1、ICS 13.060.50Deutsche Einheitsverfahren zur Wasser-, Abwasser- undSchlammuntersuchung Allgemeine Angaben (Gruppe A) Teil 71: Gleichwertigkeit von zwei Analysenverfahrenaufgrund des Vergleiches von Analysenergebnissen undderen statistischer Auswertung Vorgehensweise frquantitative Merkmale mit kontin
2、uierlichem Wertespektrum (A 71)In keeping with current practice in standards published by the International Organization for Standardization(ISO), a comma has been used throughout as the decimal marker.Ref. No. DIN 38402-71 : 2002-11English price group 11 Sales No. 011104.04DEUTSCHE NORM November 20
3、02 No part of this translation may be reproduced without the prior permission ofDIN Deutsches Institut fr Normung e.V., Berlin. Beuth Verlag GmbH, 10772 Berlin, Germany,has the exclusive right of sale for German Standards (DIN-Normen).Translation by DIN-Sprachendienst.In case of doubt, the German-la
4、nguage original should be consulted as the authoritative text.German standard methods for the examination of water, waste water and sludgeGeneral information (group A)Procedure for verifying the equivalence of two analytical methods involvingquantitative characteristics with a continuous set of valu
5、es (A 71)Document comprises 22 pages.SupersedesMarch 1987 edition.38402-71ForewordThis standard has been jointly prepared by the Normenausschuss Wasserwesen (Water Practice StandardsCommittee) and the Wasserchemische Gesellschaft of the Gesellschaft Deutscher Chemiker (German Chem-ists Society) (see
6、 Explanatory notes).Expert assistance and specialized laboratories will be required to perform the analyses specified in thisstandard. Any existing safety instructions are to be observed.Depending on the objective of the analysis, a check shall be made on a case-by-case basis as to whetherand to wha
7、t extent additional boundary conditions will have to be specified.ContentsPageForeword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8、 . . . . . . . . 21 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Normative references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Concepts . . . . . . . . . . . . . . . . . . . . . .
9、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Designation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Verif
10、ying equivalence of results for samples of the same matrix . . . . . . . 47 Verifying equivalence of results for samples of different matrices . . . . . . 68 Test report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Appendix A: Flowcharts . .
11、. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Appendix B: Statistical tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Appendix C: Example of software validation . . . . . . . . . . . . . . . . . . . . . . . . . . 15Explanator
12、y notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Page 2DIN 38402-71 : 2002-11This standard differs from the March 1987 edition as follows:a) the terminology has been updated;b) the procedure has been simplified by omitting the standard additio
13、n method;c) the earlier procedure for samples of the same matrix has been supplemented by one for samples ofdifferent matrices;d) the standard has been editorially revised.Previous editionDIN 38402-71: 1987-03.IntroductionSince analytical results are subject to random or systematic errors, different
14、 analytical methods may yieldresults that differ to a greater or lesser extent. If it is decided to use two different methods as alternatives, itwill therefore be necessary to ensure that they yield equivalent results.1 ScopeThis standard specifies a method for verifying the equivalence of results o
15、btained for quantitative water analysisparameters using two different methods. The method is intended to be used for comparing reference methodswith alternative methods or with modified reference methods. However, it is also suitable for comparing twoalternative methods or two modified reference met
16、hods directly. In the former case, the more customarymethod shall be used as the reference method.The standard covers two methods, the one being designed to verify the equivalence of two analytical methodsfor samples of the same matrix (see clause 6) and the other for samples of different matrices (
17、see clause 7).2 Normative referencesThis standard incorporates, by dated or undated reference, provisions from other publications. These norma-tive references are cited at the appropriate places in the text, and the titles of the publications are listed below.For dated references, subsequent amendme
18、nts to or revisions of any of these publications apply to thisstandard only when incorporated in it by amendment or revision. For undated references, the latest edition ofthe publication referred to applies.DIN 38402-51 German standard methods for the examination of water, waste water and sludge Gen
