A new test for multivariate normality and homoscedasticity

Douglas M. Hawkins

doi:10.1080/00401706.1981.10486244

A new test for multivariate normality and homoscedasticity

Douglas M. Hawkins

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

84 Scopus citations

Abstract

Given data X_ijj = 1 to n_ii = 1 to g, one may wish to test whether the X_ij are normal with common covariance matrix. Letting X_i. denote the mean of the ith group and S the pooled covariance matrix, the quantities V_ij = (X_ij – X_i.)′S⁻¹(X_ij – X_i.) are used in the test. The exact null distribution of V_ij 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 language	English (US)
Pages (from-to)	105-110
Number of pages	6
Journal	Technometrics
Volume	23
Issue number	1
DOIs	https://doi.org/10.1080/00401706.1981.10486244
State	Published - 1981

Keywords

Discriminant analysis
Homoscedasticity
Test for normality

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AB - 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.

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A new test for multivariate normality and homoscedasticity

Abstract

Keywords

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