being counted. This is the fraction of all 

 decays that result in an emission of the characteristic radiation (alpha, beta, or gamma);

Y is the chemical yield of the analysis;

e is the detector efficiency for the particular emission of the radionuclide;

λ is the decay constant of the radionuclide (λ = 0.69315/t1⁄2); and t1⁄2 is the half-life of the 

 radionuclide (λ1 for parent and λ2 for the decay product);

DFP or is the decay correction factor for the parent from sample collection to second 

 chemical separation;

DFDP or is the decay correction factor for decay product from second chemical separation to start 

 of counting;

I or is the ingrowth correction factor for the ingrowth of the decay product used to calculate the 

 activity of a parent;

T1 is the time interval between sampling and beginning the sample count;

T2 is the time interval between first and second decay product chemical separations;

T3 is the time interval between second decay product chemical separation and count;

 is the correction factor for radioactive decay of the decay product during the counting interval.

Note: Because measurement parameters are never truly known exactly, each factor has an associated standard uncertainty.

Concentration Gross Instrument Signal Blank Signal Es  ( ) 
  ( timated Interferences

Sensitivity Factor

)

( )

Concentration pCi L

CF B Y V I DF DF

N

t

N

t

s

s

B

B

tS

P

 	 /

¥

§

 ́

¶ 

s

s s s s s s s


 



2

DP

t s 
 e S 
  	 1 2

e


 T

 	 1 1

e


 T  	  2 3

1 2 2 
 
  	 e  T

  2 s 1 t 
 
 t ( ( e 2 s
24 Interpreting and Reporting Radiological Water-Quality Data

For a simple analysis, such as gross alpha and beta analysis, the following equation is used: 

 (A3)

A2. Calculating the Combined Standard Uncertainty

As presented in section A1, each factor in the equation used to calculate the concentration has an associated uncertainty 

called the standard uncertainty. By convention, a standard uncertainty is quoted at the 68-percent or 1-sigma confidence level. 

For example, the determination of the detector efficiency is not exact because of the uncertainty in the radioactive source used to 

determine the detector efficiency and the Poisson random counting uncertainty when counting the radioactive source.

The uncertainty for the stated concentration is calculated by combining (or propagating) these standard uncertainties into an 

overall uncertainty called the combined standard uncertainty. MARLAP (2004, chapter 19) uses a first-order uncertainty propagation formula shown in equation A4 to propagate the standard uncertainties. The general formula uses the partial differential of 

each factor (xi) to calculate the concentration y. Equation A4 is used to calculate the variance of the concentration based 

on the uncertainty propagation with uncorrelated inputs.

 (A4)

The combined standard uncertainty uc (y) is calculated by taking the square root of the variance .

For the simple concentration equation A3, the resulting equation (MARLAP, 2004, chapter 19) used to calculate the 

variance is the following:

 (A5)

where the uncertainties in the time variables are assumed to be negligible compared to the uncertainties of the other terms. Equation A5 reduces to equation A6 using the same parameters defined for equation A2.

 (A6)

The combined standard uncertainty of is calculated by

 (A7)

A3. Calculating the Critical Level

A3.1 General Principles

An analysis of a radiological sample will produce a gross signal response that is related to the quantity of analyte present in 

the sample. However, random measurement uncertainties will cause this signal to vary somewhat if the measurement is repeated 

on the same sample. A nonzero signal may be (and usually is) produced even when no analyte is present. For this reason, a 

laboratory analyzes a blank (or an instrument background) to determine the signal observed when no analyte is present in the 

blank sample and subtracts this blank signal from the gross signal to obtain a net signal for the sample being analyzed. In fact, 

because the signal varies when the blank measurement is repeated, there is a blank signal distribution whose parameters must be 

estimated. In a similar manner, the net signal response will have a distribution with an average value (assumed to be zero or μ0) 

and a standard deviation (σ0).

