# ASTM D7782-13

Designation: D7782 − 13Standard Practice forDetermination of the 99 %/95 % Critical Level (WCL) and aReliable Detection Estimate (WDE) Based on Within-laboratory Data1This standard is issued under the fixed designation D7782; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.Note—Balloted information was included and the year date changed on March 28, 2013.1. Scope1.1 This practice provides a procedure for computing a99 %⁄95 % Within-laboratory Detection Estimate (WDE) andthe associated critical level/value (WCL). The WDE is theminimum concentration, with false positives and false negativeappropriately controlled, such that values above these mini-mums are reliable detections. The WCL is the point at whichonly false positives are controlled appropriately. A false posi-tive is the reporting of an analyte as present when the analyteis not actually present; false negatives are reports of analyteabsence when the analyte is actually present. This practice isdistinguished from the Interlaboratory Detection Estimate(IDE) practice in that the IDE Standard utilizes data frommultiple, independent laboratories, while this practice is for useby a single laboratory. The IDE would be utilized whereinterlaboratory issues are of concern (for example, limits forpublished methods); this practice (and values derived from it)are applicable where the results from a single laboratory, singleoperator, single instrument, etc. are involved (for example, inunderstanding, censoring and reporting data).1.2 The establishment of a WDE involves determining theconcentration below which the precision and bias of ananalytical procedure indicates insufficient confidence in false-positive and false-negative control to assert detection of theanalyte in the future analysis of an unknown number ofsamples. Most traditional approaches attempt to determine thisdetection “limit” by estimating precision at only a single,arbitrary point. The WDE approach is intended to be a moretechnically rigorous replacement for other approaches forestimating detection limits. The WDE practice addresses anumber of critical issues that are ignored in other approaches.1.2.1 First, rather than making a single-point estimate ofprecision, the WDE protocol requires an estimate of precisionat multiple points in the analytical range, especially in therange of the expected detection limit. These estimates are thenused to create an appropriate model of the method’s precision.This approach is a more credible way to determine the pointwhere relative precision has become too large for reliabledetection. This process requires more data than has beenhistorically required by single-point approaches or by pro-cesses for modeling the relationship between standard devia-tion and concentration.1.2.2 Second, unlike most other approaches, the WDEprocess accounts for analytical bias at the concentrations ofinterest. The relationship of true concentration to measuredconcentration (that is, the recovery curve) is established andutilized in converting from as-measured to true concentration.1.2.3 Third, most traditional approaches to detection limitsonly address the issue of false positives. Although falsenegatives may not be of concern in some data uses, there aremany uses where understanding and/or control of false nega-tives is important. Without the false-negative-controlinformation, data reported with just a critical-level value areincompletely described and the qualities of data at these levelsincompletely disclosed.1.2.4 Fourth and last, the WDE standard utilizes astatistical-tolerance interval in calculations, such that futuremeasurements may reasonably be expected to be encompassedby the WDE 90 % of the time. Many older approaches haveused the statistical confidence interval, which is not intended toencompass individual future measurements, and has beenmisunderstood and misapplied. Procedures using the confi-dence interval cannot provide the stated control when thedetection-limit value is applied to future sample results; suchapplication is the primary use of these values.1.3 To summarize, the WDE is computed to be the lowesttrue concentration at which there is 90 % confidence that asingle (future) measurement (from the studied laboratory) willhave a true detection probability of at least 95 % and a truenon-detection probability of at least 99 % (when measuring ablank sample). For the laboratory in the study, the critical value1This practice is under the jurisdiction of ASTM Committee D19 on Water andis the direct responsibility of Subcommittee D19.02 on Quality Systems,Specification, and Statistics.Current edition approved March 28, 2013. Published April 2013. DOI: 10.1520/D7782–13.