Multivariate Analysis of Variance

The multivariate analysis of variance (MANOVA) is an extension of the univariate analysis of variance to multidimensional, or vector-valued, observations. The same experimental design or treatment layout applies to each of the observed response variables. The univariate assumption of a normal distribution is replaced by the multivariate normal distribution for the data vectors and the random error components in the mathematical model of the design. Keywords: covariance matrix; mean vectors; Roy's greatest root; Wilks' determinantal ratio; Lawley–Hotelling; Pillai trace; multivariate general linear model; union–intersection model