Statistics for research

634 Pages·2004·3.134 MB·English

by  Shirley Dowdy, Stanley Wearden, Daniel Chilko

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
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Statisticsforresearch/ShirleyDowdy,StanleyWeardon,DanielChilko.
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Includesbibliographicalreferencesandindex.
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