1、Designation: D6708 131An American National StandardStandard Practice forStatistical Assessment and Improvement of ExpectedAgreement Between Two Test Methods that Purport toMeasure the Same Property of a Material1This standard is issued under the fixed designation D6708; the number immediately follow
2、ing 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.1NOTEEq X2.1 and Eq X2.2 in su
3、bsection X2.2 were corrected editorially in February 2015.1. Scope1.1 This practice covers statistical methodology for assess-ing the expected agreement between two standard test methodsthat purport to measure the same property of a material, anddeciding if a simple linear bias correction can furthe
4、r improvethe expected agreement. It is intended for use with resultscollected from an interlaboratory study meeting the require-ment of Practice D6300 or equivalent (for example, ISO 4259).The interlaboratory study must be conducted on at least tenmaterials that span the intersecting scopes of the t
5、est methods,and results must be obtained from at least six laboratories usingeach method.1.2 The statistical methodology is based on the premise thata bias correction will not be needed. In the absence of strongstatistical evidence that a bias correction would result in betteragreement between the t
6、wo methods, a bias correction is notmade. If a bias correction is required, then the parsimonyprinciple is followed whereby a simple correction is to befavored over a more complex one.NOTE 1Failure to adhere to the parsimony principle generally resultsin models that are over-fitted and do not perfor
7、m well in practice.1.3 The bias corrections of this practice are limited to aconstant correction, proportional correction or a linear (propor-tional + constant) correction.1.4 The bias-correction methods of this practice are methodsymmetric, in the sense that equivalent corrections are obtainedregar
8、dless of which method is bias-corrected to match theother.1.5 A methodology is presented for establishing the 95 %confidence limit (designated by this practice as the betweenmethods reproducibility) for the difference between two resultswhere each result is obtained by a different operator usingdiff
9、erent apparatus and each applying one of the two methodsX and Y on identical material, where one of the methods hasbeen appropriately bias-corrected in accordance with thispractice.NOTE 2In earlier versions of this standard practice, the term “cross-method reproducibility” was used in place of the t
10、erm “between methodsreproducibility.” The change was made because the “between methodsreproducibility” term is more intuitive and less confusing. It is importantto note that these two terms are synonymous and interchangeable with oneanother, especially in cases where the “cross-method reproducibilit
11、y” termwas subsequently referenced by name in methods where a D6708assessment was performed, before the change in terminology in thisstandard practice was adopted.NOTE 3Users are cautioned against applying the between methodsreproducibility as calculated from this practice to materials that aresigni
12、ficantly different in composition from those actually studied, as theability of this practice to detect and address sample-specific biases (see6.8) is dependent on the materials selected for the interlaboratory study.When sample-specific biases are present, the types and ranges of samplesmay need to
13、 be expanded significantly from the minimum of ten asspecified in this practice in order to obtain a more comprehensive andreliable 95 % confidence limits for between methods reproducibility thatadequately cover the range of sample specific biases for different types ofmaterials.1.6 This practice is
14、 intended for test methods which mea-sure quantitative (numerical) properties of petroleum or petro-leum products.1.7 The statistical methodology outlined in this practice isalso applicable for assessing the expected agreement betweenany two test methods that purport to measure the same propertyof a
15、 material, provided the results are obtained on the samecomparison sample set, the standard error associated with eachtest result is known, the sample set design meets the require-ment of this practice, and the statistical degree of freedom ofthe data set exceeds 30.1This practice is under the juris
16、diction of ASTM Committee D02 on PetroleumProducts, Liquid Fuels, and Lubricants and is the direct responsibility of Subcom-mittee D02.94 on Coordinating Subcommittee on Quality Assurance and Statistics.Current edition approved May 1, 2013. Published June 2013. Originallyapproved in 2001. Last previ
17、ous edition approved in 2008 as D6708 08. DOI:10.1520/D6708-13E01.Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States12. Referenced Documents2.1 ASTM Standards:2D5580 Test Method for Determination of Benzene, Toluene,Ethylbenzene, p/m-Xyl
18、ene, o-Xylene, C9and HeavierAromatics, and Total Aromatics in Finished Gasoline byGas ChromatographyD5769 Test Method for Determination of Benzene, Toluene,and Total Aromatics in Finished Gasolines by GasChromatography/Mass SpectrometryD6299 Practice for Applying Statistical Quality Assuranceand Con
19、trol Charting Techniques to Evaluate AnalyticalMeasurement System PerformanceD6300 Practice for Determination of Precision and BiasData for Use in Test Methods for Petroleum Products andLubricantsD7372 Guide for Analysis and Interpretation of ProficiencyTest Program Results2.2 ISO Standard:3ISO 4259
20、 Petroleum ProductsDetermination and applica-tion of precision data in relation to methods of test.3. Terminology3.1 Definitions:3.1.1 between-method bias, na quantitative expression forthe mathematical correction that can statistically improve thedegree of agreement between the expected values of t
21、wo testmethods which purport to measure the same property.3.1.2 between methods reproducibility (RXY), na quantita-tive expression of the random error associated with thedifference between two results obtained by different operatorsusing different apparatus and applying the two methods X andY, respe
22、ctively, each obtaining a single result on an identicaltest sample, when the methods have been assessed and anappropriate bias-correction has been applied in accordancewith this practice; it is defined as the 95 % confidence limit forthe difference between two such single and independentresults.3.1.
