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

Nikos Ntoumanis, Nicholas D. Myers, Nikos Ntoumanis, Nicholas D. Myers

• Publisher: Wiley
• Year: 2015
• Print ISBN: 9781118962053
• eBook ISBN: 9781118962046
• Edition: 1
• Topic: Medicine
• Subtopic: Probability & Statistics

"Ntoumanis and Myers have done sport and exercise science researchers and students a tremendous service in producing An Introduction to Intermediate and Advanced Statistical Analyses for Sport and Exercise Scientists. This book has an outstanding compilation of comprehensible chapters dealing with the important concepts and technical minutia of the statistical analyses that sport and exercise science scholars use (or should be using!) in their efforts to conduct meaningful research in the field. It is a resource that all sport and exercise scientists and their students should have on their book shelves."
—Robert Eklund, School of Sport, University of Stirling, UK

"Motivating, to have a statistics text devoted to enabling researchers studying sport and exercise science to apply the most sophisticated analytical techniques to their data. Authors hit the mark between using technical language as necessary and user-friendly terms or translations to keep users encouraged. Text covers traditional and well-used tools but also less common and more complex tools, but always with familiar examples to make their explanations come alive. As a dynamic systems theorist and developmentalist, I would love to see more researchers in my area create study designs that would enable the use of tools outlined here, such as multilevel structural equation modeling (MSEM) or mediation & moderation analyses, to uncover cascades of relations among subsystems contributing to motor performance, over time. This text can facilitate that outcome."
—Beverly D. Ulrich, School of Kinesiology, University of Michigan, USA

"The domain of quantitative methods is constantly evolving and expanding.  This means that there is tremendous pressure on researchers to stay current, both in terms of best practices and improvements in more traditional methods as well as increasingly complex new methods. With this volume Ntoumanis and Myers present a nice cross-section of both, helping sport and exercise science researchers to address old questions in better ways, and, even more excitingly, to address new questions entirely. I have no doubt that this volume will quickly become a lovingly dog-eared companion for students and researchers, helping them to continue to move the field forward."
—Gregory R. Hancock, University of Maryland and Center for Integrated Latent Variable Research (CILVR), USA

1
Factorial ANOVA and MANOVA

Minsoo Kang¹ and Ying Jin²

¹ Health and Human Performance, Middle Tennessee State University, Murfreesboro, TN, USA

² Quantitative Psychology, Middle Tennessee State University, Murfreesboro, TN, USA

General Introduction

The ANOVA is a statistical method used to test mean differences among groups. In its simplest form, a one-way ANOVA with two groups functions the same as a t-test for independent samples. Unlike the t-test, however, more elaborate forms of ANOVA have the ability to test for mean differences among three or more groups of a single variable. The independent variable or variables in an ANOVA, also called factors or predictors, are categorical variables. Nominal and ordinal variables are common independent variables. The dependent variables are continuous (i.e., interval and ratio) variables.

The true advantage of the ANOVA, compared to t-test, comes from its ability to test for mean differences between two or more groups across multiple independent variables. When an ANOVA model has two independent variables, it is called a two-way ANOVA; when there are three independent variables, the ANOVA is called a three-way ANOVA; and so on. However, any ANOVA with two or more independent variables falls under the label of a factorial ANOVA. The multivariate analysis of variance (MANOVA) is an extension of the ANOVA that allows for multiple dependent variables. The following sections will discuss the hypotheses and assumptions of a factorial ANOVA analysis with one dependent variable and also with multiple dependent variables (i.e., factorial MANOVA).

Hypothesis Testing

The factorial ANOVA and MANOVA test the main effects for each independent variable on a dependent variable, as well as any possible interactions between independent variables. A hypothesis test is required for each main effect and interaction effect.

A significant main effect indicates that the independent variable is a significant predictor of the dependent variable(s). A significant main effect in a factorial ANOVA indicates that at least one group in the independent variable differs on the dependent variable. In a factorial ANOVA, there is only one dependent variable for the independent variables to differ on. The null hypothesis for each main effect in a factorial MANOVA is that the dependent variables are the same across all conditions of that independent variable. The alternative hypothesis is that at least one group in the independent variable differs on at least one dependent variable.

For an interaction, the null hypothesis is that the effect of one independent variable on the dependent variable(s) is the same across each level of another independent variable. The alternative hypothesis is that the effect of an independent variable on the dependent variable(s) differs for the levels of another independent variable. For example, the benefits associated with being physically active (low, medium, and high) on health outcomes are likely to be different depending on an individual’s body mass index (underweight, normal, overweight, and obese). To test this hypothesis, an interaction term between physical activity and body mass index groups is introduced and tested along with the main effects of these variables.

Alpha Level

Alpha level is related to the type I error rate, the chance that a researcher infers that there is a significant difference when the groups do not differ. The nominal alpha level is what the researcher sets as the chance of a type I error rate, usually 0.05 (or 5% chance). The empirical alpha level is the actual chance that a type I error occurs. Various approaches have been proposed to control the empirical alpha level in post hoc procedures. In a two-way factorial ANOVA, each main effects and interaction are...

Table of contents

• Cover
• Title Page
• Table of Contents
• List of contributors
• About the editors
• Foreword
• Preface
• 1 Factorial ANOVA and MANOVA
• 2 Repeated measures ANOVA and MANOVA
• 3 Mediation and moderation via regression analysis
• 4 Item response theory and its applications in Kinesiology
• 5 Introduction to factor analysis and structural equation modeling
• 6 Invariance testing across samples and time
• Chapter 7: Cross-lagged structural equation modeling and latent growth modeling
• 8 Exploratory structural equation modeling and Bayesian estimation
• 9 A gentle introduction to mixture modeling using physical fitness performance data
• 10 Multilevel (structural equation) modeling
• 11 Application of meta-analysis in sport and exercise science
• 12 Reliability and stability of variables/instruments used in sport science and sport medicine
• 13 Sample size determination and power estimation in structural equation modeling
• Index
• End User License Agreement