Designation:E1325−02(Reapproved2008)AnAmericanNationalStandardStandardTerminologyRelatingtoDesignofExperiments1ThisstandardisissuedunderthefixeddesignationE1325;thenumberimmediatelyfollowingthedesignationindicatestheyearoforiginaladoptionor,inthecaseofrevision,theyearoflastrevision.Anumberinparenthesesindicatestheyearoflastreapproval.Asuperscriptepsilon(´)indicatesaneditorialchangesincethelastrevisionorreapproval.1.Scope1.1Thisstandardincludesthosestatisticalitemsrelatedtotheareaofdesignofexperimentsforwhichstandarddefini-tionsappearsdesirable.2.ReferencedDocuments2.1ASTMStandards:2E456TerminologyRelatingtoQualityandStatistics3.SignificanceandUse3.1ThisstandardisasubsidiarytoTerminologyE456.3.2Itprovidesdefinitions,descriptions,discussion,andcomparisonofterms.4.Terminologyaliases,n—inafractionalfactorialdesign,twoormoreeffectswhichareestimatedbythesamecontrastandwhich,therefore,cannotbeestimatedseparately.DISCUSSION—(1)Thedeterminationofwhicheffectsina2nfactorialarealiasedcanbemadeoncethedefiningcontrast(inthecaseofahalfreplicate)ordefiningcontrasts(forafractionsmallerthan1⁄2)arestated.Thedefiningcontrastisthateffect(oreffects),usuallythoughttobeofnoconsequence,aboutwhichallinformationmaybesacrificedfortheexperiment.Anidentity,I,isequatedtothedefiningcontrast(ordefiningcontrasts)and,usingtheconversionthatA2=B2=C2=I,themultiplicationofthelettersonbothsidesoftheequationshowsthealiases.Intheexampleunderfractionalfactorialdesign,I=ABCD.Sothat:A=A2BCD=BCD,andAB=A2B2CD=CD.(2)Withalargenumberoffactors(andfactorialtreatmentcombi-nations)thesizeoftheexperimentcanbereducedto1⁄4,1⁄8,oringeneralto1⁄2ktoforma2n-kfractionalfactorial.(3)Thereexistgeneralizationsoftheabovetofactorialshavingmorethan2levels.balancedincompleteblockdesign(BIB),n—anincompleteblockdesigninwhicheachblockcontainsthesamenumberkofdifferentversionsfromthetversionsofasingleprincipalfactorarrangedsothateverypairofversionsoccurstogetherinthesamenumber,λ,ofblocksfromthebblocks.DISCUSSION—Thedesignim...
