Sample size and power estimates for a confirmatory factor analytic model in exercise and sport: a Monte Carlo approach

Monte Carlo methods can be used in data analytic situations (e.g., validity studies) to make decisions about sample size and to estimate power. The purpose of using Monte Carlo methods in a validity study is to improve the methodological approach within a study where the primary focus is on construct validity issues and not on advancing statistical theory. The purpose of this study is to demonstrate how Monte Carlo methods can be used to determine sample size and to estimate power for a confirmatory factor analytic model under model-data conditions commonly encountered in exercise and sport. Because the purpose is pursued by way of demonstration with the Coaching Efficacy Scale II-High School Teams, related sample size recommendations are provided: N > or = 200 for the theoretical model; N > or = 300 for the population model. Technical terms (e.g., coverage) are defined when necessary.