"c " Concentration

N

t

N

t

CF

S

S

B

B p 	 Ci L

¥

§

¦  ́

¶

μ






s s A E V

uc

2

 	 y

u y

f

x

u x c

i i

N

i

2

1

2

2  	 ¥

§

¦  ́

¶

μ   	 u

 u ¤

uc

2

 	 y

u c

c

N

u N

c

N

u N

c

c

S

S

B

B

2

2

2

2

2



   



 	 ¥

§

¦  ́

¶

μ  	 ¥

§

¦  ́

¶

μ  	 ¥

§

¦  ́

¶  u

u



u

u



u

u μ  	 ¥

§

¦  ́

¶

μ   	 u

u

2

2

2

2 u

c

V

 u V

u c

N t N t

t t V

N

t

N

t

V c

S

S

B

B 2

2 2 2 2 2 2

2 2



 

 	  	

¥

§

¦  ́

¶

μ

 s 
 s

s s s






s

s

u u V

V

2

2

2

2





 ̈  	  	

a

© ·

1

 ̧  S B B S

S B

u c c   	 c

u c 	  u c 	 2

c A c A
A3. Calculating the Critical Level 25

To determine how large an instrument signal must be to provide high confidence for the presence of the analyte in a sample, 

one calculates a threshold value for the net signal called the critical level LC (Currie, 1968). The critical level also is denoted by 

SC (MARLAP, 2004, chapter 20). If the observed net signal for a sample being analyzed exceeds the critical level, the radiological constituent is considered detected; otherwise, it is not detected. Because the measurement process is statistical in nature, it 

is possible for the net signal related to a blank sample to exceed the critical level, leading one to conclude incorrectly that the 

sample contains a positive amount of the analyte. Such an error is sometimes called a “false positive,” although the term Type 

I error terminology is favored by MARLAP (2004, chapter 20). The probability of a Type I error is often denoted by α. Before 

calculating the critical level, one must choose a level for α. The most commonly used level is 0.05, or 5 percent. If α = 0.05, 

then one expects the net instrument signal to exceed the critical level in only about 5 percent of cases (1 in 20) when analyte-free 

samples or blank samples are analyzed. These concepts are shown graphically in figure A1.

Figure A1. The curve representing the critical level concept by using 

a theoretical distribution of the net instrument signal (concentration) 

obtained when analyzing an analyte-free sample. The chosen Type I error 

probability σ determines the location of the critical level of the net signal 

LC. For an α = 0.05 or 5 percent, the critical level corresponds to the 95th 

quantile value of the normal distribution. The probability α is depicted 

as the area under the curve to the right of the dashed line. Note that 

decreasing the value of α requires increasing the critical value (shifting 

the dashed line to the right) and increasing the value of α decreasing the 

critical level (shifting the dashed line to the left). The α quantile of the 

standard normal distribution, using a default level of 1.645, is kα; the mean 

of the net signal responses of blank sample distribution is μ0; and the 

standard deviation of the net signal response of blank sample distribution 

is σ0. PROBABILITY

NET RESPONSE OF BLANK SAMPLES

(INSTRUMENT BACKGROUND SUBTRACTED)

M

S

A

 LC

<kAS

A3.2 Calculating the Sample-Specific Critical Level (ssLC)

The sample-specific critical level (ssLC) is calculated by the contract laboratory using all the sample-specific parameter 

values. A sample-specific critical level is calculated using the net instrument background counting distribution and samplespecific factors, and by assuming that the mean value of the net instrument background distribution is zero. The ssLC is 

commonly calculated using equations A8a and A8b (Currie, 1968). 
26 Interpreting and Reporting Radiological Water-Quality Data

 (A8a)

and

 (A8b)

where:

σ0 is the standard deviation of the net instrument background (counts);

NB is the background counts in background counting interval

CF is the unit conversion factor, typically 2.22 disintegrations per minute per picocurie;

t

S is the counting time of sample (minute);

t

B is the counting time of background (minute);

V is the sample size (mass or volume);

B is the branching fraction of the particle emission being counted;

ε is the fractional detector efficiency for the particular emission of the radionuclide;

Y is the chemical yield of the analysis;

DF is the decay factor; and

I is the correction factor for the ingrowth of progeny used to calculate the activity of a parent.

