To Log or Not to Log: Bootstrap as an Alternative to the Parametric Estimation of Moderation Effects in the Presence of Skewed Dependent Variables

Abstract

When gross deviations from parametric assumptions are observed, conventional data transformations are often applied with little regard for substantive theoretical implications. One such transformation involves using the logarithm of positively skewed dependent variables. Log transformations were shown to severely decrease estimates of true moderator effects using moderated regression procedures in a Monte Carlo simulation. Estimates of moderator effect sizes were substantially better estimates of the true latent moderator effect (i.e., larger by a multiple of 2.6 to 534) when estimated using a simple percentile bootstrap procedure in the original, positively skewed data. Conclusions with regard to the presence or absence of a true moderator effect using a simple bootstrap procedure were unaffected by the violation of parametric assumptions in the original, positively skewed data. In contrast, moderated regression analysis performed on a log-transformed dependent variable severely increased Type-II error. Implications are drawn for applied psychological and management research.