STATISTICS FOR RESEARCH THIRD EDITION WILEYSERIESINPROBABILITYANDSTATISTICS EstablishedbyWALTERA.SHEWHARTandSAMUELS.WILKS Editors:DavidJ.Balding,NoelA.C.Cressie,NicholasI.Fisher, IainM.Johnstone,J.B.Kadane,LouiseM.Ryan,DavidW.Scott, AdrianF.M.Smith,JozefL.Teugels EditorsEmeriti:VicBarnett,J.StuartHunter,DavidG.Kendall Acompletelistofthetitlesinthisseriesappearsattheendofthisvolume. STATISTICS FOR RESEARCH THIRD EDITION Shirley Dowdy Stanley Weardon West Virginia University DepartmentofStatistics and ComputerScience Morgantown, WV Daniel Chilko West Virginia University DepartmentofStatistics and ComputerScience Morgantown, WV AJOHN WILEY& SONS, INC. PUBLICATION Thisbookisprintedonacid-freepaper. Copyright#2004byJohnWiley&Sons,Inc.,Hoboken,NewJersey.Allrightsreserved. PublishedsimultaneouslyinCanada. 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ISBN0-471-26735-X(cloth:acid-freepaper) 1.Mathematicalstatistics.I.Wearden,Stanley,1926–II.Chilko,DanielM.III.Title.IV.Series. QA276.D662003 519.5–dc21 2003053485 PrintedintheUnitedStatesofAmerica. 10 9 8 7 6 5 4 3 2 1 CONTENTS PrefacetotheThirdEdition ix PrefacetotheSecondEdition xiii PrefacetotheFirstEdition xv 1 TheRoleofStatistics 1 1.1 TheBasicStatisticalProcedure 1 1.2 TheScientificMethod 11 1.3 ExperimentalDataandSurveyData 19 1.4 ComputerUsage 20 ReviewExercises 21 SelectedReadings 22 2 Populations,Samples,andProbabilityDistributions 25 2.1 PopulationsandSamples 25 2.2 RandomSampling 27 2.3 LevelsofMeasurement 30 2.4 RandomVariablesandProbabilityDistributions 33 2.5 ExpectedValueandVarianceofaProbabilityDistribution 39 ReviewExercises 47 SelectedReadings 47 3 BinomialDistributions 49 3.1 TheNatureofBinomialDistributions 49 3.2 TestingHypotheses 59 3.3 Estimation 70 3.4 NonparametricStatistics:MedianTest 77 ReviewExercises 78 SelectedReadings 80 4 PoissonDistributions 81 4.1 TheNatureofPoissonDistributions 81 4.2 TestingHypotheses 84 4.3 Estimation 87 4.4 PoissonDistributionsandBinomialDistributions 90 ReviewExercises 93 SelectedReadings 94 v vi CONTENTS 5 Chi-SquareDistributions 95 5.1 TheNatureofChi-SquareDistributions 95 5.2 Goodness-of-FitTests 104 5.3 ContingencyTableAnalysis 108 5.4 RelativeRisksandOddsRatios 117 5.5 NonparametricStatistics:MedianTestforSeveralSamples 121 ReviewExercises 124 SelectedReadings 125 6 SamplingDistributionofAverages 127 6.1 PopulationMeanandSampleAverage 127 6.2 PopulationVarianceandSampleVariance 132 6.3 TheMeanandVarianceoftheSamplingDistributionofAverages 138 6.4 SamplingWithoutReplacement 143 ReviewExercises 144 7 NormalDistributions 147 7.1 TheStandardNormalDistribution 147 7.2 InferenceFromaSingleObservation 152 7.3 TheCentralLimitTheorem 155 7.4 InferencesAboutaPopulationMeanandVariance 157 7.5 UsingaNormalDistributiontoApproximateOtherDistributions 164 7.6 NonparametricStatistics:ATestBasedonRanks 173 ReviewExercises 176 SelectedReadings 177 8 Student’stDistribution 179 8.1 TheNatureoftDistributions 179 8.2 InferenceAboutaSingleMean 182 8.3 InferenceAboutTwoMeans 190 8.4 InferenceAboutTwoVariances 197 8.5 NonparametricStatistics:Matched-PairandTwo-SampleRankTests 204 ReviewExercises 209 SelectedReadings 210 9 DistributionsofTwoVariables 211 9.1 SimpleLinearRegression 211 9.2 ModelTesting 223 9.3 InferencesRelatedtoRegression 233 9.4 Correlation 238 9.5 NonparametricStatistics:RankCorrelation 250 9.6 ComputerUsage 253 9.7 EstimatingOnlyOneLinearTrendParameter 256 ReviewExercises 262 SelectedReadings 263 CONTENTS vii 10 TechniquesforOne-wayAnalysisofVariance 265 10.1 TheAdditiveModel 265 10.2 One-WayAnalysis-of-VarianceProcedure 272 10.3 Multiple-ComparisonProcedures 283 10.4 One-Degree-of-FreedomComparisons 294 10.5 