1、Designation: D6708 16 An 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.1. Scope*1.1 This practice cov
3、ers 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 further improvethe expected agreement. It is intended for use with resultscollected from an i
4、nterlaboratory 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 test methods,and results must be obtained from at least six laboratories usingeach metho
5、d.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 two methods, a bias correction is notmade. If a bias correction is required, then the pa
6、rsimonyprinciple 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 perform well in practice.1.3 The bias corrections of this practice are limited to aconstant c
7、orrection, 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 obtainedregardless of which method is bias-corrected to match theother.1.5 A methodology is presente
8、d 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 usingdifferent apparatus and each applying one of the two methodsX and Y on identical material,
9、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 term “between methodsreproducibility.” The change was made because the “between methodsr
10、eproducibility” 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 reproducibility” termwas subsequently referenced by name in methods where a D6708assessment was perfo
11、rmed, 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 aresignificantly different in composition from those actually studied, as theability of this pr
12、actice 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 be expanded significantly from the minimum of ten asspecified in this practice in orde
13、r 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 intended for test methods which mea-sure quantitative (numerical) properties of petrol
14、eum 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 material, provided the results are obtained on the samecomparison sample set, the stan
15、dard 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 30.2. Referenced Documents2.1 ASTM Standards:2D5580 Test Method for Determination of Benzene, Toluene,Ethylbenzene, p/m-Xyl
16、ene, o-Xylene, C9and Heavier1This practice is under the jurisdiction 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 Jan. 1, 201
17、6. Published February 2016. Originallyapproved in 2001. Last previous edition approved in 2015 as D6708 15. DOI:10.1520/D6708-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume informati
18、on, refer to the standards Document Summary page onthe ASTM website.*A Summary of Changes section appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1Aromatics, and Total Aromatics in Finished Gasoline b
19、yGas ChromatographyD5769 Test Method for Determination of Benzene, Toluene,and Total Aromatics in Finished Gasolines by GasChromatography/Mass SpectrometryD6299 Practice for Applying Statistical Quality Assuranceand Control Charting Techniques to Evaluate AnalyticalMeasurement System PerformanceD630
20、0 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 Petroleum ProductsDetermination and applica-tion of precision data in relation t
21、o 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 two testmethods which purport to measure the same property.3.1.2 between methods r
22、eproducibility (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, respectively, each obtaining a single result on an identicaltest sample, when the meth
23、ods 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.3.1.2.1 DiscussionAstatement of between methods repro-ducibility must include a descr
24、iption 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 between the two methods, or ifsuch biases vary from one sample to another in such a
25、 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 the methodology ofthis practice.3.1.4 total sum of squares (TSS), na statistic use
26、d 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, re-spectivelyXijk,Yijk= single results from the X-method andY-method round robins,
27、 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 reproducibilities of the X- and Y-methods, respectivelysRXi,sRYi= the reproducibility standard
28、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 robinsampleX,Y= the weighted means of round robins (acrosssamples)xi,yi= deviations of the
29、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 reproducibilityvariances from the round robinswi= weight associated with the difference
30、 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 correction: Y= a + bXt1,t2= ratios for assessing reductions in sums ofsquaresRXY= est
31、imate 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,LY= harmonic mean numbers of laboratories sub-mitting results on round robin sampl
32、es, 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 studies meeting the requirements of PracticeD6300 or equivalent, using at least ten
33、samples in common thatspan the intersecting scopes of the methods. The arithmeticmeans of the results for each common sample obtained by eachmethod are calculated. Estimates of the standard errors of thesemeans are computed.NOTE 4For established standard test methods, new precision studiesgenerally
34、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 taken to ensure the independent test3Available from American National Standards Institute (ANSI), 25 W. 43rd St.,4th Floor, New York, NY 1
35、0036.D6708 162result 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 assessed against thestan
36、dard 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 squares are computed
37、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 against the total va
38、riation 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 determinewhether addition
39、al 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-specific biases, the
40、 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 between methodsreproduci
41、bility 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,proportional, or linear bi
42、as 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 result (Y) for the other t
43、estmethod (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 conducted,with about
44、 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.5.5 The magnitude of a statistically detectable bias isdirectly related to the uncert
45、ainties of the statistics from theexperimental study. These uncertainties are related to both thesize of the data set and the precision of the processes beingstudied. A large data set, or, highly precise test method(s), orboth, can reduce the uncertainties of experimental statistics tothe point wher
46、e the “statistically detectable” bias can become“trivially small,” or be considered of no practical consequencein the intended use of the test method under study. Therefore,users of this practice are advised to determine in advance as tothe magnitude of bias correction below which they wouldconsider
47、 it to be unnecessary, or, of no practical concern for theintended application prior to execution of this practice.NOTE 7It should be noted that the determination of this minimum biasof no practical concern is not a statistical decision, but rather, a subjectivedecision that is directly dependent on
48、 the application requirements of theusers.6. ProcedureNOTE 8For an in-depth statistical discussion of the 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 P
49、ractice D6300 to the datamay involve elimination of some results as outliers, and it mayalso involve applying 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 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 ithm
