What is the significance of difference in phenotypic variability across SNP genotypes?

We studied the general problem of interpreting and detecting differences in phenotypic variability among the genotypes at a locus, from both a biological and a statistical point of view. The scales on which we measure interval-scale quantitative traits are man-made and have little intrinsic biological relevance. Before claiming a biological interpretation for genotype differences in variance, we should be sure that no monotonic transformation of the data can reduce or eliminate these differences. We show theoretically that for an autosomal diallelic SNP, when the three corresponding means are distinct so that the variance can be expressed as a quadratic function of the mean, there implicitly exists a transformation that will tend to equalize the three variances; we also demonstrate how to find a transformation that will do this. We investigate the validity of Bartlett's test, Box's modification of it, and a modified Levene's test to test for differences in variances when normality does not hold. We find that, although they may detect differences in variability, these tests do not necessarily detect differences in variance. The same is true for permutation tests that use these three statistics.