Analysis of Variance: Repeated-Measures
R can be used to calculate univariate and multivariate statistics for repeated-measures ANOVA. This chapter covers a few examples on how to carry out these calculations. In experimental psychology, a repeated-measures design typically refers to collecting multiple data points from the same subject. These repeated assessments are made under different experimental conditions. We are interested in the within-subject effects – to what extent the experimental conditions affected the subjects’ responses. We are also interested in between-subject effects (e.g., gender differences) and the potential interactions between within- and between-subject effects (e.g., effects of experimental manipulations differed across males and females). These effects can be approached using univariate and multivariate statistics. The univariate statistics can be calculated by the function aov() with within-subject Error() terms. Multivariate statistics can be found using several methods. We will cover two, the manova() function and lm() function when Y is a matrix. The multivariate solution using lm() generates the Greenhouse–Geisser and Huynh–Feldt epsilons. The statistics theory behind the syntax can be found in the references, so detailed explanations are not provided here.