Testing for normality

  • G. Barrie Wetherill
  • P. Duncombe
  • M. Kenward
  • J. Köllerström
  • S. R. Paul
  • B. J. Vowden
Part of the Monographs on Statistics and Applied Probability book series (MSAP)


Before setting out on a discussion of tests for normality, we must consider briefly the consequences of non-normality. Clearly, if we know that the distribution of the disturbances is, say gamma, then a different model, and different methods, should be used than those discussed in this volume. However, in many situations we may have at least ‘near’ normality, and we wish to know how serious the effect of deviation from normality might be. Box and Watson (1962) showed that this depends on the distribution of the explanatory variables. If the explanatory variables can be regarded as approximately normal, then the F-test for multiple regression is insensitive to non-normality. If the explanatory variables cannot be so regarded, then there can be a substantial effect on the ‘F-test’ distribution.


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Copyright information

© G. Barrie Wetherill 1986

Authors and Affiliations

  • G. Barrie Wetherill
    • 1
  • P. Duncombe
    • 2
  • M. Kenward
    • 3
  • J. Köllerström
    • 3
  • S. R. Paul
    • 4
  • B. J. Vowden
    • 3
  1. 1.Department of StatisticsThe University of Newcastle upon TyneUK
  2. 2.Applied Statistics Research UnitUniversity of Kent at CanterburyUK
  3. 3.Mathematical InstituteUniversity of Kent at CanterburyUK
  4. 4.Department of Mathematics and StatisticsUniversity of WindsorCanada

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