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Probing Moderation Analysis in Two-Instance Repeated-Measures Designs

Methods for testing and probing interactions in betweenparticipant designs are well known; however, how to handle these effects when one variable involved is a within-participant factor is underdeveloped. Twoinstance repeated-measures designs, where each participant is measured on the outcome variable in each of two conditions, are common in psychology. Judd,McClelland, and Smith (1996) propose a method for estimating and conducting inference on an interaction between a withinparticipant factor and a between-participant moderator using linear regression. One way to understand interactions is by using probing analyses to estimate and conduct inference on conditional effects, the relationship between two variables (e.g., X and Y) conditional on a third (e.g., M). I describe how to probe interactions in a two-instance repeated-measures design using both the pick-a-point approach and the Johnson-Neyman procedure. The picka-point approach can be used to estimate and conduct inference on the effect of a focal predictor on an outcome at a specific value of a moderator. The Johnson-Neyman procedure defines the regions along the range of themoderator where the predictor and outcome variable are significantly related. I provide an example using data from clinical psychology examining the efficacy of behavioral treatment for chronic pain as moderated by baseline inflammation (Lasselin et al., 2016). Figure 1 provides a visualization of the results of the Johnson-Neyman procedure. In this figure the effect of the focal predictor (behavioral treatment) on the outcome (pain) is significant and positive when the moderator (inflammation) is below −0.626 and non-significant when the moderator is above −0.626 (α = 0.05). This analysis suggests that the treatment is only effective for those relatively low on baseline inflammation. To ease the computational burden for