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

Edward J. Bedrick, Ronald Christensen

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)471-484
Number of pages14
JournalCanadian Journal of Statistics
Issue number3
StatePublished - Sep 1999
Externally publishedYes


  • Analysis of variance
  • Between clusters
  • Pure error
  • Regression analysis
  • Regression diagnostics
  • Replication
  • Within clusters

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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