Correct Confidence Intervals for Various Regression Effect Sizes and Parameters: The Importance of Noncentral Distributions in Computing Intervals

Abstract

The advantages that confidence intervals have over null-hypothesis significance testing have been presented on many occasions to researchers in psychology. This article provides a practical introduction to methods of constructing confidence intervals for multiple and partial R² and related parameters in multiple regression models based on “noncentral” F and χ² distributions. Until recently, these techniques have not been widely available due to their neglect in popular statistical textbooks and software. These difficulties are addressed here via freely available SPSS scripts and software and illustrations of their use. The article concludes with discussions of implications for the interpretation of findings in terms of noncentral confidence intervals, alternative measures of effect size, the relationship between noncentral confidence intervals and power analysis, and the design of studies.