Within Groups Designs: Inferences Based on A Robust Nonparametric Measure of Effect Size

Abstract

AbstractThe paper deals with a robust, projection-type measure of effect size when comparing $$J>1$$ J > 1 dependent groups. The measure of effect size is scale invariant and does not assume or require that the underlying multivariate distribution is elliptically contoured. By design the measure of effect size is equal to zero when the corresponding measures of location are equal. A simple method is suggested for testing the hypothesis that this effect size is zero. The method is readily extended to comparing K-variate distributions associated with two independent groups. One of the main goal is to report simulation results on how well the method performs in terms of controlling the Type I error probability. The method, when comparing independent groups, is used to reveal new insights into the connection between depression and cortisol levels.