About the editors xiii

List of contributors xv

Foreword xix

Preface xxi

**1 Factorial ANOVA and MANOVA 1**

General Introduction 1

Hypothesis Testing 2

Alpha Level 2

Assumptions 3

Further Considerations 4

Utility in Sport and Exercise Sciences 6

Treatment Conditions 6

Existing Conditions 6

Individual Characteristics 7

Recent Usage 7

The Substantive Example 7

Univariate: Factorial ANOVA 8

Univariate Assumptions 8

The Synergy 10

Factorial ANOVA Analysis Plan 10

Example of a Write]Up Compatible with the APA Publication Manual 11

Factorial MANOVA Analysis Plan 13

Example of a Write]Up Compatible with the APA Publication Manual 13

Summary 16

Acknowledgment 18

References 18

**2 Repeated measures ANOVA and MANOVA 19**

General Introduction 19

Between] versus Within]Subjects Variables 19

Hypothesis Testing 20

Assumptions 20

Further Considerations 21

Utility in Sport and Exercise Sciences 22

Multiple Treatment Conditions 23

Multiple Assessments 23

Longitudinal Studies 23

Recent Usage 24

The Substantive Example 24

Univariate: Repeated Measures ANOVA 24

Univariate Assumptions 25

Multivariate: Repeated Measures MANOVA 26

Multivariate Assumptions 26

The Synergy 27

Repeated Measures ANOVA Analysis Plan 27

Example of a Write]Up Compatible with the APA Publication Manual 29

Repeated Measures MANOVA Analysis Plan 29

Example of a Write]Up Compatible with the APA Publication Manual 31

Summary 32

Acknowledgment 34

References 34

**3 Mediation and moderation via regression analysis 35**

General Introduction 35

Utility of the Methods in Sport and Exercise Science 36

The Substantive Example 38

Mediation 38

The Synergy 38

Mediation 38

The Substantive Example 44

Moderation 44

The Synergy 45

Moderation 45

Summary 53

References 55

**4 Item response theory and its applications in Kinesiology 57**

General Introduction 57

What Is IRT? 59

Other Commonly Used IRT Models 60

Assumptions Related to IRT 62

Unidimensionality 62

Local Independence 62

Addressing Model]Data Fit 62

Inspecting Model Assumptions 63

Inspecting Expected Model Features 63

Inspecting Overall Model]Data Fit 64

Computer Simulation for Model]Data Fit Testing 64

Unique Features and Advantages of IRT 65

Estimation Invariance 65

Common Metric Scale 65

Item and Test Information 66

Test Relative Efficiency 68

Global “Reliability” Is no Longer a Concern 69

Item Bank and IRT]Based Test Construction 69

Parameter Estimation and Software 71

Utility of the Methodology in Kinesiology 71

IRT Limitations and Future Direction 72

Conclusion 73

References 74

**5 Introduction to factor analysis and structural equation modeling 79**

General Introduction 79

Utility of the Method in Sport and Exercise Science 80

Terminology and Methodology 83

Evaluating Model Fit 86

Interpreting Parameter Estimates 88

The Substantive Example 89

The Synergy 91

EFA: Establishing the Factor Structure 91

CFA: Testing the Measurement Models 93

Structural Equation Modeling: Adding the Regression Paths 96

Summary 98

References 99

**6 Invariance testing across samples and time: Cohort]sequence analysis of perceived body composition 101**

General Introduction to the Importance of Measurement Invariance 102

Cohort]Sequential Designs: Longitudinal Invariance across Samples and Time 106

Substantive Application: Physical Self]Concept 107

Methodology 111

The PSDQ Instrument 111

Statistical Analyses 111

Goodness of Fit 112

Results 113

Basic Cohort]Sequence Model: Four Cohort Groups and Four Waves 113

Cohort]Sequence Design of Multiple Indicators, Multiple Causes Models 115

Use of Model Constraint with Orthogonal Polynomial Contrasts to Evaluate Cohort Sequence and MIMIC Latent Means 116

