Introduction to Intermediate and Advanced Statistical Analyses for Sport and Exercise Scientists

Nikos Ntoumanis, School of Sport, Exercise and Rehabilitation Sciences, University of Birmingham, Birmingham, UK. Nikos has been teaching statistics to sport and exercise sciences university students for 14 years in two UK universities and delivered statistics workshops in the UK and overseas.Nicholas Daniel Myers, Department of Educational and Psychological Studies, University of Miami, Florida, USA. His expertise is in advanced statistical methods with an emphasis on applications in sport and exercise science. Nicholas serves as Director of the Research, Measurement, and Evaluation (RME) doctoral program at the University of Miami. The RME doctoral program has been rated a top-20 program nationally by Academic Analytics since 2006 and has served as a statistical consultant for the Research Methodology Services component of the Dunspaugh-Dalton Community and Educational Well-Being (CEW) Research Centre at the University of Miami.

• About the editors xiiiList of contributors xvForeword xixPreface xxi1 Factorial ANOVA and MANOVA 1General Introduction 1Hypothesis Testing 2Alpha Level 2Assumptions 3Further Considerations 4Utility in Sport and Exercise Sciences 6Treatment Conditions 6Existing Conditions 6Individual Characteristics 7Recent Usage 7The Substantive Example 7Univariate: Factorial ANOVA 8Univariate Assumptions 8The Synergy 10Factorial ANOVA Analysis Plan 10Example of a Write]Up Compatible with the APA Publication Manual 11Factorial MANOVA Analysis Plan 13Example of a Write]Up Compatible with the APA Publication Manual 13Summary 16Acknowledgment 18References 182 Repeated measures ANOVA and MANOVA 19General Introduction 19Between] versus Within]Subjects Variables 19Hypothesis Testing 20Assumptions 20Further Considerations 21Utility in Sport and Exercise Sciences 22Multiple Treatment Conditions 23Multiple Assessments 23Longitudinal Studies 23Recent Usage 24The Substantive Example 24Univariate: Repeated Measures ANOVA 24Univariate Assumptions 25Multivariate: Repeated Measures MANOVA 26Multivariate Assumptions 26The Synergy 27Repeated Measures ANOVA Analysis Plan 27Example of a Write]Up Compatible with the APA Publication Manual 29Repeated Measures MANOVA Analysis Plan 29Example of a Write]Up Compatible with the APA Publication Manual 31Summary 32Acknowledgment 34References 343 Mediation and moderation via regression analysis 35General Introduction 35Utility of the Methods in Sport and Exercise Science 36The Substantive Example 38Mediation 38The Synergy 38Mediation 38The Substantive Example 44Moderation 44The Synergy 45Moderation 45Summary 53References 554 Item response theory and its applications in Kinesiology 57General Introduction 57What Is IRT? 59Other Commonly Used IRT Models 60Assumptions Related to IRT 62Unidimensionality 62Local Independence 62Addressing Model]Data Fit 62Inspecting Model Assumptions 63Inspecting Expected Model Features 63Inspecting Overall Model]Data Fit 64Computer Simulation for Model]Data Fit Testing 64Unique Features and Advantages of IRT 65Estimation Invariance 65Common Metric Scale 65Item and Test Information 66Test Relative Efficiency 68Global “Reliability” Is no Longer a Concern 69Item Bank and IRT]Based Test Construction 69Parameter Estimation and Software 71Utility of the Methodology in Kinesiology 71IRT Limitations and Future Direction 72Conclusion 73References 745 Introduction to factor analysis and structural equation modeling 79General Introduction 79Utility of the Method in Sport and Exercise Science 80Terminology and Methodology 83Evaluating Model Fit 86Interpreting Parameter Estimates 88The Substantive Example 89The Synergy 91EFA: Establishing the Factor Structure 91CFA: Testing the Measurement Models 93Structural Equation Modeling: Adding the Regression Paths 96Summary 98References 996 Invariance testing across samples and time: Cohort]sequence analysis of perceived body composition 101General Introduction to the Importance of Measurement Invariance 102Cohort]Sequential Designs: Longitudinal Invariance across Samples and Time 106Substantive Application: Physical Self]Concept 107Methodology 111The