Estimation 300 10.6 BonferroniProcedures 303 10.7 NonparametricStatistics:Kruskal–WallisANOVAforRanks 309 ReviewExercises 313 SelectedReadings 314 11 TheAnalysis-of-VarianceModel 317 11.1 RandomEffectsandFixedEffects 317 11.2 TestingtheAssumptionsforANOVA 324 11.3 Transformations 329 ReviewExercises 337 SelectedReadings 338 12 OtherAnalysis-of-VarianceDesigns 341 12.1 NestedDesign 341 12.2 RandomizedCompleteBlockDesign 350 12.3 LatinSquareDesign 360 12.4 a(cid:1)bFactorialDesign 368 12.5 a(cid:1)b(cid:1)cFactorialDesign 376 12.6 Split-PlotDesign 387 12.7 SplitPlotwithRepeatedMeasures 398 ReviewExercises 407 SelectedReadings 408 13 AnalysisofCovariance 409 13.1 CombiningRegressionwithANOVA 409 13.2 One-WayAnalysisofCovariance 413 13.3 TestingtheAssumptionsforAnalysisofCovariance 418 13.4 Multiple-ComparisonProcedures 423 ReviewExercises 428 SelectedReadings 429 14 MultipleRegressionandCorrelation 431 14.1 MatrixProcedures 431 14.2 ANOVAProceduresforMultipleRegressionandCorrelation 439 14.3 InferencesAboutEffectsofIndependentVariables 444 14.4 ComputerUsage 451 14.5 ModelFitting 458 14.6 LogarithmicTransformations 475 14.7 PolynomialRegression 484 viii CONTENTS 14.8 LogisticRegression 495 ReviewExercises 507 SelectedReadings 508 AppendixofUsefulTables 511 AnswerstoMostOdd-NumberedExercisesandAllReviewExercises 603 Index 629 PREFACE TO THE THIRD EDITION Inpreparationforthethirdedition,wesentanelectronicmailquestionnairetoeverystatistics departmentintheUnitedStateswithagraduateprogram.Wewantedmodalopiniononwhat statisticalproceduresshouldbeaddressedinastatisticalmethodscourseinthetwenty-first century.Ourfindingscanreadilybesummarizedasaseemingcontradiction.Thecoursehas changedlittlesinceR.A.Fisherpublishedtheinauguraltextin1925,butitalsohaschanged greatlysincethen.Thegoals,procedures,andstatisticalinferenceneededforgoodresearch remainunchanged,butthenearlyuniversalavailabilityofpersonalcomputersandstatistical computingapplicationpackagesmakeitpossible,almostdaily,todomorethaneverbefore. TheroleofthecomputerinteachingstatisticalmethodsisaproblemFisherneverhadtoface, buttoday’sinstructormustfaceit,fortunatelywithouthavingtomakeanall-or-nonechoice. We have always promised to avoid the black-box concept of computer analysis by showingtheactualarithmeticperformedineachanalysis,andweremaintruetothatpromise. However,exceptforsomesimplecomputations,witheveryexampleofastatisticalprocedure inwhichwedemonstratethearithmetic,wealsogivetheresultsofacomputeranalysisofthe samedata.Foreasycomparisonweoftenlocatethemneareachother,butinsomeinstances we find it better to have a separate section for computer analysis. Because of greater familiaritywiththem,wehavechosentheSASwandJMPw,computerapplicationsdeveloped bytheSASInstitute.†SASwasinitiallywrittenforuseonlargemainframecomputers,but hasbeenadaptedforpersonalcomputers.JMPwasdesignedforpersonalcomputers,andwe finditmoreinteractivethanSAS.Itisalsomorevisuallyoriented,withgraphicspresentedin the output before any numerical values are given. But because SAS seems to remain the computerapplicationofchoice,wepresentitmorefrequentlythanJMP. Two additions to the text are due to responses to our survey. In the preface to the first edition,westatedourpreferencefordiscussingprobabilityonlywhenitisneededtoexplain someaspectofstatisticalanalysis,butmanyrespondentsfeltacourseinstatisticalmethods needs a formal discussion of probability. We have attempted to “have it both ways” by includingaveryshortpresentationofprobabilityinthefirstchapter,butcontinuingtodiscuss it as needed. Another frequent response was the idea that a statistical analysis course now should include some minimal discussion of logistic