23、2.1 DiscussionAstatement of between methods repro-ducibility must include a description of any bias correctionused in accordance with this practice.3.1.2.2 DiscussionBetween methods reproducibility is ameaningful concept only if there are no statistically observablesample-specific relative biases be
24、tween the two methods, or ifsuch biases vary from one sample to another in such a way thatthey may be considered random effects. (see 6.7.)3.1.3 closeness sum of squares (CSS), na statistic used toquantify the degree of agreement between the results from twotest methods after bias-correction using t
25、he methodology ofthis practice.3.1.4 total sum of squares (TSS), na statistic used toquantify the information content from the inter-laboratorystudy in terms of total variation of sample means relative to thestandard error of each sample mean.3.2 Symbols:X,Y = single X-method and Y-method results, r
26、e-spectivelyXijk,Yijk= single results from the X-method andY-method round robins, respectivelyXi,Yi= means of results on the ithround robinsampleS = the number of samples in the round robinLXi,LYi= the numbers of laboratories that returnedresults on the ithround robin sampleRX,RY= the reproducibilit
27、ies of the X- and Y-methods, respectivelysRXi,sRYi= the reproducibility standard deviations,evaluated at the means of the ithround robinsamplesrXi,srYi= the repeatability standard deviations, evalu-ated at the means of the ithround robinsamplesXi,sYi= standard errors of the means ithround robinsampl
28、eX,Y= the weighted means of round robins (acrosssamples)xi,yi= deviations of the means of the ithround robinsample results from Xand Y, respectively.TSSX, TSSY= total sums of squares, around Xand YF = a ratio for comparing variances; notuniquemore than one usevX,vY= the degrees of freedom for reprod
29、ucibilityvariances from the round robinswi= weight associated with the difference be-tween mean results (or corrected mean re-sults) from the ithround robin sampleCSS = weighted sum of squared differences be-tween (possibly corrected) mean results fromthe round robina,b = parameters of a linear corr
30、ection: Y= a + bXt1,t2= ratios for assessing reductions in sums ofsquaresRXY= estimate of between methods reproducibilityY= Y-method value predicted from X-methodresultYi= ithround robin sample Y-method mean, pre-dicted from corresponding X-method meani= standardized difference between Yiand Yi.LX,L
31、Y= harmonic mean numbers of laboratories sub-mitting results on round robin samples, by X-and Y- methods, respectivelyRXY= estimate of between methods reproducibility,computed from an X-method result only4. Summary of Practice4.1 Precisions of the two methods are quantified usinginter-laboratory stu
32、dies meeting the requirements of PracticeD6300 or equivalent, using at least ten samples in common thatspan the intersecting scopes of the methods. The arithmetic2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book
33、of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 10036.D6708 1312means of the results for each common sample obtained by eachmethod are calculated.