19、eralinformation (group A) Calibration of analytical methods, evaluation of analytical resultsand linear calibration functions used to determine performance characteristics of analyti-cal methods (A 51)DIN EN 1189 Water quality Determination of phosphorus by the ammonium molybdate spectrometricmethod
20、DIN EN ISO 11885 Water quality Determination of 33 elements by inductively coupled plasma atomic emis-sion spectrometry (ISO 11885 : 1996)ISO 8466-2 : 1993 Water quality Calibration and evaluation of analytical methods and estimation of perfor-mance characteristics Part 2: Calibration strategy for n
21、on-linear second-order calibra-tion functions1 Verordnung zur Novellierung der Trinkwasserverordnung (German Regulation amending the GermanDrinking Water Regulation), as of 21 May 2001, BGBl. (German Federal Law Gazette) I, 2001, No. 24,pp. 9599803 Concepts3.1 EquivalenceThe ability of two analytica
22、l methods to yield results that do not differ by more than the chosen statisticaluncertainty.NOTE: Two analytical methods may be deemed equivalent if comparison by the procedure described in thisstandard meets the given requirements.3.2 Quantitative characteristic with continuous set of valuesParame
23、ters that can be determined quantitatively and for which continuous sets of values and not only discretevalues are obtained.3.3 Reference methodA standardized method, required by law or regulation, specified for determining a certain parameter.Page 3DIN 38402-71 : 2002-113.4 Modified reference metho
24、dReference method involving slight modifications (e.g. in the required volumes, equipment dimensions, times,temperatures, etc.).3.5 Comparison methodAny analytical method (alternative method or modified reference method) whose equivalence with the referencemethod is to be checked.3.6 Alternative met
25、hodAny analytical method to be checked for equivalence as an alternative to the specified reference method.3.7 Outlier value pairA value pair deviating markedly from the regression line or exhibiting a conspicuously large difference.4 Symbolsa Intercept of regression lineb Slope of regression lineDi
26、Difference in the analytical results for a value pairDMean of differences (bias)D* Difference suspected of being an outlierf Number of degrees of freedomfRNumber of degrees of freedom for reference methodfVNumber of degrees of freedom for comparison methodn Number of replicate measurementsN Number o
27、f value pairsNRNumber of analytical results for reference methodNVNumber of analytical results for comparison methodP Statistical probability (significance level)PG Test valueQiRatio of pairs of results for reference method and comparison methodQMean of QiratiosQ* Ratio Q suspected of being an outli
28、ers Standard deviation of results of a series of measurements or common estimate for the standard deviationof value pairs (xi, yi)sdMean standard deviation for two measurement seriessDStandard deviation of differencessDrelRelative precisionsQStandard deviation of ratio QisRStandard deviation of resu
29、lts for reference methodsVStandard deviation of results for comparison methodsxStandard deviation of reference valuessyStandard deviation of comparison valuessxyEstimate of covariance of measured values xiand yiVRCoefficient of variation of results for reference methodVVCoefficient of variation of r
30、esults for comparison methodVxoCoefficient of variation of the procedure for method as in DIN 38402-51 or ISO 8466-2VxoRCoefficient of variation for reference methodVxoVCoefficient of variation for comparison methodxMean of measured values or of reference valuesxiIndividual result for reference meth
31、od for regression analysis or difference methodx* Individual value suspected of being an outlierxRiIndividual result for reference methodxViIndividual result for comparison methodxRMean of measured values of a reference method measurement seriesPage 4DIN 38402-71 : 2002-11xVMean of measured values o
32、f a comparison method measurement seriesyiIndividual result for comparison method for regression analysis or difference methodyMean of comparison valuesX2Test value for x2testrMN,PTabular value for rM (for f = N degrees of freedom and significance level P)tf,PTabular value of t-distribution (for f =
33、 N 1 degrees of freedom and significance level P)FfV,fR,PTabular value of F-distribution (for fV= fR= N 2 degrees of freedom and significance level P)5 DesignationDesignation of the method of verifying the equivalence of two analytical methods involving quantitative char-acteristics with a continuou
34、s set of values (A 71):Method DIN 38402 A 716 Verifying equivalence of results for samples of the same matrix6.1 GeneralThis method makes possible a simplified comparison of results obtained by two different analytical methodsprovided that the precision of results of both methods does not differ sig
