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Behav Genet. 2009 Sep;39(5):580-95. doi: 10.1007/s10519-009-9281-0. Epub 2009 Jun 14.

Rank-based inverse normal transformations are increasingly used, but are they merited?

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Department of Biostatistics, Section on Statistical Genetics, University of Alabama at Birmingham, Ryals Public Health Building, Suite 327, Birmingham, AL, 35294, USA.


Many complex traits studied in genetics have markedly non-normal distributions. This often implies that the assumption of normally distributed residuals has been violated. Recently, inverse normal transformations (INTs) have gained popularity among genetics researchers and are implemented as an option in several software packages. Despite this increasing use, we are unaware of extensive simulations or mathematical proofs showing that INTs have desirable statistical properties in the context of genetic studies. We show that INTs do not necessarily maintain proper Type 1 error control and can also reduce statistical power in some circumstances. Many alternatives to INTs exist. Therefore, we contend that there is a lack of justification for performing parametric statistical procedures on INTs with the exceptions of simple designs with moderate to large sample sizes, which makes permutation testing computationally infeasible and where maximum likelihood testing is used. Rigorous research evaluating the utility of INTs seems warranted.

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