Repeated measures analysis of variance: application to tree research

A discussion of model construction, univariate versus multivariate solutions, and statistical assumptions is motivated by examples from a tree physiology experiment, and several examples from the forestry literature are reviewed.

Abstract

Repeated measures data occur in a wide variety of experimental situations and are often analyzed without full consideration of the statistical issues involved. In this paper, a discussion of model construction, univariate versus multivariate solutions, and statistical assumptions is motivated by examples from a tree physiology experiment. In addition, several examples from the forestry literature are reviewed. It is hoped that this discussion will help scientists with little statistical training to become aware of the different analyses available and perhaps to recognize the associated models in their own research. The examples range from a simple repeated measures design with one within-subject factor and no between-subjects factors to a more complex design involving multiple within-subject and between-subjects factors. The modelling approach used here permits a straightforward comparison between the univariate and multivariate solutions. Although no single approach is consistently best, the multivariate approach is always appropriate and provides the same interpretations as the univariate approach. However, when appropriate assumptions such as sphericity are met, power considerations tend to favor the more traditional univariate analysis.