Assumptions: What is assumed for ANCOVA, along with homogeneity of slopes,
is the homogeneity of initial means. Neither is apt to be a problem for designed
studies where the group membership was randomized.
I thought about tossing in a comment about the need for the Pre means to be equal
(or you can't do valid inference), but I didn't give a thought to the slopes. It is not
that the assumption does not matter: but I have seldom seen it violated, and I have
never seen it violated with equal means for Pre, and Pre as covariate -- except, maybe,
if that was an expected part of a weird outcome. If the slopes are not readily *assumed*
to be equal, then I sort of expect that the "unequal slopes" might be a major aspect
of whatever is being concluded. - Maybe I should leave further commentary on actually
using "unequal slopes" to people who have somehow found them useful, instead of
a symptom to be cured. I can say more about the bad symptom.
When means of the covariate are unequal, there are usually other problems.
Covariance is problematic when the groups are Observational, especially when
they are created by the high/low dichotomy of some variable correlated with the
covariate. It is problematic for inference even when there are *no* scaling problems
on the measures, such as basement/ ceiling effects. (Combining those problems
will often create "unequal slopes".)
It is easy to make mistakes with unequal Pre, even with homogeneous regressions.
It is not "fair", for instance, to conclude that the high-scoring group "did worse" when
the plots show that high and low groups both merely "regressed toward the mean" as
any statistician should expect.
--
Rich Ulrich
> Date: Thu, 5 Jun 2014 09:08:30 -0400
> From:
[hidden email]> Subject: Re: Simple Main Effects Pairwise Comparisons vs Univariate Tests
> To:
[hidden email]>
> Has somebody declared there is no longer any need to satisfy the homogeneity of slopes assumption before ANCOVA? I keep seeing presentations and publications where everything is “adjusted” for covariates like “pre” or “age” and there is no mention of the test to see if group slopes are NSD. How can one adjust means from a common regression line when subgroups may have completely opposing slopes?
>
> I did check with a former stats consultant faculty at U. Waterloo — now retired, and she was rather scathing about what she saw as cavalier application of ANCOVA for “adjustment” of group means. I have even seen one solution for situations where slopes are sig. different (in another forum): “just don’t call it ANCOVA” !
>
> I’d be interested in feedback, since some colleagues stuck my name on a ms and were surprised when I queried them about the pre-condition for ANCOVA. Am I olde fashioned or misinformed?
>
> Ian Martin
> Ian D. Martin, Ph.D.