ASTM_E_178_-_16a.pdf

Designation:E17816aAn American National StandardStandard Practice forDealing With Outlying Observations1This standard is issued under the fixed designation E178;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.NoteCorrections were made to Table 2 and the year date was changed on Sept.7,2016.1.Scope1.1 This practice covers outlying observations in samplesand how to test the statistical significance of outliers.1.2 The system of units for this standard is not specified.Dimensional quantities in the standard are presented only asillustrations of calculation methods.The examples are notbinding on products or test methods treated.1.3 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 requirements prior to use.2.Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and StatisticsE2586 Practice for Calculating and Using Basic Statistics3.Terminology3.1 DefinitionsThe terminology defined in TerminologyE456 applies to this standard unless modified herein.3.1.1 order statistic x(k),nvalue of the kth observed valuein a sample after sorting by order of magnitude.E25863.1.1.1 DiscussionIn this practice,xkis used to denoteorder statistics in place of x(k),to simplify the notation.3.1.2 outliersee outlying observation.3.1.3 outlying observation,nan extreme observation ineither direction that appears to deviate markedly in value fromother members of the sample in which it appears.4.Significance and Use4.1 An outlying observation,or“outlier,”is an extreme onein either direction that appears to deviate markedly from othermembers of the sample in which it occurs.4.2 Statistical rules test the null hypothesis of no outliersagainst the alternative of one or more actual outliers.Theprocedures covered were developed primarily to apply to thesimplest kind of experimental data,that is,replicate measure-ments of some property of a given material or observations ina supposedly random sample.4.3 A statistical test may be used to support a judgment thata physical reason does actually exist for an outlier,or thestatistical criterion may be used routinely as a basis to initiateaction to find a physical cause.5.Procedure5.1 In dealing with an outlier,the following alternativesshould be considered:5.1.1 An outlying observation might be the result of grossdeviation from prescribed experimental procedure or an errorin calculating or recording the numerical value.When theexperimenter is clearly aware that a deviation from prescribedexperimental procedure has taken place,the resultant observa-tion should be discarded,whether or not it agrees with the restof the data and without recourse to statistical tests for outliers.If a reliable correction procedure is available,the observationmay sometimes be corrected and retained.5.1.2 An outlying observation might be merely an extrememanifestation of the random variability inherent in the data.Ifthis is true,the value should be retained and processed in thesame manner as the other observations in the sample.Trans-formation of data or using methods of data analysis designedfor a non-normal distribution might be appropriate.5.1.3 Test units that give outlying observations might be ofspecial interest.If this is true,once identified they should besegregated for more detailed study.5.2 In many cases,evidence for deviation from prescribedprocedure will consist primarily of the discordant value itself.In such cases it is advisable to adopt a cautious attitude.Use ofone of the criteria discussed below will sometimes permit aclearcut decision to be made.1This practice is under the jurisdiction ofASTM Committee E11 on Quality andStatistics and is the direct responsibility of Subcommittee E11.10 on Sampling/Statistics.Current edition approved Sept.7,2016.Published September 2016.Originallyapproved in 1961.Last previous edition approved in 2016 as E178 16.DOI:10.1520/E0178-16A.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 5.2.1 When the experimenter cannot identify abnormalconditions,he should report the discordant values and indicateto what extent they have been used in the analysis of the data.5.3 Thus,as part of the over-all process of experimentation,the process of screening samples for outlying observations andacting on them is the following:5.3.1 Physical