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1is the true concentration at which, on average, (with approxi-mately 90 % confidence) will not be exceeded by 99 % of allmeasurements of samples with true concentration of zero (thatis, blanks). These values are established by modeling theprecision and establishing the recovery/bias over a range ofconcentrations, as well as by using a tolerance interval. Thecomplexities of the WDE procedure may appear daunting, butthe additional considerations are necessary if meaningfullyestimates of the actual detection capabilities of analyticalmethods are to be made. The concepts are tractable by degreedchemists, and the use of the available ASTM DQCALCExcel-based software makes the data analysis and limit deter-minations easy.1.4 A within-laboratory detection estimate is useful incharacterizing the concentration below which a method, for ananalyte, as implemented in a specific laboratory, does not (withhigh confidence) discriminate the presence of the analyte fromthat of the absence of an analyte. As such an estimator, theWDE Standard (and the WDE and WCL values producedthrough its application) are useful where a trace-analysistesting method needs to be used.2. Referenced Documents2.1 ASTM Standards:2D1129 Terminology Relating to WaterD6091 Practice for 99 %/95 % Interlaboratory DetectionEstimate (IDE) for Analytical Methods with NegligibleCalibration ErrorD7510 Practice for Performing Detection and QuantitationEstimation and Data Assessment Utilizing DQCALCSoftware, based onASTM Practices D6091 and D6512 ofCommittee D19 on WaterE1763 Guide for Interpretation and Use of Results fromInterlaboratory Testing of Chemical Analysis Methods3. Terminology3.1 Definitions—For definitions of terms used in thispractice, refer to Terminology D1129.3.2 Definitions of Terms Specific to This Standard:3.2.1 99 % ⁄95 % Within-laboratory Detection Estimate,n—(99 % ⁄95 % WDE, also denoted LD for Limit of Detection,analogous to Currie (1)3The lowest concentration at whichthere is 90 % confidence that a single measurement from thelaboratory studied will have a true detection probability of atleast 95 % and a true non-detection probability of at least 99 %.3.2.2 Probability of False Detection (α), n—The within-laboratory false-positive probability that a single measurementof a blank sample will result in a detection; see Fig. 1.3.2.2.1 Discussion—This probability is often referred to asthe Type-1-error probability; it depends on the analyte, mea-surement system, analytical method, matrix, analyst, andmeasurement (recovery) threshold (measurement criticalvalue) used to decide whether detection has occurred.3.2.3 Probability of True Non-detection (1-α), n—Thewithin-laboratory true-negative probability that a single mea-surement of a blank sample will result in a non-detection.3.2.3.1 Discussion—This concept is the complement of theprobability of false detection. (See Fig. 1) This probability alsodepends on the analyte, measurement system, analyticalmethod, matrix, analyst, and response threshold.3.2.4 Probability of True Detection (1-β or 1-β(T)), n—Thewithin-laboratory probability that a single measurement of asample containing a nonzero analyte concentration, T, willresult in a detection; see Fig. 1.3.2.4.1 Discussion—This probability: 1) is often referred toas statistical power or the power of detection, 2) dependsexplicitly on the concentration (T), and 3) depends implicitlyon the analyte, measurement system, analytical method,matrix, analyst, and critical value for detection.3.2.5 Probability of False Non-detection (β or β(T)), n—Thewithin-laboratory false-negative probability that a single mea-surement of a sample containing a nonzero analyteconcentration, T, will result in a non-detection.3.2.5.1 Discussion—This concept is the complement of theprobability of true detection. (See Fig. 1.) This probabilityfunction: 1) is often referred to as the Type-2-error probabilityfunction, 2) depends explicitly on the concentration (T), and 3)2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.FIG. 1 Normal Distribution of Zero Concentration (without bias), Low Concentration (near zero) and Simplest Case of Reliable DetectionD7782 − 132depends implicitly on the analyte, measurement system, ana-lytical method, matrix, analyst, and critical value for detection.3.2.6 Detection Limit (DL) or Limit of Detection (LD),n—For the studied laboratory, a numerical value, expressed inphysical units or proportion, intended to represent the lowestlevel of reliable detection (that is, a level that can be discrimi-nated from zero with high probability, while simultaneouslyallowing high probability of non-detection when blank samplesare measured).3.2.7 Censored Measurement, n—Ameasurement that is notreported numerically or reported missing, but reported as anondetect or a less-than (for example, “less than 0.1 