title: What is the significance of difference in phenotypic variability across SNP genotypes?
abstract: 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.
authors.affiliation: Department of Epidemiology and Biostatistics, School of Medicine, Case Western Reserve University, Cleveland, Ohio 44106, USA.
authors.forename: Xiangqing
authors.initials: X
authors.lastname: Sun
authors.forename: Robert
authors.initials: R
authors.lastname: Elston
authors.forename: Nathan
authors.initials: N
authors.lastname: Morris
authors.forename: Xiaofeng
authors.initials: X
authors.lastname: Zhu
mesh_terms: D000465:Algorithms; D000483:Alleles; D056426:Genetic Loci; D005838:Genotype; D006801:Humans; D008957:Models, Genetic; D010641:Phenotype; D020641:Polymorphism, Single Nucleotide
references.citation: Biometrics. 1968 Jun;24(2):277-93
references.pmid: 5683870
references.citation: Biometrics. 1947 Mar;3(1):39-52
references.pmid: 20240416
references.citation: Hum Hered. 2010;70(4):269-77
references.pmid: 21150212
references.citation: Ann Hum Genet. 1978 Jul;42(1):109-20
references.pmid: 686678
references.citation: Nature. 2012 Oct 11;490(7419):267-72
references.pmid: 22982992
references.citation: PLoS Genet. 2010 Jun 17;6(6):e1000981
references.pmid: 20585554
references.citation: Stat Med. 2013 Mar 30;32(7):1164-90
references.pmid: 23018341
references.citation: BMC Genet. 2010 Oct 13;11:92
references.pmid: 20942902
references.citation: BMC Genet. 2012 Jan 24;13:4
references.pmid: 22272569