Variance-vs-mean plot of β and M. Panels A, B show the dependence of variance (SD in the upper panels and IQR in the lower panels) on mean values of β. Panels C, D report the same plots for M (logit transformation of β). Both show a bias of the dispersion especially when SD is used as variance indicator, either toward the middle (for β) or toward the 2 extremes (for M). Collectively these plots show that the logit transformation does not significantly improve heteroscedasticity.
Lu et al. BMC Medical Genomics 2014 7:12 doi:10.1186/1755-8794-7-12