ppb”).3.2.7.1 Discussion—A non-zero report means that ameasurement-system algorithm determined that the measure-ment should not be reported numerically because: 1)itwasconsidered insufficiently precise or insufficiently unbiased, or2) the identification of the analyte was suspect. A reported“less-than” may have the same meaning; however, such areport also implies (perhaps erroneously) that any concentra-tion greater than or equal to the accompanying value (forexample, 0.1 ppb) can be measured and will be reportednumerically.3.2.8 100(1-γ) %—Confidence Statistical Tolerance Limitfor 100(1-δ) % of a Population (also known as a One-SidedStatistical Tolerance Interval), n—A statistically determinedlimit that will, with 100(1-γ) % confidence, exceed (or fallbelow) 100(1-δ) % of the population (that is, the 100(1-δ)%quantile). See Hahn and Meeker (2) for further explanation andtables of values.3.3 Acronyms:3.3.1 ILSD—Intralaboratory standard deviation3.3.2 WCL3.3.3 WDE3.3.4 YC3.3.5 YD4. Summary of Practice4.1 Data representative of the laboratory, method, andmedia at multiple (at least five) concentrations of the analyte,covering the range from zero (or near zero) to at or above thelevel of expected quantitation, are generated. The fundamentalassumption is that the media tested, the concentrations tested,and the protocols followed are representative of the written testmethod as implemented in the laboratory. The WDE compu-tations must be based on retained data (after optional outlierremoval) from at least six independent measurements at aminimum of five concentrations.4.2 The relationship between the within-laboratory mea-surement standard deviation and the true concentration isestablished by evaluating a series of potentially appropriatemodels, from simplest to most complex (that is, constant,straight-line, hybrid, and exponential). This evaluation ofmodels includes statistical significance and residual analysis.Asingle model (selected by the user, based on statistical best-fit,visual review of fit and residuals, and judgment) is then used topredict within-laboratory measurement standard deviation atany true concentration.4.3 If the within-laboratory standard deviation is notconstant, weights must be generated for fitting the true versusmeasured concentration relationship (that is, the straight-linerelationship between measured concentration and trueconcentration, known as the mean-recovery relationship), us-ing weighted least squares; software such as DQCALC will dothis modeling. For constant standard deviation, ordinary least-squares is used to fit the mean-recovery relationship. Thetrue-versus-measured linear fit is evaluated for statistical sig-nificance and behavior of the residuals.4.4 The modeled within-laboratory standard deviation atzero concentration is used to compute YC, the measuredconcentration that (with 90% confidence) 99 % of sampleswith true concentrations of zero will be less than (that is, lessthan the YC). The YD is computed to be the measuredconcentration that (with approximately 90 % confidence) willproduce measurements that will exceedYC at least 95 % of thetime; simultaneously when blank samples are measured, YDwill not exceed YC more than1%ofthetime (that is, will notexceed the reliable detection level, YD). In turn, the WCL andthe WDE are the true concentrations corresponding to YC andYD, respectively, from the recovery regression.4.5 While the application of this practice does require theuse of statistics, the complex calculations are performed by theadjunct software, DQCALC. Practice D6091 provides thecomplete mathematical basis for the calculations. Appendix X1provides an example WDE calculation.5. Significance and Use5.1 This practice can be used in a single laboratory for traceanalysis (that is, where: 1) there are concentrations near thelower limit of the method and 2) the measurements system’scapability to discriminate analyte presence from analyte ab-sence is of interest). In these testing situations, a reliableestimate of the minimum level at which there is confidence thatdetection of the analyte by the method represents true presenceof the analyte in the sample is key. Where within-laboratorydetection is important to data use, the WDE procedure shouldbe used to establish the within-laboratory detection capabilityfor each unique application of a method.5.2 When properly applied, theWDE procedure ensures thatthe 99 %⁄95 % WDE has the following properties:5.2.1 Routinely Achievable Detection—The laboratory isable to attain detection performance routinely, using studiedmeasurement systems, without extraordinary effort, and there-fore at reasonable cost. This property is needed for a detectionlimit to be practically useful while scientifically sound. Rep-resentative equipment and analysts must be inc