PSDQ Instrument 111Statistical Analyses 111Goodness of Fit 112Results 113Basic Cohort]Sequence Model: Four Cohort Groups and Four Waves 113Cohort]Sequence Design of Multiple Indicators, Multiple Causes Models 115Use of Model Constraint with Orthogonal Polynomial Contrasts to Evaluate Cohort Sequence and MIMIC Latent Means 116Use of Latent Growth Curve Models to Evaluate Stability/Change over Time 119LGC Results 123Summary, Implications, and Further Directions 123Methodological Implications, Limitations, and Further Directions 123References 1257 Cross]lagged structural equation modeling and latent growth modeling 131General Introduction 131A Theoretical Framework for the Study of Change 132Utility of the Method in Sport and Exercise Science 132Analysis of Change 132The Substantive Example 134Theoretical Background 134The Data: Participants and Measurement 134The Synergy 135CLPM 135CLPM Example 137Latent Growth Modeling 140LGM Example 141Model 2a: Unconditional LGM 143Model 2b: Conditional LGM 145Model 2c: Unconditional LGM with TVCs 145Model 3: Parallel Process LGM 146Model 4: Second]Order LGM 148Summary 150References 1518 Exploratory structural equation modeling and Bayesian estimation 155General Introduction 155Utility of the Methods in Sport and Exercise Science 156The Substantive Example(s) 159The Motivational Correlates of Mentally Tough Behavior 159Developing Synergies through Statistical Modeling 161ESEM 161Bayesian Estimation 168Summary 179References 1809 A gentle introduction to mixture modeling using physical fitness performance data 183General Introduction 183Utility of the Method in Sport and Exercise Science 186The Substantive Example(s) 187Class Enumeration in Mixture Models 188The Estimation of Mixture Models 190The Synergy 190LPA of Grade 5 Students and Tests of Invariance across Gender Groups 190Inclusion of Covariates in LPA Solutions 195LTA 196Mixture Regression Analyses of Grade 5 Students 198Latent Basis Growth Mixture Analyses: Cardiovascular Fitness 202Piecewise Growth Mixture Analyses: Physical Strength 203Summary 204Acknowledgments 205References 20610 Multilevel (structural equation) modeling 211General Introduction 211Multilevel Structural Equation Modeling 212Utility of the Methodology in Sport and Exercise Science 214The Substantive Examples 215Coaching Competency–Collective Efficacy–Team Performance: 1–1–2 216Action Planning Intervention–Physical Activity Action Plans–Physical Activity: 2–1–1 217The Synergy 218Coaching Competency–Collective Efficacy–Team Performance: 1–1–2 219Action Planning Intervention–Physical Activity Action Plans–Physical Activity: 2–1–1 222Summary 229References 23011 Application of meta]analysis in sport and exercise science 233General Introduction 233Stages of Meta]Analysis 233Key Elements of Meta]Analysis 234Goals of Meta]Analysis 236Utility of the Methodology in Sport and Exercise Science 238The Substantive Example 238The Synergy 241Univariate Meta]Analysis 241Multivariate Meta]Analysis 245Summary 249Acknowledgment 251References 25112 Reliability and stability of variables/instruments used in sport science and sport medicine 255Introduction 255A. Assessment of Test–Retest Agreement Using Interval/Ratio Data 256A Worked Example Using the Test–Retest Differences of the Biceps Skinfold Measurements 257B. Utility of the Assessment of Test–Retest Stability Using Categorical/Likert]Type Data 260The Substantive Example 261Utility of the Test–Retest Stability Using Nonparametric Data 261The Synergy 262Utility of the Item by Item Approach to Test–Retest Stability 263The Synergy 263Summary 265References 26613 Sample size determination and power estimation in structural equation modeling 267General Introduction 267Power 268Power Analysis in SEM 268Utility of the Methodology in Sport and Exercise Science 269Power Analysis Regarding Model]Data Fit: An Introduction 269Power Analysis Regarding Focal Parameters: An Introduction 270The Substantive Example 272Bifactor Model in Sport and Exercise Science 272Bifactor Model and the PETES 273The Synergy 275Power Analysis Regarding Model]Data Fit: A Demonstration 276Power Analysis Regarding Focal Parameters: A Demonstration 278Summary 281References 282Index 285