Statistical Applications for the Behavioral and Social Sciences, 2nd edition

922 Pages·2019·8.817 MB·English

by  K. Paul Nesselroade Jr, Laurence G. Grimm

StatisticalApplications for
the Behavioral andSocial
Sciences
Statistical Applications for the Behavioral
and Social Sciences
Second Edition
K. Paul Nesselroade, Jr.
Asbury University
Laurence G. Grimm†
University of Illinois at Chicago
Thiseditionfirstpublished2019
©2019JohnWiley&Sons,Inc.
EditionHistory
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LibraryofCongressCataloging-in-PublicationData
Names:Grimm,LaurenceG.,author.|Nesselroade,K.Paul,Jr.,author.
Title:Statisticalapplicationsforthebehavioralandsocialsciences/K.
PaulNesselroade,Jr.,AsburyUniversity,LaurenceG.Grimm,Universityof
IllinoisatChicago.
Othertitles:Statisticalapplicationsforthebehavioralsciences
Description:2ndedition.|Hoboken,NJ:JohnWiley&Sons,Inc.,2019.|
Includesindex.|Earliereditionpublishedin1993as: Statistical
applicationsforthebehavioralsciences[by]LaurenceG.Grimm.|
Identifiers:LCCN2018022259(print)|LCCN2018025247(ebook)|ISBN
9781119355380(AdobePDF)|ISBN9781119355366(ePub)|ISBN9781119355397
(hardcover)
Subjects: LCSH:Socialsciences–Statisticalmethods.
Classification:LCCHA29(ebook)|LCCHA29.G77352019(print)|DDC
300.1/5195–dc23
LCrecordavailableathttps://lccn.loc.gov/2018022259
Coverdesign:CourtesyofMegSanchez
Coverimage:CourtesyofMaxOstrozhinskiyonUnsplash
Setin10/12ptWarnockbySPiGlobal,Pondicherry,India
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
For Cheryl, Andrew, Sarah, and Lisa
– each ofyou bring special meaning to life
vii
Contents
Preface xv
Acknowledgments xix
AbouttheCompanionWebsite xxi
Part1 Introduction 1
1 BasicConceptsinResearch 3
1.1 The Scientific Method 3
1.2 The Goals of the Researcher 5
1.3 Types of Variables 7
1.4 Controlling Extraneous Variables 10
1.5 Validity Issues 18
1.6 Causality and Correlation 23
1.7 The Role of Statistical Analysis and the Organization of the
Textbook 26
Summary 27
Part2 DescriptiveStatistics 35
2 ScalesofMeasurementandDataDisplay 37
2.1 Scales of Measurement 37
2.2 Discrete Variables, Continuous Variables, and the Real Limits of
Numbers 41
2.3 UsingTables to Organize Data 45
2.4 UsingGraphs to Display Data 50
2.5 The Shape of Things to Come 59
® ®
2.6 Introduction to Microsoft Excel and SPSS 62
Summary 64
viii Contents
3 MeasuresofCentralTendency 69
3.1 Describing a Distribution of Scores 69
3.2 Parameters and Statistics 70
3.3 The Rounding Rule 70
3.4 The Mean 71
3.5 The Median 76
3.6 The Mode 81
3.7 How the Shape of Distributions Affects Measures of Central
Tendency 82
3.8 When to Use the Mean, Median, and Mode 83
3.9 Experimental Research and the Mean: A Glimpse of Things
to Come 85
Summary 89
® ®
UsingMicrosoft ExcelandSPSS toFindMeasuresofCentrality 90
4 MeasuresofVariability 97
4.1 The Importance of Measures of Variability 97
4.2 Range 97
4.3 Mean Deviation 100
4.4 The Variance 102
4.5 The Standard Deviation 109
4.6 Simple Transformations and Their Effect on the Mean and
Variance 111
4.7 Deciding Which Measure of Variability to Use 113
Summary 116
® ®
UsingMicrosoft Excel and SPSS to Find Measures
of Variability 117