Use of Latent Growth Curve Models to Evaluate Stability/Change over Time 119

LGC Results 123

Summary, Implications, and Further Directions 123

Methodological Implications, Limitations, and Further Directions 123

References 125

**7 Cross]lagged structural equation modeling and latent growth modeling 131**

General Introduction 131

A Theoretical Framework for the Study of Change 132

Utility of the Method in Sport and Exercise Science 132

Analysis of Change 132

The Substantive Example 134

Theoretical Background 134

The Data: Participants and Measurement 134

The Synergy 135

CLPM 135

CLPM Example 137

Latent Growth Modeling 140

LGM Example 141

Model 2a: Unconditional LGM 143

Model 2b: Conditional LGM 145

Model 2c: Unconditional LGM with TVCs 145

Model 3: Parallel Process LGM 146

Model 4: Second]Order LGM 148

Summary 150

References 151

**8 Exploratory structural equation modeling and Bayesian estimation 155**

General Introduction 155

Utility of the Methods in Sport and Exercise Science 156

The Substantive Example(s) 159

The Motivational Correlates of Mentally Tough Behavior 159

Developing Synergies through Statistical Modeling 161

ESEM 161

Bayesian Estimation 168

Summary 179

References 180

**9 A gentle introduction to mixture modeling using physical fitness performance data 183**

General Introduction 183

Utility of the Method in Sport and Exercise Science 186

The Substantive Example(s) 187

Class Enumeration in Mixture Models 188

The Estimation of Mixture Models 190

The Synergy 190

LPA of Grade 5 Students and Tests of Invariance across Gender Groups 190

Inclusion of Covariates in LPA Solutions 195

LTA 196

Mixture Regression Analyses of Grade 5 Students 198

Latent Basis Growth Mixture Analyses: Cardiovascular Fitness 202

Piecewise Growth Mixture Analyses: Physical Strength 203

Summary 204

Acknowledgments 205

References 206

**10 Multilevel (structural equation) modeling 211**

General Introduction 211

Multilevel Structural Equation Modeling 212

Utility of the Methodology in Sport and Exercise Science 214

The Substantive Examples 215

Coaching Competency–Collective Efficacy–Team Performance: 1–1–2 216

Action Planning Intervention–Physical Activity Action Plans–Physical Activity: 2–1–1 217

The Synergy 218

Coaching Competency–Collective Efficacy–Team Performance: 1–1–2 219

Action Planning Intervention–Physical Activity Action Plans–Physical Activity: 2–1–1 222

Summary 229

References 230

**11 Application of meta]analysis in sport and exercise science 233**

General Introduction 233

Stages of Meta]Analysis 233

Key Elements of Meta]Analysis 234

Goals of Meta]Analysis 236

Utility of the Methodology in Sport and Exercise Science 238

The Substantive Example 238

The Synergy 241

Univariate Meta]Analysis 241

Multivariate Meta]Analysis 245

Summary 249

Acknowledgment 251

References 251

**12 Reliability and stability of variables/instruments used in sport science and sport medicine 255**

Introduction 255

A. Assessment of Test–Retest Agreement Using Interval/Ratio Data 256

A Worked Example Using the Test–Retest Differences of the Biceps Skinfold Measurements 257

B. Utility of the Assessment of Test–Retest Stability Using Categorical/Likert]Type Data 260

The Substantive Example 261

Utility of the Test–Retest Stability Using Nonparametric Data 261

The Synergy 262

Utility of the Item by Item Approach to Test–Retest Stability 263

The Synergy 263

Summary 265

References 266

**13 Sample size determination and power estimation in structural equation modeling 267**

General Introduction 267

Power 268

Power Analysis in SEM 268

Utility of the Methodology in Sport and Exercise Science 269

Power Analysis Regarding Model]Data Fit: An Introduction 269

Power Analysis Regarding Focal Parameters: An Introduction 270

The Substantive Example 272

Bifactor Model in Sport and Exercise Science 272

Bifactor Model and the PETES 273

The Synergy 275

Power Analysis Regarding Model]Data Fit: A Demonstration 276

Power Analysis Regarding Focal Parameters: A Demonstration 278

Summary 281

References 282

Index 285