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

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