5 TheNormalCurveandTransformations:PercentilesandzScores 127
5.1 Percentile Rank 127
5.2 The Normal Distributions 133
5.3 Standard Scores (zScores) 137
Summary 150
® ®
UsingMicrosoft Excel and SPSS to Find z Scores 151
Part3 InferentialStatistics:TheoreticalBasis 161
6 BasicConceptsofProbability 163
6.1 Theoretical Support forInferential Statistics 163
6.2 The Taming of Chance 165
6.3 What Is Probability? 168
Contents ix
6.4 Samplingwithand Without Replacement 170
6.5 A Priori and A Posteriori Approaches to Probability 171
6.6 The Addition Rule 171
6.7 The Multiplication Rule 175
6.8 ConditionalProbabilities 179
6.9 Bayes’ Theorem 184
Summary 188
7 HypothesisTestingandSamplingDistributions 195
7.1 Inferential Statistics 195
7.2 Hypothesis Testing 197
7.3 SamplingDistributions 203
7.4 Estimating the Features of Sampling Distributions 210
Summary 212
Part4 InferentialStatistics:zTest,tTests,andPowerAnalysis 219
8 TestingaSingleMean:TheSingle-SamplezandtTests 221
8.1 The Research Context 221
8.2 Usingthe Sampling Distribution of Means for the Single-Sample
z Test 222
8.3 Type I and Type IIErrors 233
8.4 Is a Significant Finding “Significant?” 237
8.5 TheStatisticalTestfortheMeanofaPopulationWhenσIsUnknown:
The t Distributions 240
8.6 Assumptionsof the Single-Sample z and t Tests 249
8.7 Interval Estimation of the Population Mean 250
8.8 How toPresent Formally the Findings from a Single-Sample
t Test 252
Summary 253
® ®
UsingMicrosoft ExcelandSPSS toRunSingle-SampletTests 253
9 TestingtheDifferenceBetweenTwoMeans:TheIndependent-Samples
tTest 265
9.1 The Research Context 265
9.2 The Independent-Samples t Test 268
9.3 The Appropriateness of Unidirectional Tests 283
9.4 Assumptionsof the Independent-Samples t Test 288
9.5 Interval Estimation of the Population Mean Difference 289
9.6 HowtoPresentFormallytheConclusionsforanIndependent-Samples
t Test 291
x Contents
Summary 291
® ®
UsingMicrosoft Excel and SPSS to Run anIndependent-Samples
t Test 292
10 TestingtheDifferenceBetweenTwoMeans:TheDependent-Samples
tTest 311
10.1 The Research Context 311
10.2 The SamplingDistribution for the Dependent-Samples t Test 315
10.3 The t Distribution forDependent Samples 318
10.4 Comparing the Independent- and Dependent-Samples t Tests 322
10.5 The One-Tailedt Test Revisited 323
10.6 Assumptions of the Dependent-Samples t Test 323
10.7 Interval Estimation of the Population Mean Difference 323
10.8 How to Present Formally the Conclusionsfor a Dependent-Samples
t Test 327
Summary 327
® ®
UsingMicrosoft Excel and SPSS to Run aDependent-Samples
t Test 328
11 PowerAnalysisandHypothesisTesting 343
11.1 Decision-Making While Hypothesis Testing 343
11.2 Why Study Power? 344
11.3 The Five Factors that Influence Power 345
11.4 Decision Criteria that Influence Power 348
11.5 UsingthePower Table 351
11.6 DeterminingEffectSize:TheAchillesHeelofthePowerAnalysis 354
11.7 Determining Sample Size fora Single-Sample Test 356
11.8 Failing to Reject the Null Hypothesis:Can a Power Analysis
Help? 358
Summary 361
Part4Review ThezTest,tTests,andPowerAnalysis 365
Part5 InferentialStatistics:AnalysesofVariance 375
12 One-WayAnalysisofVariance 377
12.1 The Research Context 377
