ASTM_E_178_-_08.pdf

Designation:E17808An 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.1.Scope1.1 This practice covers outlying observations in samplesand how to test the statistical significance of them.An outlyingobservation,or“outlier,”is one that appears to deviate mark-edly from other members of the sample in which it occurs.Inthis connection,the following two alternatives are of interest:1.1.1 An outlying observation may 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.1.1.2 On the other hand,an outlying observation may be theresult of gross deviation from prescribed experimental proce-dure or an error in calculating or recording the numerical value.In such cases,it may be desirable to institute an investigationto ascertain the reason for the aberrant value.The observationmay even actually be rejected as a result of the investigation,though not necessarily so.At any rate,in subsequent dataanalysis the outlier or outliers will be recognized as probablybeing from a different population than that of the other samplevalues.1.2 It is our purpose here to provide statistical rules that willlead the experimenter almost unerringly to look for causes ofoutliers when they really exist,and hence to decide whetheralternative 1.1.1 above,is not the more plausible hypothesis toaccept,as compared to alternative 1.1.2,in order that the mostappropriate action in further data analysis may be taken.Theprocedures covered herein apply primarily to the simplest kindof experimental data,that is,replicate measurements of someproperty of a given material,or observations in a supposedlysingle random sample.Nevertheless,the tests suggested docover a wide enough range of cases in practice to have broadutility.2.Referenced Documents2.1 ASTM Standards:2E456 Terminology Relating to Quality and Statistics3.Terminology3.1 Definitions:The terminology defined in TerminologyE456 applies to this standard unless modified herein.3.1.1 outliersee outlying observation.3.1.2 outlying observation,nan observation that appearsto deviate markedly in value from other members of the samplein which it appears.4.Significance and Use4.1 When the experimenter is clearly aware that a grossdeviation from prescribed experimental procedure has takenplace,the resultant observation should be discarded,whether ornot it agrees with the rest of the data and without recourse tostatistical tests for outliers.If a reliable correction procedure,for example,for temperature,is available,the observation maysometimes be corrected and retained.4.2 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 aclear-cut decision to be made.In doubtful cases the experi-menters judgment will have considerable influence.When theexperimenter cannot identify abnormal conditions,he should atleast report the discordant values and indicate to what extentthey have been used in the analysis of the data.4.3 Thus,for purposes of orientation relative to the over-allproblem of experimentation,our position on the matter ofscreening samples for outlying observations is precisely thefollowing:4.3.1 Physical Reason Known or Discovered for Outlier(s):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 Oct.1,2008.Published November 2008.Originallyapproved in 1961.Last previous edition approved in 2002 as E178 02.DOI:10.1520/E0178-08.2For 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 4.3.1.1 Reject observation(s).4.3.1.2 Correct observation(s)on physical grounds.4.3.1.3 Reject it(them)and possibly take additional obser-vation(s).4.3.2 Physical Reason UnknownUse Statistical Test:4.3.2.1 Reject observation(s).4.3.2.2 Correct observation(s)statistically.4.3.2.3 Reject it(them)and possibly take additional obser-vation(s).4.3.2.4 Employ truncated-sample theory for censored obser-vations.4.4 The statistical test may always be used to support ajudgment that a physical reason does actually exist for