Fig. 4

Multivariate sex differences and similarities estimated from Pclass scores in the raw and PCP datasets. A and E Scaled density function for the males (blue) and females’ (red) distributions of the Pclass scores in the raw and PCP datasets. Within each panel, the percent of overlap (O) as well as the probabilities of superiority for males and females (PS) as well as the p-value associated and an R² effect size index derived from the comparison of these PS values using Cliff’s delta are provided. Panels B and F Cumulative density functions (CDF) of Pclass scores of males (blue) and females (red), along with the tenths of these distributions (colored rectangles), the decile values (vertical lines). The size of the estimated sex differences in these deciles is also included (see further details of these comparisons in Additional file 1: Table S3C). C and G Scaled density functions of all the pairwise differences between females and males. Within each density plot, two different areas are colored according to the direction of these differences (F > M, red; M > F, blue) and, at the top of the panel, the percent of pairwise differences favoring the reference sex category (males in the raw dataset, females in the PCP dataset) as well as its 95% CI are included. Each of these two panels also includes the CDFs of pairwise differences’ distributions (black line), the tenths of these distributions (colored rectangles) and the size of the estimated deciles’ differences. D and H Scatterplots depicting the bivariate relationship (quantified by a robust analog of Pearson’s r correlation index) between the Pclass and TIV scores (M = males, F = females)