Multivariate analysis of variance (MANOVA)

Abstract

St»hle, L. and Wold, S., 1990. Multivariate analysis of variance (MANOVA). Chemometrics and Intelligent Laboratory Systems, 9: 127–141. In this tutorial we illustrate the practical use of multivariate analysis of variance (MANOVA). MANOVA concerns the situation where several response variables, e.g. the high-performance liquid chromatographic retention times of a number of compounds, have been measured in a set of experiments in which one or several factors (treatments) have been changed (e.g. solvent, stationary phase). The experiment is repeated a number of times for each combination of factors. MANOVA is then used to test whether the changes in the factors have any effect on the response variables. The mathematical models underlying one-factor MANOVA and crossed two-factor MANOVA are discussed in some detail. Hypothesis tests based on generalization of the univariate F-test are discussed and compared. Follow up, using Hotelling's T 2 -test, univariate ANOVA and discriminant variate analysis, is described. The assumptions of MANOVA are discussed in some detail. Alternative approaches are discussed, in particular partial least squares analysis (PLS) corresponding to MANOVA is put forward as a useful method for situations in which the assumptions of MANOVA are not fulfilled.