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Analysis of Variance, Multivariate (MANOVA)

Statistical Theory and Methods

  1. Martin Bilodeau

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.vnn075

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Bilodeau, M. 2013. Analysis of Variance, Multivariate (MANOVA). Encyclopedia of Environmetrics. 1.

Author Information

  1. Université de Montréal, Montréal, Canada

Publication History

  1. Published Online: 15 JAN 2013


A designed experiment is set up in which the system studied is under the control of an investigator. The individuals, the treatments, and the variables measured are decided by the investigator. In a clinical trial, patients satisfying some eligibility criteria are assigned at random, either to a new treatment or to a placebo. Patients are followed for some time and a few responses are recorded for each patient. In an agricultural experiment, a field is divided into plots of shape and size determined by the investigator. The plots are assigned at random one among a few treatments which could be, for example, different fertilizers. The variables measured on each plot could be the yields of some crops. The general objective of a designed experiment is to assess the effects of different treatments on the responses. These effects are evaluated by statistical estimates and confidence intervals of the magnitude of the differences between treatments. The estimates should avoid biases and the random errors should be minimized as much as possible. The statistical methodology used to analyze such designed experiments in which there are several responses is termed MANOVA, an acronym for multivariate analysis of variance.


  • linear model;
  • factor;
  • experiment