Women have Relatively Larger Brains than Men: A Comment on the Misuse of General Linear Models in the Study of Sexual Dimorphism

Abstract

General linear models (GLM) have become such universal tools of statistical inference, that their applicability to a particular data set is rarely questioned. These models are designed to minimize residuals along the y-axis, while assuming that the predictor (x-axis) is free of statistical noise (ordinary least square regression, OLS). However, in practice, this assumption is often violated, which can lead to erroneous conclusions, particularly when two predictors are correlated with each other. This is best illustrated by two examples from the study of allometry, which have received great interest: (1) the question of whether men or women have relatively larger brains after accounting for body size differences, and (2) whether men indeed have shorter index fingers relative to ring fingers (digit ratio) than women. In depth analysis of these examples clearly shows that GLMs produce spurious sexual dimorphism in body shape where there is none (e.g. relative brain size). Likewise, they may fail to detect existing sexual dimorphisms in which the larger sex has the lower trait values (e.g. digit ratio) and, conversely, tend to exaggerate sexual dimorphism in which the larger sex has the relatively larger trait value (e.g. most sexually selected traits). These artifacts can be avoided with reduced major axis regression (RMA), which simultaneously minimizes residuals along both the x and the y-axis. Alternatively, in cases where isometry can be established there are no objections against and good reasons for the continued use of ratios as a simple means of correcting for size differences.