Equation A8a is not suitable when the number of detector background counts is small or zero over the background counting 

time. This may be the case for analyses that use low background detection systems, such as alpha or gamma ray spectrometers. 

For such applications, the equations discussed in chapter 20, attachment 20A of MARLAP (2004) need to be reviewed and 

applied.

The specific equation that is used by the contract laboratories to calculate the ssLC for various radioanalytical methods will 

be specified by the NWQL in the PWS.

A3.3 Practical Approach for Verifying the Reported Sample-Specific Critical Level

From a practical point of view, when the sample and background counting times are nearly equal, multiplying the CSU 

associated with a QC blank’s result by 2 approximates the critical level of a method (not an individual result). However, this 

approximation is only good when the parameters used to calculate the concentration for the blank are nearly equal to the average 

values used for the method.

An approximation of 2 times the CSU of the sample or blank result (or sometimes slightly greater depending on the 

background of the instrument used for the measurement) can be used for verifying the reported ssLC. This assumes near equal 

sample and background counting times. For example, if a radiological result is 0.121 ± 0.091 pCi/L, the ssLC can be estimated 

to be 0.18 or about 0.20 pCi/L. This ssLC approximation is useful to verify that the laboratory has not made a substantial error 

in calculating the sample-specific critical level. The approximation of 2 times the CSU may provide reasonable estimates for 

most applications but should not be used to categorically indicate that a mistake has been made without evaluating the relation 

between the reported result, CSU, ssLC, and ssMDC.

A4. Calculating the Minimum Detectable Concentration

A4.1 General Principles

The a priori minimum detectable concentration (a priori MDC) is a hypothetical predictive concept that is used to estimate 

the detection capability of a measurement process (method) under defined circumstances. The concept is a priori or before the 

fact (before a sample measurement) and is not to be used to evaluate individual measurement results. After a measurement has 

been made, the result and its Combined Standard Uncertainty (CSU) are the important quantities that are used to compare analytical results to historical values for the sampling site.

Once the critical level LC (instrument response) has been defined for a method based on a distribution of blank samples and 

an α probability of Type I error (false detection) rate, an a priori MDC may be established by specifying the acceptable Type 

II error rate β (false nondetection) and the standard deviation of the probability distribution σD of the net signal response when 

ssL

CF t V B Y DF I C

s

 s

s s s s s s s

1 645 0 . 



 0  1

¥

§

¦  ́

¶

μ N

t

t

t

t

B

S

B

S

B
A4. Calculating the Minimum Detectable Concentration 27

the true value SD is equal to the MDC value (Currie, 1968). The concept assumes no systematic errors such as method bias. The 

a priori MDC is defined so that the probability distribution of the possible measurement responses when SD equals the MDC 

crosses the critical level LC at the 1-β fraction of the distribution.

Graphically, the theoretical a priori MDC distribution and its relation to the critical level are shown in figure A2 (based on 

figure 20.1 in MARLAP, 2004). In this figure, SD corresponds to the a priori MDC value. Under the a priori MDC concept, the 

shaded area under the SD distribution corresponds to the β or the lower 5 percent of the distribution. Analytical results with values in the shaded area would not be considered different from background because their values are below the critical level. The 

nonshaded area of the SD distribution corresponds to the 1-β or the upper 95 percent of the distribution. Analytical results with 

values in this region would be considered positive because their values are greater than the critical level. Note that all possible 

analytical result values between LC and SD (45 percent of the SD distribution) would be considered different from background 

and thus positive values.

