ASTM_E_2935_-_15.pdf

Designation:E293515An American National StandardStandard Practice forConducting Equivalence Testing in Laboratory Applications1This standard is issued under the fixed designation E2935;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 provides statistical methodology for con-ducting equivalence testing on numerical data from twosources to determine if their true means differ by no more thanpredetermined limits.1.2 Applications include(1)equivalence testing for biasagainst an accepted reference value,(2)determining equiva-lence of two test methods,test apparatus,instruments,reagentsources,or operators within a laboratory,and(3)equivalenceof two laboratories in a method transfer.1.3 The current guidance in this standard applies only toexperiments conducted on a single material.Guidance is givenfor determining the amount of data required for an equivalencetrial.1.4 The statistical methodology for determining equivalenceused is the two one-sided tests(TOST)procedure.The controlof risks associated with the equivalence decision is discussed.1.5 The values stated in SI units are to be regarded asstandard.No other units of measurement are included in thisstandard.1.6 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.Referenced Documents2.1 ASTM Standards:2E177 Practice for Use of the Terms Precision and Bias inASTM Test MethodsE456 Terminology Relating to Quality and StatisticsE2282 Guide for Defining the Test Result of a Test MethodE2586 Practice for Calculating and Using Basic Statistics3.Terminology3.1 DefinitionsSee Terminology E456 for a more exten-sive listing of statistical terms.3.1.1 accepted reference value,na value that serves as anagreed-upon reference for comparison,and which is derivedas:(1)a theoretical or established value,based on scientificprinciples,(2)an assigned or certified value,based on experi-mental work of some national or international organization,or(3)a consensus or certified value,based on collaborativeexperimental work under the auspices of a scientific orengineering group.E1773.1.2 bias,nthe difference between the expectation of thetest results and an accepted reference value.E1773.1.3 confidence interval,nan interval estimate L,Uwith the statistics L and U as limits for the parameter andwith confidence level 1 ,where Pr(L U)1.E25863.1.3.1 DiscussionThe confidence level,1 ,reflects theproportion of cases that the confidence interval L,U wouldcontain or cover the true parameter value in a series of repeatedrandom samples under identical conditions.Once L and U aregiven values,the resulting confidence interval either does ordoes not contain it.In this sense“confidence”applies not to theparticular interval but only to the long run proportion of caseswhen repeating the procedure many times.3.1.4 confidence level,nthe value,1 ,of the probabilityassociated with a confidence interval,often expressed as apercentage.E25863.1.4.1 Discussion is generally a small number.Confi-dence level is often 95%or 99%.3.1.5 confidence limit,neach of the limits,L and U,of aconfidence interval,or the limit of a one-sided confidenceinterval.E25863.1.6 degrees of freedom,nthe number of independentdata points minus the number of parameters that have to beestimated before calculating the variance.E25863.1.7 equivalence,ncondition that two population param-eters differ by no more than predetermined limits.3.1.8 intermediate precision conditions,nconditions un-der which test results are obtained with the same test methodusing test units or test specimens taken at random from a single1This test method is under the jurisdiction of ASTM Committee E11 on Qualityand Statistics and is the direct responsibility of Subcommittee E11.20 on TestMethod Evaluation and Quality Control.Current edition approved Oct.1,2015.Published October 2015.Originallyapproved in 2013.Last previous edition approved in 2014 as E2935 14.DOI:10.1520/E2935-15.2For referenced ASTM standards,visit the ASTM website,www.astm.org,orcontact ASTM Customer Service at serviceastm.org.For Annual Book of ASTMStandards volume information,refer to the standards Document Summary page onthe ASTM website.Copyright ASTM International,100 Barr Harbor Drive,PO Box C700,West Conshohocken,PA 19428-2959.United States1 quantity of material that is as nearly homogeneous as possible,and with changing conditions such as operator,measuringequipment,location within the laboratory,and time.E1773.1.9 mean,nof a population,average or expectedvalue of a characteristic in a population of a sa