Multivariate Analysis of Variance for Simple Designs

Abstract

The analysis of variance is a well known tool for testing how treatments change the average response of experimental units. The essence of the procedure is to compare the variation among means of groups of units subjected to the same treatment with the within treatment variation. If the variation among means is large with respect to the within group variation we are likely to conclude that the treatments caused the variation and hence we say the treatments cause some change in the group means. The usual analysis of variance checks how far apart the group means are in a single scale of measurement. Almost all researchers are interested in how the treatments affect more than one characteristic (variable) of their experimental units. A typical usage of such data is to run a standard analysis of variance on each variable. This procedure can be very misleading when trying to interpret the results. Most of the time there are strong correlations among these variables and hence if one variable tests significant the others will also. The multivariate analysis of variance provides a way of performing valid tests regardless of the correlation structure among the variables of interest.

Cite this paper

@article{chen2021multivariate,
  title = {{Multivariate Analysis of Variance for Simple Designs}},
  author = {Chen, Yinyin},
  journal = {Digital Commons - USU (Utah State University)},
  year = {2021},
  doi = {10.26076/19b0-2b21}
}

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