Testing Normality in Designs With Many Parameters

Goodness-of-fit tests are proposed for the assumption of normality of random errors in experimental designs where the variance of the response may vary with the levels of the covariates. The exact distribution of standardized residuals is used to make the probability integral transform for use in tests based on the empirical distribution function. A different mean and variance is estimated for each level of the covariate; corresponding large sample theory is provided. The proposed tests are robust to a possible misspecification of the model and permit data collected from several similar experiments to be pooled to improve the power of the test.