Lecture Business statistics in practice (7/e): Chapter 12 - Bowerman, O'Connell, Murphree

Chapter 12 - Experimental design and analysis of variance. After mastering the material in this chapter, you will be able to: Explain the basic terminology and concepts of experimental design, compare several different population means by using a one-way analysis of variance, compare treatment effects and block effects by using a randomized block design.
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Lecture Business statistics in practice (7/e): Chapter 12 - Bowerman, OConnell, Murphree Chapter12 ExperimentalDesignandAnalysisof VarianceMcGrawHill/Irwin Copyright©2014byTheMcGrawHillCompanies,Inc.Allrightsreserved.ExperimentalDesignandAnalysisofVariance12.1 BasicConceptsofExperimentalDesign12.2 OneWayAnalysisofVariance12.3 TheRandomizedBlockDesign12.4 TwoWayAnalysisofVariance 122LO12-1: Explain thebasicterminology andconcepts ofexperimental design. 12.1BasicConceptsofExperimental Design Upuntilnow,wehaveconsideredonlytwo waysofcollectingandcomparingdata: ◦Usingindependentrandomsamples ◦Usingpaired(ormatched)samples Oftendataiscollectedastheresultofan experiment ◦Tosystematicallystudyhowoneormorefactors (variables)influencethevariablethatisbeing studied 123LO12-1 ExperimentalDesign#2 Inanexperiment,thereisstrictcontrolover thefactorscontributingtotheexperiment ◦Thevaluesorlevelsofthefactorsarecalled treatments  Forexample,intestingamedicaldrug,the experimentersdecidewhichparticipantsinthe testgetthedrugandwhichonesgettheplacebo, insteadofleavingthechoicetothesubjects Theobjectistocompareandestimatethe effectsofdifferenttreatmentsonthe responsevariable 124LO12-1 ExperimentalDesign#3 Thedifferenttreatmentsareassignedto objects(thetestsubjects)called experimentalunits ◦Whenatreatmentisappliedtomorethanone experimentalunit,thetreatmentisbeing “replicated” Adesignedexperimentisanexperiment wheretheanalystcontrolswhichtreatments areusedandhowtheyareappliedtothe experimentalunits 125LO12-2: Compareseveral differentpopulation 12.2OneWayAnalysisofVariancemeans by using a one-way analysis ofvariance.  Wanttostudytheeffectsofallptreatmentsona responsevariable ◦ Foreachtreatment,findthemeanandstandarddeviationof allpossiblevaluesoftheresponsevariablewhenusingthat treatment ◦Fortreatmenti,findtreatmentmeanµi  Onewayanalysisofvarianceestimatesand comparestheeffectsofthedifferenttreatmentson theresponsevariable ◦ Byestimatingandcomparingthetreatmentmeans µ1,µ2,…,µp ◦ Onewayanalysisofvariance,oronewayANOVA 126LO12-2 ANOVANotation  nidenotesthesizeofthesamplerandomlyselected fortreatmenti  xijisthejthvalueoftheresponsevariableusing treatmenti  iisaverageofthesampleofnivaluesfortreatment i ◦iisthepointestimateofthetreatmentmeanµi  siisthestandarddeviationofthesampleofnivalues fortreatmenti ◦ siisthepointestimateforthetreatment(population) standarddeviationσi 127LO12-3: Comparetreatment effects andblock effects by using a 12.3TheRandomizedBlockDesignrandomized blockdesign. Arandomizedblockdesigncomparesp treatments(forexample,production methods)oneachofbblocks(or experimentalunitsorsetsofunits;for example,machineoperators) Eachblockisusedexactlyoncetomeasure theeffectofeachandeverytreatment Theorderinwhicheachtreatmentis assignedtoablockshouldberandom 128LO12-3 TheRandomizedBlockDesignContinued Ageneralizationofthepaireddifference design;thisdesigncontrolsforvariabilityin experimentalunitsbycomparingeach treatmentonthesame(notindependent) experimentalunits Differencesinthetreatmentsarenothidden bydifferencesintheexperimentalunits(the blocks) 129LO12-3 RandomizedBlockDesign xij Thevalueoftheresponsevariablewhen blockjusestreatmenti i• Themeanofthebresponsevariableobserved whenusingtreatmenti(thetreatmentimean) •j Themeanofthepvaluesoftheresponse variablewhenusingblockj(theblockj mean) Themeanofalltheb•pvaluesoftheresponse variableobservedintheexperiment(the o ...