My understanding is that, in general, continuous variables offer more power over dichotomous variables. For example, doing a between groups (e.g., men vs. women) t-test testing height would be better than doing a chi-square test (e.g., men vs. women) testing height with dichotomous groups (e.g., tall vs. short).
I am interested in testing moderation, namely, whether depression (moderator) affects outcomes differentially across two different anxiety treatments. I think depressed people will do better in one treatment over the other.
I was going to test for moderation using a continuous depression variable, but landed upon the following statement (http://davidakenny.net/cm/moderation.htm): "Power for tests of moderation is very low when one or both of the variables are continuous (McClelland & Judd, 1993)." I took a look at McClelland & Judd, 1993 and could not find the rational for this. I am now wondering whether I should split depression into high/low groups and examine slopes in each group rather than test for interaction using a continuum
Do dichotomous or continuous moderators lead to most statistical power when testing interactions?