regression. This caused us almost to surrender to black-box instruction. It is fairly easy to understand the results of a computer analysisoflogisticregression,butmanyofourstudentshaveamathematicalbackgroundabit shy of that needed for performing logistic regression analysis. Thus we discuss it, with a worked example, in the last section to make it available for those with the necessary †SASandJMPareregisteredtrademarksofSASInstituteInc.,Cary,NC,USA. ix x PREFACETOTHETHIRDEDITION mathematical background, but to avoid alarming other students who might see the mathematicsandfeeltheyrecognizethemselvesinStevieSmith’spoem†: Nobodyheardhim,thedeadman, Butstillhelaymoaning: Iwasmuchfurtheroutthanyouthought Andnotwavingbutdrowning. ConsultingwithresearchworkersatWestVirginiaUniversityhascausedustoaddsome topicsnotfoundinearliereditions.Manyofourexamplesandexercisesreflectactualresearch problemsforwhichweprovidedthestatisticalanalysis.Thathasnotchanged,buttheresearch areasthatseekourhelphavebecomemoreglobal.Inearlieryearsweassistedagricultural, biological,andbehavioralscientistswhocandesignprospectivestudies,andinourtextwe tried to meet the needs of their students. After helping researchers in areas such as health sciencewhomustdependonretrospectivestudies,wemadeadditionsforthebenefitoftheir studentsaswell.Weaddedexamplestoshowhowstatisticsisappliedtohealthresearchand nowdiscussrisks,oddsandtheirratios,aswellasrepeated-measuresanalysis.Whilehelping researchers prepare manuscripts for publication, we learned that some journals prefer the moreconservativeBonferroniprocedures,sowehaveaddedthemtothediscussionofmean separation techniques in Chapter 10. We also have a discussion of ratio and difference estimation.However,thatinclusionmaybeself-servingtoavoidyetanotherexplanationof “Whygototheallthetroubleofleastsquareswhenitissomucheasiertousearatio?”Now wecanreferthequestionertotheappropriatesectioninChapter9. Thereareadditionstotheexercisesaswellasthebodyofthetext.Webelieveourstudents enjoyhearingabouttheresearcheffortsofSirFrancisGalton,thatdelightfullyeccentricbut remarkably ingenious gentleman scientist of Victorian England. To make them suitable exercises, we have taken a few liberties with some of his research efforts, but only to demonstratethebreadthofideasofapioneerwhothoughteverythingismeasurableandhence tractabletoquantitativeanalysis.Inrespectforamanwho—darewesay?—“thoughtoutside theblackbox,”manyoftheexercisesthatrelatetoGaltonwillrequirestudentstothinkon theirownashedid.Wehopethat,likeGaltonhimself,thosewhoattempttheseexerciseswill acceptthechallengeandnotbetooconcernedwhentheydonotsucceed. We are pleased that Daniel M. Chilko, a long-time colleague, has joined us in this endeavor.Histalentshavemadeiteasiertoupdatesectionsoncomputeranalysis,andhewill serveaswebmasterforthewebsitethatwillnowaccompanythetext. Wewishtoacknowledgethehelpwereceivedfrommanypeopleinpreparationofthis edition. Once again, we thank SAS Institute for permission to discuss their SAS and JMP software. Wewanttoexpressourappreciationtothemanyreaderswhocalledtoourattentionaflaw inthealgorithmusedtopreparethePoissonconfidenceintervalsinTableA8.Becausethey alertedus,wemadecorrectionsandverifiedalltablesgeneratedbyusforthisedition. To all who responded to our survey, we are indeed indebted. We especially thank Dr. Marta D. Remmenga, Professor at New Mexico State University. She provided us with a detailedaccountofhowsheusesthetexttoteachstatisticsandgaveusanumberofhelpful suggestionsforthisedition.Allresponseswerehelpful,andwedoappreciatethetimetaken bysomanytoanswerourquestionnaire. †NotWavingButDrowning,TheTop500Poems,ColumbiaUniversityPress,NewYork.