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Biometrika 1980 67(2):485-488; doi:10.1093/biomet/67.2.485
© 1980 by Biometrika Trust
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MISCELLANEA

A normal approximation for the distribution of the likelihood ratio statistic in multivariate analysis of variance

GOVIND S. MUDHOLKAR and MADHUSUDAN C. TRIVEDI

Department of Statistics, University of Rochester New York
Pharmaceutical Division, Pennwalt Corporation, Rochester New York

A normal approximation to the null distribution of the likelihood ratio statistic for testing the multivariate general linear hypothesis is developed. This approximation is compared with the well-known approximations due to Box (1949) and Rao (1948). It is found that the approximations due to Box and Rao deteriorate as the number of variables or, in the terminology of one-way classification, the number of groups increases. Moreover, both approximations give poor results when the number of degrees of freedom for error is small. The normal approximation is nowhere strikingly poor.

Key Words: Likelihood ratio statistic • Multivariate analysis of variance • Normal approximation.


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