Enhancing power while controlling family-wise error: an illustration of the issues using electrocortical studies

This study examined the relative family-wise error (FWE) rate and statistical power of multivariate permutation tests (MPTs), Bonferroni-adjusted alpha, and uncorrected-alpha tests of significance for bivariate associations. Although there are many previous applications of MPTs, this is the first to apply it to testing bivariate associations. Electrocortical studies were selected as an example class because the sample sizes that are typical of electrocortical studies published in 2001 and 2002 are small and their multiple significance tests are typically nonindependent. Because Bonferroni adjustments assume independent predictors, we expected that MPTs would be more powerful than the Bonferroni adjustment. Results support the following conclusions: (a) failure to control for multiple significance testing results in unacceptable FWE rates, (b) the FWE rate for the MPTs approximated the alpha set for the analyses, and (c) the statistical power advantage that MPTs provide over Bonferroni adjustments is important when using small sample sizes such as those that are typical of recent electrocortical studies.