The effect of nonnormality on near-replicate lack-of-fit tests

We examine the effect of nonnormality on the distributions of near-replicate lack-of-fit F-tests. We show that when the number of clusters is large, the distributions of the lack-of-fit tests depend on the kurtosis of the error distribution, and that heavy-tailed error distributions can inflate significantly the sizes of the tests. This behaviour is also evident in small samples, where some lack-of-fit tests are clearly more affected than others by nonnormality. Two modifications of the F-tests are suggested to eliminate the effect of the kurtosis on the limiting null distributions, and their behaviour is studied for small samples.