12.2 The Conceptual Basis of ANOVA: Sources of Variation 380
12.3 The Assumptionsof the One-Way ANOVA 384
12.4 Hypotheses and Error Terms forthe One-Way ANOVA 384
12.5 Computing the F Ratio ina One-Way ANOVA 388
Contents xi
12.6 TestingNull Hypotheses 396
12.7 The One-Way ANOVA Summary Table 399
12.8 An Example of anANOVA with Unequal Numbers of
Participants 399
12.9 MeasuringEffect Size fora One-Way ANOVA 400
12.10 Locating the Source(s)of Significance 403
12.11 How toPresent Formally the Conclusions fora One-Way
ANOVA 409
Summary 410
® ®
Using Microsoft Excel and SPSS to Run a One-Way
ANOVA 411
13 Two-WayAnalysisofVariance 425
13.1 The Research Context 425
13.2 The Logic of the Two-Way ANOVA 437
13.3 Definitionaland Computational Formulas for the Two-Way
ANOVA 441
13.4 Usingthe FRatios to Test NullHypotheses 451
13.5 Assumptionsof the Two-Way ANOVA 456
13.6 MeasuringEffect Sizes fora Two-Way ANOVA 456
13.7 MultipleComparisons 457
13.8 Interpreting the Factors ina Two-Way ANOVA 462
13.9 How toPresent Formally the Conclusions fora Two-Way
ANOVA 463
Summary 464
® ®
UsingMicrosoft ExcelandSPSS toRunaTwo-WayANOVA 465
14 Repeated-MeasuresAnalysisofVariance 483
14.1 The Research Context 483
14.2 The Logic of the Repeated-Measures ANOVA 486
14.3 The Formulas forthe Repeated-Measures ANOVA 489
14.4 Usingthe FRatio to Test the Null Hypothesis 497
14.5 Interpreting the Findings 497
14.6 The ANOVA Summary Table 498
14.7 Assumptionsof the Repeated-Measures ANOVA 500
14.8 MeasuringEffect Size forRepeated-Measures ANOVA 500
14.9 Locating the Source(s)of Statistical Evidence 501
14.10 How toPresent Formally the Conclusions fora Repeated-Measures
ANOVA 504
Summary 505
® ®
UsingMicrosoft Excel and SPSS to Run a Repeated-Measures
ANOVA 506
xii Contents
Part5Review AnalysesofVariance 521
Part6 InferentialStatistics:BivariateDataAnalyses 529
15 LinearCorrelation 531
15.1 The Research Context 531
15.2 The Correlation Coefficient and Scatter Diagrams 536
15.3 The Coefficient of Determination, r2 545
15.4 UsingthePearson r for Hypothesis Testing 549
15.5 Factors That Can Create Misleading Correlation Coefficients 556
15.6 How to Present Formally the Conclusionsof a Pearson r 561
Summary 562
® ®
UsingMicrosoft Excel and SPSS to Calculate Pearson r 564
16 LinearRegression 579
16.1 The Research Context 579
16.2 Overview ofRegression 580
16.3 Establishing the Regression Line 585
16.4 Putting ItAllTogether: A Worked Problem 600
16.5 The Coefficient of Determination inthe Context of Prediction 606
16.6 The Pitfalls of Linear Regression 607
16.7 How to Present Formally the Conclusionsof a Linear Regression
Analysis 610
Summary 611
® ®
UsingMicrosoft Excel and SPSS to Create a Linear Regression
Line 612
Part6Review LinearCorrelationandLinearRegression 625
Part7 InferentialStatistics:NonparametricTests 633
17 TheChi-SquareTest 635
17.1 The Research Context 635
17.2 The Chi-SquareTest for One-Way Designs: The Goodness-of-Fit
Test 637
17.3 The Chi-SquareDistribution and Degrees of Freedom 644
17.4 Two-Way Designs: The Chi-Square Test for Independence 647
17.5 The Chi-SquareTest for a 2×2Contingency Table 653
17.6 A Measure of Effect Size forChi-SquareTests 656