Statistical Analysis of Experiments with Repeated Measurements

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Abstract Experiments with data collected at several points in time on the same sampling unit are called experiments with repeated measurements or repeated measures experiments. The sampling unit is usually a plant in a greenhouse experiment or a plot in a field experiment. Objectives are usually to investigate response over time, often growth of a plant, to several treatments. These experiments have been called split-plot in time experiments (Steel and Torrie, 1960) because data are often analyzed in a split-plot fashion, taking time as the subplot factor. The term “split-plot” in reference to experiments with repeated measurements has fallen into disfavor (Damon and Harvey, 1987; Little and Hills, 1978; Snedecor and Cochran, 1980; Steel and Torrie, 1980; Yates, 1982). This change is in part due to the fact that experiments with repeated measurements are not true split-plot experiments because time is not an experimental factor whose levels are randomly assigned to subplot units. Therefore, mathematical conditions required for validity of the split-plot type of analysis of variance might not hold. Furthermore, objectives of repeated measures experiments are usually different from objectives of split-plot experiments. In the general statistical literature, the expression “univariate repeated measures analysis of variance” usually refers to the split-plot type of analysis of variance, and the term “subject” refers to a sampling unit. Mainplot and subplot portions of an analysis of variance in the split-plot vernacular are more generally referred to as the between- and within-subjects portions of the analysis, respectively. Computer programs, such as SAS GLM and ANOVA (SAS Institute, 1985) use the terminology of the general literature.