DOI: 10.1101/498931Dec 20, 2018Paper

Violating the normality assumption may be the lesser of two evils

BioRxiv : the Preprint Server for Biology
Ulrich Knief, Wolfgang Forstmeier

Abstract

Researchers are often uncertain about the extent to which it may be acceptable to violate the assumption of normality of errors, which underlies the most-frequently used tests for statistical significance (regression, t-test, ANOVA, and linear mixed models with Gaussian error). Here we use Monte Carlo simulations to show that such Gaussian models are remarkably robust to even the most dramatic deviations from normality. We find that P-values are generally reliable if either the dependent variable Y or the predictor X are normally distributed and that bias only occurs if both are heavily skewed (resulting in outliers in both X and Y). In the latter case, judgement of significance at an α-level of 0.05 is still safe unless sample size is very small. Yet, with more stringent significance criteria as is used when conducting numerous tests (e.g. α = 0.0001) there is a greater risk of making erroneous judgements. Generally we conclude that violating the normality assumption appears to be the lesser of two evils, when compared to alternative solutions that are either unable to account for levels of non-independence in the data (most non-parametric tests) or much less robust (e.g. Poisson models which require control of overdispersion ...Continue Reading

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