In the presence of a significant group effect AND a significant interaction, one shouldn't focus SOLELY on anything: you need somehow to include everything that's going on in your interpretation.
First, draw pictures. Display the plot of response variable (ordinate) vs. covariate (abscissa), showing the several regression lines. (Don't include the scatterplot of data at the moment, it'll only confuse things. But sometime you should examine that scatterplot, with regression line superimposed, for each group separately, to see (inter alia) whether there is evidence that the model is still inadequate -- e.g., whether there may be curvature in the relationship.) Once you see what the lines are doing, you'll have a clearer notion of what's important to report. If all the lines have much the same range on the covariate, the interaction means that they're not all parallel. If the lines are distant each from the others, and don't cross, it's likely that the group effect is, as one might say, sturdy (or robust), and doesn't depend on the value of the covariate; here the modelling of interaction hasn't complicated things much and probably has reduced the error variance, making the analysis more sensitive to group effects than would have been the case without the interaction term(s). If the lines meet, or cross, (or even if they come close to meeting), then there is a range of values of the covariate for which the groups do not differ (in the general vicinity of the meeting point; this may be more complicated to describe, but will be easy enough to see, if you have more than two groups, since nobody can guarantee that the meeting point for lines A and B is anywhere near the meeting point for lines B and C, etc.). If the lines do cross (some of them, anyway), then there are probably regions of the covariate for which group A > group B, group A < group B, and group A = group B approximately (in the sense of "no significant difference"). In general, as for any interaction, you need to start with the fact of interaction, display results so you can see them (graphically, that usually means), and then see how the interaction modifies the main effect(s) which you would also like to interpret. HTH -- Don Burrill. On 22 Sep 2003, emma wrote in part (edited): > When running an ancova - I have a significant effect for both my > between grps variable (which we will call group) - and an interaction > between the covariate and grp (indicating lack of homogeneity of > regression slopes). I have heard conflicting things re: > interpretation i.e. should I focus solely on the interaction as this > would also explain any significant main effect for group -or whether > this main effect already has the covariate partialled out and so would > account for some unique variance too. ----------------------------------------------------------------------- Donald F. Burrill [EMAIL PROTECTED] 56 Sebbins Pond Drive, Bedford, NH 03110 (603) 626-0816 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
