A new test for multivariate normality and homoscedasticity

Douglas M. Hawkins

Research output: Contribution to journalArticlepeer-review

78 Scopus citations


Given data Xijj = 1 to nii = 1 to g, one may wish to test whether the Xij are normal with common covariance matrix. Letting Xi. denote the mean of the ith group and S the pooled covariance matrix, the quantities Vij = (Xij – Xi.)′S−1(Xij – Xi.) are used in the test. The exact null distribution of Vij is noted, and the Anderson-Darling statistic is proposed for testing whether the data fit this null distribution. The new test has acceptable power, is flexible, and is easily implemented. © 1981 Taylor & Francis Group, LLC.

Original languageEnglish (US)
Pages (from-to)105-110
Number of pages6
Issue number1
StatePublished - 1981


  • Discriminant analysis
  • Homoscedasticity
  • Test for normality


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