Constructing confidence intervals for effect size measures of an indirect effect

Confidence intervals for an effect size can provide the information about the magnitude of an effect and its precision as well as the binary decision about the existence of an effect. In this study, the performances of five different methods for constructing confidence intervals for ratio effect size measures of an indirect effect were compared in terms of power, coverage rates, Type I error rates, and widths of confidence intervals. The five methods include the percentile bootstrap method, the bias-corrected and accelerated (BCa) bootstrap method, the delta method, the Fieller method, and the Monte Carlo method. The results were discussed with respect to the adequacy of the distributional assumptions and the nature of ratio quantity. The confidence intervals from the five methods showed similar results for samples of more than 500, whereas, for samples of less than 500, the confidence intervals were sufficiently narrow to convey the information about the population effect sizes only when the effect sizes of regression coefficients defining the indirect effect are large.