Abstract
In decision making in statistics, the p-value has been exclusively used in statistical hypothesis testing to determine whether the hypothesis is accepted. However, the p-value has a major drawback : when the sample size is large, the p-value falls below the significance threshold by default, leading to inappropriate conclusions regarding statistical significance. In recent years, apart from the p-value, effect size is considered important in the process of statistical decision making. Effect sizes are measures of the strength of a phenomenon (e.g., an experiment or treatment), and they do not depend on the sample size. As a related issue, in structural equation modeling (SEM), analysts can use many fit indices in model selection. In addition, the t-test and analysis of variance (ANOVA), frequently used in hypothesis testing, are sub-models of the SEM. Therefore, analysts can consider many fit indices in the t-test and ANOVA in statistical decision making. In this study, we provide an example of model selection that references many fit indices by using a one-way within-subjects ANOVA.
