Tests for Normality Based on Robust Regression Residuals

We consider the effects of using residuals from robust regression in place of OLS residuals in test statistics for the normality of the errors. We find that this can lead to substantially improved ability to detect lack of normality in suitable situations. Using simulations, we find that situations where a small subpopulation exhibits characteristics different from the main population are those ideally suited to the use of robust normality tests. We give several examples from the literature to show that these type of situations arise frequently in real data sets