35、nificantly in a matrix-free solution. Theequivalence of results shall be verified with samples by the mean t-test using the variance F-test. The analysesshall be carried out within a short time in the same laboratory or in two laboratories using different methods.The equivalence shall be checked usi
36、ng a sample homogenized and divided shortly before the analyses.6.2 Comparison of dispersion in a matrix-free solution for methods capable of calibrationThe dispersion of the calibration data for the two methods (an equal number in both methods) shall be describedusing the coefficients of variation
37、of the procedure (Vxo), as specified in DIN 38402-51 or DIN ISO 8466-2. Datafrom the description of the reference method, or, if the latter are not available, current data or new data shallbe used to compare the Vxovalues. The comparison shall be made by the variance F-test using equation (1):(VxoV)
38、2PG = (1)(VxoR)2The test value, PG, so obtained shall be compared with the corresponding tabular value for the F-distribution(with fR= fV= N 2 and P = 99%). The variance F-test shall only be performed if the coefficient of variationfor the comparison method is greater than that for the reference met
39、hod. If the test value is greater than thetabular value, this is indicative of a significant difference between the methods and there is thus no questionof reproducibility because of the coefficients of variation of the method. If it is less than or equal to the tabularvalue, there is no significant
40、 difference and therefore the dispersion in results can be deemed equivalent.6.3 Comparison of dispersion in a matrix-free solution for methods incapable of calibrationFor methods incapable of calibration, the dispersion in results shall be compared by means of a precision testusing standard solutio
41、ns as specified in the reference methods. To compare the coefficients of variation, useshall be made of data from the description of the reference method or, if the latter are not available, current dataor new data. The precision test is to be performed using at least five outlier-free individual da
42、ta in each caseof one concentration level by means of the variance F-test. For this purpose, the test value, PG, shall bedetermined using equation (2):(VV)2PG = (2)(VR)2and compared with the corresponding tabular value of the F-distribution (with fR= fV= N 1 and P = 99%).This test shall only be perf
43、ormed if the coefficient of variation of the comparison method is greater than thatof the reference method. If the test value is greater than the tabular value, this is indicative of a significantdifference and there is thus no question of reproducibility because of the coefficients of variation. If
44、 it is lessthan or equal to the tabular value, the difference is not significant and therefore the dispersion in results canbe deemed equivalent.NOTE: The dispersion for a method capable of calibration shall be compared with that for a method incapableof calibration in the same way as the comparison
45、 of the dispersion for two methods incapable of calibration.Page 5DIN 38402-71 : 2002-116.4 Verifying equivalence of results for samples using the mean t-test6.4.1 GeneralSubsamples of a sample representative of the particular application shall always be analysed at least insextuplicate under repeat
46、ability conditions using two methods to be compared.6.4.2 Outlier testThe results of the two analytical series shall be subjected to a Grubbs outlier test, one outlier being allowablefor each series and method. The test value shall be calculated using equation (3):|x* x|PG = (3)sand compared with th
47、e corresponding tabular value rM (with f = N and P = 95%). If it is greater than the tabularvalue, the checked analytical value shall be discarded as an outlier, and the mean and standard deviation beingrecalculated from the remainder of the data set. Other individual data suspected of being outlier
48、s shall bechecked by the method described, and if further outliers are found, the data set shall be discarded and a freshset used to check for equivalence.6.4.3 Test for homogeneity of variancesThe variances of the two analytical series shall be compared with one another using the variance F-test. F
49、or thispurpose, the test value shall be determined using equation (4):(sV)2PG = (4)(sR)2and compared with the corresponding tabular value of the F-distribution (with fV= NV 1, fR= NR 1 andP = 99%).If the test value is greater than the tabular value, this is indicative of a significant difference and there can beno question of reproducibility because of the existing variances. If it is less than or equal to the tabular value,there is no significant difference and the dispersion of results can be deemed equivalent.NOTE: For this test