Figure A2. Graphical representation of the a priori Minimum Detectable Concentration concept (taken from 

figure 20.1; in MARLAP, 2004). The false nondetection Type I error (α, 5-percent probability), the false detection 

Type II error (β, 5-percent probability), the critical level (LC), and the a priori minimum detectable concentration 

(SD) are shown in the figure. PROBABILITY

Net signal distribution for

analyte-free samples

Net signal distribution for

samples at the a priori MDC

LC SD

<45%>

B A

If each sample in a set of 100 samples were spiked with a radionuclide at the a priori MDC concentration and analyzed, the 

mean concentration of the 100 analyses would be the a priori MDC value (SD) and the relative one standard deviation of the distribution of analytical results around the a priori MDC would be about 30 percent. Therefore, the spread in the individual results 

from the set of 100 samples would range from slightly less (about 5 percent) than the critical level to about twice the a priori

MDC value. However, 95 out of the 100 results would exceed the critical level. By specifying the a priori MDC in the PWS, a 

false nondetection β probability of 5 percent could be assumed for a distribution of results (from multiple samples or analyses 

of the same sample) when the true concentration is at the hypothetical MDC. For USGS applications, typically only one sample 

from a particular site may be provided and only one analysis of the sample performed. A result from a single analysis that is 

less than the hypothetical a priori MDC may be from the MDC distribution, but it also could be from distributions whose true 

concentration is less than or greater than the MDC. When a single analysis of an individual sample is made, the true concentration in the sample can be estimated with approximately 95-percent confidence to be within the range described by the reported 

value ± 2 CSU.

Mathematically, the a priori MDC SD can be calculated using many equations, each having a different assumption and 

approach. MARLAP (2004, chapter 20) discusses these different approaches. The most simplified approach assumes a Gaussian 

distribution for LC and SD instrument responses. Currie (1968) used a version of the following simplified equation for instrument 

response, not concentration: 

 SD = LC + kβ × σD (A9)

where:

kβ is the 1 – β quantile of the standard normal distribution, default value of 1.645;

LC is the critical level response, defined earlier; and
28 Interpreting and Reporting Radiological Water-Quality Data

σD is the standard deviation of the SD distribution (net response).

When α=β, kα=kβ, and σD∼σ0 and where σ0 is the standard deviation of the net background response distribution, equation A9 

reduces to the most simplified form:

 SD = 2.71 + 3.29 × σ0 (A10)

When the net response background distribution is more like a Poisson distribution (when the background or sample counts 

for the analysis are less than 70) rather than like the assumed Gaussian distribution, the use of this equation may give an MDC 

wherein the observed probability of false detection may be higher than the assumed α value.

An approach has been suggested by Rucker (2001) for determining a method a priori MDC-based net background standard 

deviation SB0, in picocuries per liter, from a population of blank sample results (instrument background subtracted) as a substitute for use in equations A8 and A11. In addition, the kα and kβ for equations A10 and A11 are replaced with the Student’s t

factor for the appropriate number of degrees of freedom. The MDC equation proposed by Rucker is

 (A11)

where:

SB0 is the standard deviation of the distribution net blank results in picocuries per liter; and

t is the Student’s t factor for the number of blank samples used to determine SB and for the default α and β

probabilities of 0.05.

As noted by Rucker, this approach accounts for all of the uncertainty in the measurements (due to the variability in the parameter 

values used to calculate the result), not just the counting uncertainty. As such, this approach is useful in estimating the a priori 

MDC for a method, not a sample-specific MDC, and can be applied to defining the sensitivity requirements for contract laboratory work.

