When to Use Different Inferential Methods for Power Analysis and Data Analysis for Between-Subjects Mediation

Abstract

Several options exist for conducting inference on indirect effects in mediation analysis. Although methods that use bootstrapping are the preferred inferential approach for testing mediation, they are time-consuming when the test must be performed many times for a power analysis. Alternatives that are more computationally efficient are not as robust, meaning accuracy of the inferences from these methods is more affected by nonnormal and heteroskedastic data. Previous research has shown that different sample sizes are needed to achieve the same amount of statistical power for different inferential approaches with data that meet all the statistical assumptions of linear regression. By contrast, we explore how similar power estimates are at the same sample size, including when assumptions are violated. We compare the power estimates from six inferential methods for between-subjects mediation using a Monte Carlo simulation study. We varied the path coefficients, inferential methods for the indirect effect, and degree to which assumptions are met. We found that when the assumptions of linear regression are met, three inferential methods consistently perform similarly: the joint significance test, the Monte Carlo confidence interval, and the percentile bootstrap confidence interval. When the assumptions were violated, the nonbootstrapping methods tended to have vastly different power estimates compared with the bootstrapping methods. On the basis of these results, we recommend using the more computationally efficient joint significance test for power analysis only when no assumption violations are hypothesized a priori. We also recommend the joint significance test to pick an optimal starting sample size value for power analysis using the percentile bootstrap confidence interval when assumption violations are suspected.