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On the Effects of Moderate Multivariate Nonnormality on Roy's Largest Root Test

A. W. Davis
Journal of the American Statistical Association
Vol. 77, No. 380 (Dec., 1982), pp. 896-900
DOI: 10.2307/2287324
Stable URL: http://www.jstor.org/stable/2287324
Page Count: 5
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On the Effects of Moderate Multivariate Nonnormality on Roy's Largest Root Test
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Abstract

The asymptotic distribution of Roy's largest root statistic in multivariate Edgeworth populations is expanded to terms of the first order. To this order, the effects of nonnormality are expressed by Mardia's measures of multivariate skewness and kurtosis, together with a supplementary skewness measure. Tables of corrections to the nominal significance level are presented for the k-sample MANOVA situation. Comparison with simulation results indicates that the correction terms provide a useful indication both of the magnitude and the direction of the effect of nonnormality on the nominal 5 percent Type I error, even when the underlying population is not well represented by an Edgeworth expansion, provided that the skewness and kurtosis are not too large.

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