Savic and Lindström (1) claim to have discovered significant differences in cerebral asymmetry and functional connectivity between homo- and heterosexual subjects. Unfortunately, the statistical analysis they present is strongly undermined by an inappropriate choice of variables. For example, in their analysis of cerebral asymmetry, the authors measure right and left cerebral volumes (R and L, respectively) and use these to construct an “asymmetry index” for each subject defined by V = (R − L)/(R + L) ≡ X/Y; they call this index AI. No details about the distribution of R and L are given in ref. 1, but if we assume that they are (correlated) bivariate normal variables then X = R − L and Y = R + L are in fact uncorrelated normal variables for which the exact ratio distribution is known (2) to have very long “tails.” This is a general problem with ratio distributions. Standard statistical methods, which assume normal distributions with rapidly decreasing tails, are not generally appropriate for this type of variable. Unfortunately, Savic and Lindström (1) seem unaware of this difficulty and proceed to use a standard t test and ANOVA: the P values emerging from this analysis are meaningless if the variables involved are ill conditioned.
One way to work around this problem is to use a different variable, such as U = (μx − μyV)/(σx2 + σy2V2)1/2, which is normally distributed (2) if X and Y are independent normal variables with means μx and μy and variances σx2 and σy2. Standard methods applied to U would give much more conclusive results than those obtained by using V. An alternative is to use the median instead of the mean (3).
Either way, a much more convincing statistical analysis is needed to establish whether the differences reported in ref. 1 are indeed significant.
Author contributions: P.C. wrote the paper.
The author declares no conflict of interest.