A4.2 Calculating the Sample-Specific Minimum Detectable Concentration (ssMDC)

Some laboratories calculate the sample-specific Minimum Detectable Concentration (ssMDC) based on the instrument 

background and applicable sample-specific parameters according to the following general equation:

 (A12a)

and

 (A12b)

where:

σ0 is the standard deviation of the net instrument background (counts);

NB is the background counts in background counting interval;

CF is the unit conversion factor, typically 2.22 disintegrations per picocurie;

t

S is the counting time of sample (minute);

t

B is the counting time of background (minute);

V is the sample size (mass or volume);

B is the branching fraction of the particle emission being counted;

ε is the fractional detector efficiency for the particular emission of the radionuclide;

Y is the chemical yield of the analysis;

DF is the decay factor; and

I is the correction factor for the ingrowth of progeny used to calculate the activity of a parent.

Equations A12a and A12b are not used when the number of detector background counts is small or zero over the background counting time. This may be the case for analyses that use low background detection systems, such as alpha- or gammaray spectrometers. For such applications, the equations discussed by MARLAP (2004, chapter 20, attachment 20A) need to be 

reviewed and applied.

MDC t t S   s s B

2

0 2

ssMDC

CF t B Y V DF I s

 s 

s s s s s s s

3 29 2 71 0 . . 



 0  1

¥

§

¦  ́

¶

μ N

t

t

t

t B

S

B

S

B
A4. Calculating the Minimum Detectable Concentration 29

In the original concept, the average values of the applicable parameters were used to calculate the a priori MDC for a 

method. However, more recently, sample-specific values of the parameters are used to calculate the ssMDC to show that the 

laboratory has met the required a priori MDC specified in a contract. The ssMDC is not used to determine if results are different 

from an instrument background or a blank sample.

The specific equation that is used by the contract laboratories to calculate the ssMDC for various radioanalytical methods 

will be specified in the PWS by the NWQL.

A4.3 Practical Approach for Verifying the Reported Sample-Specific Minimum Detectable 

Concentration

There are at least two approaches or rules of thumb that can be used to estimate whether a reported ssMDC has been 

calculated properly. The first approach compares the reported ssMDC to the reported ssLC. The ssMDC should be approximately 

2 times the reported ssLC (or slightly greater depending on the background of the instrument used for the measurement). The 

second approach is to compare the reported ssMDC of a sample to a multiple of the reported CSU. This approach is only 

applicable when dealing with acceptable blank and negative results or with acceptable positive results whose absolute value is 

less than approximately 3 times the reported ssMDC value. For such cases, the reported ssMDC should be approximately 

3 to 4 times the CSU of the sample result. Different multipliers may be applied for certain methods of analysis and instrument 

backgrounds. Analytical concentrations at or near the ssMDC should have a relative CSU of approximately 30 percent for most 

methods, with the exception of methods for the low-level determination of alpha-emitting nuclides. The relative CSU decreases 

with successively higher concentrations above the MDC. These rules of thumb are based on the assumed relation of the relative 

CSU at the MDC for paired observations.

A4.4 The Effect of Sample Size and Counting Time on the Reported Sample-Specific Minimum 

Detectable Concentration (ssMDC)

The magnitude of the ssMDC is inversely proportional to the sample volume analyzed and inversely proportional to the 

square root of the counting time (see equations A12a and A12b in section A4.2). Figure A3 shows the effect of reducing the size 

of a 1-liter sample on the magnitude of the ssMDC. When the sample volume analyzed is reduced by a factor of 2 (1 L to 0.5 L), 

the magnitude of ssMDC is increased by a factor of 2 (1 pCi/L to 2 pCi/L). Figure A4 shows the effect of reducing the amount 

of time a sample is analyzed by a radiation detector (instrument counting time) on the magnitude of the ssMDC. When the 

counting time is reduced by a factor of 2 from 200 minutes to 100 minutes, the magnitude of the MDC is increased by a factor of 

√2 from 1 pCi/L to 1.41 pCi/L (see equations A12a and A12b).

