Motivation: It is well known that data deficiencies, such as coding/rounding errors, outliers or missing values, may lead to misleading results for many statistical methods. Robust statistical methods are designed to accommodate certain types of those deficiencies, allowing for reliable results under various conditions. We analyze the case of statistical tests to detect associations between genomic individual variations (SNP) and quantitative traits when deviations from the normality assumption are observed. We consider the classical analysis of variance tests for the parameters of the appropriate linear model and a robust version of those tests based on M-regression. We then compare their empirical power and level using simulated data with several degrees of contamination. Results: Data normality is nothing but a mathematical convenience. In practice, experiments usually yield data with non-conforming observations. In the presence of this type of data, classical least squares statistical methods perform poorly, giving biased estimates, raising the number of spurious associations and often failing to detect true ones. We show through a simulation study and a real data example, that the robust methodology can be more powerful and thus more adequate for association studies than the classical approach.