Analysis of interaction effect between within- and between-subject factors in repeated measures analysis of variance for longitudinal data

Repeated measures analysis of variance (RM-ANOVA) is a specialized form of analysis of variance used for analyzing data involving repeated measurements, such as longitudinal data commonly encountered in anesthesia and pain medicine research. When data are collected at multiple time points across more than one group, RM-ANOVA evaluates the between-subject (group) effect, within-subject (time) effect, and interaction between these two factors. The group-by-time interaction effect indicates whether changes in an outcome variable over the study period differ among groups. Analyzing interaction contrasts between specific time points is particularly useful for identifying intervals where this interaction effect is significant. For instance, if an outcome variable is measured at multiple time points in two groups, the interaction contrast for any two time points represents the difference between the change in the outcome variable over that interval in one group and the corresponding change in the other group. An independent two-sample Student's t-test can then compare these differences to determine the statistical significance of the group-by-time interaction for the selected time points. Thus, incorporating interaction contrast analysis into RM-ANOVA enhances the interpretation of longitudinal data by pinpointing specific time intervals where significant interactions occur. Keywords: Analysis of variance; Data interpretation; Linear models; Longitudinal studies; Research design; Time factors.