Recurring errors in studies of gender differences in variability

The past quarter century has seen a resurgence of research on the controversial topic of gender differences in variability, in part because of its potential implications for the issue of under- and over-representation of various subpopulations of our society, with respect to different traits. Unfortunately, several basic statistical, inferential, and logical errors are being propagated in studies on this highly publicized topic. These errors include conflicting interpretations of the numerical significance of actual variance ratio values; a mistaken claim about variance ratios in mixtures of distributions; incorrect inferences from variance ratio values regarding the relative roles of sociocultural and biological factors; and faulty experimental designs. Most importantly, without knowledge of the underlying distributions, the standard variance ratio test statistic is shown to have no implications for tail ratios. The main aim of this note is to correct the scientific record and to illuminate several of these key errors in order to reduce their further propagation. For concreteness, the arguments will focus on one highly influential paper.