Multivariate Analysis of Variance for a Special Covariance Case
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1963-09
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Abstract
Multivariate analysis of variance tests are developed for situations where the underlying covariance structure is uniform (equal variance! and covariances) in terms of statistics analogous to Hotelling's T2 and T20. Extensions are made to several populations as well as to blocki of uniform covariance matrices. A special case, which is typical of the test procedures given here, is the problem of testing whether the mean vector of a bivariate normal distribution is equal to some specified vector based on n observations. The uniform structure assumes that the two unknown variances are equal though the correlation is arbitrary. The testing procedure leads to a statistic U which is distributed as the sum of two independent F1,n-1 ratios which may be contrasted with the T2 statistic proportional to F2,n-2 used in the situation where the variances are not assumed equal.
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American Statistical Association Journal, September 1963