Re: 2way mixed ANOVA significant interaction, but main effects not significant. What does this mean

Posted by Bruce Weaver on Apr 27, 2016; 5:32pm
URL: http://spssx-discussion.165.s1.nabble.com/2way-mixed-ANOVA-significant-interaction-but-main-effects-not-significant-What-does-this-mean-tp5732027p5732051.html

Another way to handle heterogeneity of variance is to estimate the model via MIXED, allowing for heterogeneous group variances.  See below.

* ANCOVA with DV = post, covariate = pre  estimated in the usual way.

UNIANOVA post  BY grp  WITH pre
  /PRINT = parameter
  /EMMEANS = table(grp)
  /DESIGN = pre grp
.

* Same model via MIXED.

MIXED post BY grp WITH pre
 /FIXED=pre grp | SSTYPE(3)
 /PRINT=SOLUTION TESTCOV
 /EMMEANS = tables(grp)
.

* Now include /REPEATED sub-command to
* allow for heterogenous group variances.

MIXED post BY grp WITH pre
 /FIXED=pre grp | SSTYPE(3)
 /PRINT=SOLUTION TESTCOV
 /REPEATED=grp | SUBJECT(ID) COVTYPE(DIAG)
 /EMMEANS = tables(grp)
.

HTH.

Rich Ulrich wrote

There is a ton of literature on the subject of analyzing change.  Unfortunately,
much of it is not very well informed.  On a quick Google, I found that the first
answer at the URL below (the Reply referencing Senn) gives a pretty good overview,
plus references.  (The Reply-er endorses using ANCOVA for controlled studies.)

http://stats.stackexchange.com/questions/3466/best-practice-when-analysing-pre-post-treatment-control-designs

I will add:
On assumptions:  It is nice to have (1) equal variances everywhere, (2) equal means at Pre, and
(3) a shared regression line.  Given those, it is hard to fault the ANCOVA.  In my experience,
"unequal variances" are sometimes fixed by suitable transformation of the criterion.  But the
failure of the assumptions is why (at least, in my off-hand thoughts here) you might want to
analyze the Outcome while ignoring Pre, or analyze the simple change score.  Unequal-at-Pre
raises serious logical conundrums, at times, and regression-not-to-the-shared-mean  on top of
unequal-at-Pre puts you into statistical complication, and controversy.  The latter was the case
of analyzing long-term outcome for Headstart vs. other students -- where Expected outcome with
no intervention, according to other experience, would be that the lower-achieving target cases
should fall further and further behind.  

--
Rich Ulrich

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