# ASTM D7729-12

Designation: D7729 − 12Standard Practice forDetermining and Expressing Precision of MeasurementResults, in the Analysis of Water, as Relative StandardDeviation, Utilizing DQCALC Software1This standard is issued under the fixed designation D7729; 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.1. Scope1.1 This Practice describes a procedure for developing agraphical model of relative standard deviation vs concentrationfor a analytical methods used in the analysis of water (methodsthat are subject to non-additive random errors) for the purposeof assigning a statement of noise or randomness to analyticalresults (commonly referred to as a precision statement), ineither a manual or an automated fashion.1.2 Data analysis and modeling is done with D19 AdjunctDQCALC (an Excel based tool).1.3 The values stated in SI units are to be regarded as thestandard. The values given in parentheses are for informationonly.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Introduction2.1 An understanding of the uncertainty associated withmeasurement results is necessary for evaluating the utility ofthose results. Without a reported uncertainty estimate, users ofmeasurement results are unable to determine if the data aresufficiently precise for any specific data use.2.2 Measurement Uncertainty is most generally understoodto be “a parameter characterizing the dispersion of the quantityvalues being attributed to a measurand” (from InternationalVocabulary of Metrology (VIM) 2.26). This definition can beimplemented as an expression (“uncertainty statement”) asso-ciated with an reported measurement that represents thestatistically based (TypeAestimate) dispersion of experimentalresults around a reported value.2.3 There is no universally agreed upon format or nomen-clature for uncertainty statements. The literature offers sugges-tions ranging from simple expressions of standard deviation or“fractional uncertainty” (standard deviation divided by re-ported result) to confidence intervals to detailed “uncertaintyreports”.2.4 In addition to the “random” errors encompassed in theideas expressed in 1.1 and 1.2, above, there are also “system-atic” errors, biases, that can be considered as part of uncer-tainty. The literature is not consistent on how unknown bias isconsidered in an uncertainty statement. For purposes of thisStandard, bias is assumed to have been corrected for orinsignificant in the reported results, and bias is not specificallyincorporated in the proposed uncertainty statement.2.5 For purposes of this Standard, the terms “MU”, uncer-tainty statement, or measurement uncertainty will be usedsynonymously to designate the expression accompanying mea-surement results for the purpose of assessing the utility of thoseresults.2.6 This Standard proposes the use of fractional uncertaintyor Relative Standard Deviation (RSD) as the expression ofMU.2.7 Traditionally, in the generation and publication of datarelated to the analysis of water, a continuous function (model)describing the relationship of uncertainty (as standard devia-tion) to concentration is not available. To compensate for thislack, discrete points bounding certain levels of uncertainty arecalculated, for example, “detection limits” (typically around33% RSD) and “quantitation limits” (often around 10% RSD).Results are flagged to indicate their relationship to one of theselimits. Alternatively, this Practice directs the creation of amodel of uncertainty (RSD vs concentration) which allowsassignment of a discrete uncertainty estimate to any resultvalue measured within the range of modeled data.2.8 This Practice is based on the use of the DQCALCsoftware that was developed to simplify the calculation of theIQE – Inter-laboratory Quantitation Estimate (D6512). ThisPractice is restricted to the development of an uncertaintymodel for the reporting of MU within a single laboratory. In1This 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 April 1, 2012. Published September 2012. DOI:10.1520/D7729–12.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1addition to providing an estimate of single-laboratory measure-ment uncertainty, the DQCALC software automatically calcu-lates LC – from Curie, equivalent to EPA’s MDL, and theASTM Detection Estimate for a single lab (this utilizes a “3sigma” tolerance interval rather than the standard confidenceinterval).2.9 This Practice provides the tools to allow a Laboratory toembed the RSD vs Concentration relationship into a suffi-ciently powerful Laboratory Information Management System(LIMS) resulting in the ability to automatically report MU withall data reported out of the LIMS for modeled parameters.2.10 The DQCALC Software is available from ASTM (seeStandard D7510).2.11 In addition, this Standard discusses the variables thatshould be considered for inclusion in the uncertainty modelingstudy.3. Referenced Documents3.1 ASTM Standards:2D6512 Practice for Interlaboratory Quantitation EstimateD7510 Practice for Performing Detection and QuantitationEstimation and Data Assessment Utilizing DQCALCSoftware, based on ASTM Practices D6091 and D6512 ofCommittee D19 on Water3.2 Other Standard:3International Vocabulary of Metrology Basic and GeneralConcepts and Associated Terms, VIM, 3rd edition, JCGM200:20084. Terminology4.1 Definitions:4.1.1 Measurement Uncertainty, n—in the analysis of water,a value representing the precision of a reported determination.4.1.2 in the analysis of water, a value representing theprecision of a reported determination, expressed as the relativestandard deviation of typical measurements of the same form.4.2 SymbolsIQE – Inter-laboratory Quantitation EstimateLIMS – Laboratory Information Management SystemMU – Measurement UncertaintyRSD – Relative Standard Deviation5. Summary of Practice5.1 The relationship between Relative Standard Deviationand concentration is modeled using a multi-replicate andmulti-level design and utilizing the curve fitting tools in theDQCALC software. The DQCALC software will return thecoefficients for the selected function/model of standard devia-tion against concentration. The general equations are given inthis Practice. From the equation, the appropriate standarddeviation for any concentration in the range represented in themodel study can be calculated. This can then be converted intoRSD, the recommended reporting format.5.2 The IQE Practice that forms the basis for this Practice,has the feature of correcting for recovery. Therefore, forpurposes of this Practice true concentrations, that is, concen-trations that have been “corrected” for recovery bias are used.Where a laboratory in use of its methods of testing does notcorrect resultant values, the calculated RSD will be marginallyhigher or lower, depending on the magnitude of the uncor-rected bias in the reported data. Where uncorrected bias is lessthan 10% of the magnitude of the result, the error in the RSDestimate may be considered insignificant.6. Sources of Imprecision6.1 When utilizing the result of a measurement to make abinary decision (yes/no, pass/fail, etc.) there is a risk of makinga false positive determination (saying a condition exists whenit does not) or a false negative determination (saying acondition does not exist when it does). The more precise theestimate of the measurement uncertainty of the result (thesmaller the relative standard deviation), the less chance there isof making such incorrect assessments.6.2 The most precise possible estimate of a result’s MUwould be obtained through replicate measurements done at thesame time as the initial measurement. (This would, of course,also give a more precise estimate of the measurement result –a mean with n 1). The greater the number of replicatesperformed, the better the estimate of MU. In practice, this levelof analytical work is rarely performed, unless there are direconsequences associated with the result.6.3 Under typical circumstances in analytical laboratories,uncertainty is not determined from replicates of real-worldsamples. An assumption (rarely tested) is made that theuncertainty of the measurements of standards of known (trace-able) concentration is comparable to the uncertainty of mea-surements on real world samples. It is well known that differentmatrices, especially matrices with suspended matter containingthe analyte, have much different measurement uncertaintiesand they are typically greater than that of measurements ontraceable standard solutions, but for pragmatic reasons this isoften ignored. This means uncertainty estimates determinedfrom standards run in replicate with the real world samplemeasurement, are estimates of uncertainty that are typicallymuch smaller (implying much better precision) than is war-ranted and are estimates of the method performance on idealsamples.6.4 But, again, under typical circumstances, replicate stan-dard determinations are not performed with each particular realworld sample measurement. They are typically performedacross different batches, different days, different operators, and,even across different laboratories. Each of these elements orvariables – batch, day, etc. – adds an extra component of“noise”, each increasing the magnitude of the uncertaintyestimate.6.5 Within each prescribed set of variables (given batch,day, operator, etc.), the replicate precision obtained is often2For 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.3Available from BIMP at http://www.bipm.org.D7729 − 122comparable. But, due to varying “conditions” (usually un-known and undeterminable) the mean result under each con-dition differs. This difference between mean results underdifferent conditions is what adds additional variability – extranoise – and increases the magnitude of the measurementuncertainty estimate. Essentially, as each new variable is addedto the uncertainty determination, biases become incorporatedas random noise.6.6 The net result of these assumptions and non-idealconditions of test during MU estimation is that the MU valueobtained and reported is itself uncertain, and the magnitude oferror in the MU estimate is difficult or impossible to determine.6.7 As a matter of practicality, even with the use ofstandards rather than real-world sample replicates and theinclusion of “extra” sources of noise, the MU estimates obtainusually bear a useful relationship to the analytical results theyare reported with, and provide a reasonable ballpark ofuncertainty for the data users.6.8 In utilizing this Practice to obtain MU estimates to bereported with real-world sample results, the user is cautioned tobe cognizant of these caveats in choosing what sources ofvariability - temporal, procedural, material, etc. – are to beincluded in the MU study design. Users will need to recognizethat estimates of MU that incorporate sources of variabilityinappropriate to the data use or exclude sources that areappropriate to the data use may produce uncertainties that aretypically smaller than would be most appropriate to the datause.7. Relative Standard Deviation vs. Concentration Models7.1 As explained in D7512 (IQE), the D19 approach toestablishing a relationship between standard deviation andconcentration involves generating independent measurementsat predetermined concentrations over the analytical range ofinterest, including down to zero concentration or the blank,where of interest.7.2 The standard deviations (and means) from the indepen-dent measurements at each concentration are calculated. Theseresults are corrected for bias. Four models of the function ofstandard deviation to true concentration are fitted. The modelwith the best fit is determined. The relationship of measuredconcentration to true concentration is established throughlinear regression. Least squares is used where the standarddeviation model selected was any model other than constant,for the other three models, the linear regression of true vsmeasured concentration is established using weighted leastsquares.7.3 The four models used for fitting standard deviation vstrue concentration are : constant, exponential, straight-line, andhybrid. Multiple statistical tools and graphs are presented tohelp the user decide which model is the best fit.7.4 It is the responsibility of the user to make the mostappropriate choice between models. The simplest model thatadequately represents the data over the range of interest for theintended use should be selected.8. Procedure8.1 Carry out a precision analysis study designed as de-scribed in D7512 (IQE). The study must have the followingcharacteristics:8.1.1 The study should have a minimum of 5 levels and 5replicates at each level. More levels and more replicatesproduce better estimates. One of the levels must be in near orin the range of detection, with analysis of an uncensored blankideal. Three of the levels should be at approximately 3, 7 and10 standard deviations of the instrument noise. The remainingtwo should be at the mid-range and undiluted maximum of theanalytical procedure. The goal is to best characterize theuncertainty (standard deviation) across the analytical range ofthe test method, with extra focus on the area of the relationshipwhere there is the most change (typically between 10% and30% relative standard deviation).8.1.2 Determine which analytical variables are appropriatefor inclusion in the study design.8.1.3 Conduct the study and tabulate the results. Individualmeasurements must be evaluated and if determined to beerroneous should be eliminated using an accepted,scientifically-based reasoning. Identification of potential out-lier for data evaluation and validation may be accomplishedusing statistical procedures, such as the optional one providedin the DQCALC software, or through visual examination of agraphical representation of the data.8.2 Tabulate the results as instructed in D7512(IQE) in anExcel spreadsheet. For this practice, the columns for Lab andBatch will contain only “1’s”. The exact format for the headersin the table are critical or the DQCALC program will notcomplete the data import.8.3 Import the data into DQCALC and complete the com-putation of the IQE, includin