34、 Estimates of the standard errors of thesemeans are computed.NOTE 4For established standard test methods, new precision studiesgenerally will be required in order to meet the common sample require-ment.NOTE 5Both test methods do not need to be run by the samelaboratory. If they are, care should be t
35、aken to ensure the independent testresult requirement of Practice D6300 is met (for example, by double-blindtesting of samples in random order).4.2 Weighted sums of squares are computed for the totalvariation of the mean results across all common samples foreach method. These sums of squares are ass
36、essed against thestandard errors of the mean results for each method to ensurethat the samples are sufficiently varied before continuing withthe practice.4.3 The closeness of agreement of the mean results by eachmethod is evaluated using appropriate weighted sums ofsquared differences. Such sums of
37、squares are computed fromthe data first with no bias correction, then with a constant biascorrection, then, when appropriate, with a proportionalcorrection, and finally with a linear (proportional + constant)correction.4.4 The weighted sums of squared differences for the linearcorrection is assessed
38、 against the total variation in the meanresults for both methods to ensure that there is sufficientcorrelation between the two methods.4.5 The most parsimonious bias correction is selected.4.6 The weighted sum of squares of differences, afterapplying the selected bias correction, is assessed to dete
39、rminewhether additional unexplained sources of variation remain inthe residual (that is, the individual Yiminus bias-corrected Xi)data. Any remaining, unexplained variation is attributed tosample-specific biases (also known as method-materialinteractions, or matrix effects). In the absence of sample
40、-specific biases, the between methods reproducibility is esti-mated.4.7 If sample-specific biases are present, the residuals (thatis, the individual Yiminus bias-corrected Xi) are tested forrandomness. If they are found to be consistent with a random-effects model, then their contribution to the bet
41、ween methodsreproducibility is estimated, and accumulated into an all-encompassing between methods reproducibility estimate.4.8 Refer to Fig. 1 for a simplified flow diagram of theprocess described in this practice.5. Significance and Use5.1 This practice can be used to determine if a constant,propo
42、rtional, or linear bias correction can improve the degreeof agreement between two methods that purport to measure thesame property of a material.5.2 The bias correction developed in this practice can beapplied to a single result (X) obtained from one test method(method X) to obtain a predicted resul
43、t (Y) for the other testmethod (method Y).NOTE 6Users are cautioned to ensure that Yis within the scope ofmethod Y before its use.5.3 The between methods reproducibility established by thispractice can be used to construct an interval around Ythatwould contain the result of test method Y, if it were
44、 conducted,with about 95 % confidence.5.4 This practice can be used to guide commercial agree-ments and product disposition decisions involving test methodsthat have been evaluated relative to each other in accordancewith this practice.6. ProcedureNOTE 7For an in-depth statistical discussion of the
45、methodology usedin this section, see Appendix X1. For a worked example, see AppendixX2.6.1 Calculate sample means and standard errors from Prac-tice D6300 results.6.1.1 The process of applying Practice D6300 to the datamay involve elimination of some results as outliers, and it mayalso involve apply
46、ing a transformation to the data. For thispractice, compute the mean results from data that have notbeen transformed, but with outliers removed in accordancewith Practice D6300. The precision estimates from PracticeD6300 are used to estimate the standard errors of these means.6.1.2 Compute the means
47、 as follows:6.1.2.1 Let Xijkrepresent the kthresult on the ithcommonmaterial by the jthlab in the round robin for method X.Similarly for Yijk. (The ithmaterial is the same for both roundrobins, but the jthlab in one round robin is not necessarily thesame lab as the jthlab in the other round robin.)
48、Let nXijbe thenumber of results on the ithmaterial from the jthX-method lab,after removing outliers that is, the number of results in cell (i,j). Let LXibe the number of laboratories in the X-method roundrobin that have at least one result on the ithmaterial remainingin the data set, after removal o
49、f outliers. Let S be the totalnumber of materials common to both round robins.6.1.2.2 The mean X-method result for the ithmaterial is:Xi51Lxi(j(kXijknXij(1)where, Xiis the average of the cell averages on the ithmaterial by method X.6.1.2.3 Similarly, the mean Y-method result for the ithmaterial is:Yi51LYi(j(kYijknYij(2)6.1.3 The standard errors (standard deviations of the meansof the results) are computed as follows:6.1.3.1 If sRXiis the estimated reproducibility standarddeviation from the X-method round robin, and srXiis theestimated repeatibility
