A test can be said to ‘detect' an alternative hypothesis only if its power against this alternative exceeds its size. We use this principle to define the implicit null and alternative for a test. We analyze the performance of several tests for location and scale parameters

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...