Multivariate Analysis of Variance for a Special Covariance Case

Multivariate analysis of variance tests are developed for situations where the underlying covariance structure is uniform (equal variances and covariances) in terms of statistics analogous to Hotelling's T 2 and T 2 0. Extensions are made to several populations as well as to blocks 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 F 1,n–1 ratios which may be contrasted with the T 2 statistic proportional to F 2,n–2 used in the situation where the variances are not assumed equal.