Premium
The effect of nonnormality on near‐replicate lack‐of‐fit tests
Author(s) -
Bedrick Edward J.,
Christensen Ronald
Publication year - 1999
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3316105
Subject(s) - kurtosis , replicate , statistics , mathematics , null hypothesis , limiting
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.