A4.5 The Relation between the Combined Standard Uncertainty and the Calculated Activity in a 

Sample for Two Radioanalytical Measurement Techniques

Several graphical illustrations of the relation between the reported activity in a sample and the Combined Standard 

Uncertainty (CSU) of the result have been developed. These relations are shown in figures A5a and A5b for gross beta activity 

analysis of water and in figures A6a and A6b for isotopic uranium analysis of water by alpha spectrometry techniques. Typical 

sources (detector efficiency and chemical yield) and their standard uncertainties were used (for illustrative purposes only) in the 

calculation of the CSU and the development of the graphs.
30 Interpreting and Reporting Radiological Water-Quality Data

Figure A3. The sample-specific Minimum Detectable Concentration 

(ssMDC) as a function of analysis sample volume.

Figure A4. The sample-specific Minimum Detectable Concentration 

(ssMDC) as a function of analysis counting time.

0 0.2 0.4 0.6 0.8 1.0

0

2

4

6

8

10

SAMPLE-SPECIFIC MINIMUM DETECTABLECONCENTRATION, IN PICOCURIES PER LITER

SAMPLEVOLUME, INLITERS

SAMPLE-SPECIFIC MINIMUM DETECTABLE

CONCENTRATION, IN PICOCURIES PER LITER

0 20 40 60 80 100 120 140 160 180 200 220

1.0

1.5

2.0

2.5

3.0

3.5

INSTRUMENTCOUNTINGTIME, INMINUTES
A4. Calculating the Minimum Detectable Concentration 31

Figure A5b. Typical relative Combined Standard Uncertainty (CSU) as a 

function of gross beta concentration.

0 5 10 15 20 25 30 35 40

0.5

1.0

1.5

2.0

2.5

3.0

COMBINED STANDARD UNCERTAINTY, 

IN PICOCURIES PER LITER

GROSSBETACONCENTRATION, ININ PICOCURIES PER LITER

Figure A5a. Typical Combined Standard Uncertainty (CSU) as a function of 

gross beta concentration. RELATIVE COMBINED STANDARD UNCERTAINTY, IN PERCENT

GROSSBETACONCENTRATION, INPICOCURIES PER LITER

0 5 10 15 20 25 30 35 40

0

20

40

60

80

100

120

140

160
32 Interpreting and Reporting Radiological Water-Quality Data

Figure A6a. Typical Combined Standard Uncertainty (CSU) as a function 

of Uranium-238 concentration.

Figure A6b. Typical relative Combined Standard Uncertainty (CSU) as a 

function of Uranium-238 concentration.

0 1 2 3 4

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

COMBINED STANDARD UNCERTAINTY, 

IN PICOCURIES PER LITER

U-238 CONCENTRATION, IN PICOCURIES PER LITER

0 1 2 3 4

10

20

30

40

50

RELATIVE COMBINED STANDARD 

UNCERTAINTY, IN PERCENT

U-238 CONCENTRATION, IN PICOCURIES PER LITER
A4. Calculating the Minimum Detectable Concentration 33

Manuscript approved for publication June 13, 2008

Prepared by the U.S. Geological Survey Publishing Service Center, Denver, Colorado

USGS Publishing Staff

Edited by Mary A. Kidd

Report approved by Keith J. Lucey

Cover designed by Suzanne C. Roberts and Sharon Powers

Report prepared by Sharon Powers

Technical Reviews

M.J. Focazio, USGS Office of Water Quality

L.D. Olsen, USGS, Water Science Center, California

L.A. Senior, USGS, Water Science Center, Pennsylvania

Szabo Zoltan, USGS, Water Science Center, New Jersey 

For more information concerning the research in this report, contact:

National Water Quality Laboratory

U.S. Geological Survey

P.O. Box 25046, MS 407

Denver Federal Center

Denver, CO 80225-0046

World Wide Web: http://nwql.cr.usgs.gov
McCurdy and others—Interpreting and Reporting Radiological Water-Quality Data—USGS TM 5–B6

Printed on recycled paper