Thomas,
I'd have to look it up to remember the precise details (b/c I never use
SPSS or ANOVA, the latter b/c it seems to me that the equivalent
regression analyses subsume ANOVA & are at least as intuitive &
direct... But I digress...)
I'd have to look up the precise details, but I believe what's happening
here is related to how ANOVA demeans the variables in the process of
"analyzing variances", which are (X-E(X))^2 type things. Try the
dummy-variable interaction regression model with DEMEANED "condition"
and/or "covariate" (I think "condition" and "covariate" are essentially
ANOVA-speak for regressors, right?). That should line up better. (A sign
of a coefficient still seems off in what you reported, though, perhaps
one of the variables has its polarity reversed from your ANOVA to your
regression? Either by you unwittingly or by SPSS for some reason "to
help you"?)
Anyway, the confusion relates to the mean-shifting in ANOVA, I'm
virtually certain. See Brambor, Clark, & Golder in PA a couple of years
ago on interaction terms, or Cindy Kam's and my little book on them last
year. (There's a section in our book that show's the math proving the
substantive identity of the demeaned ("centered") & non-centered model.)
Hope this helps,
Rob
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-----Original Message-----
From: Political Methodology Society [mailto:[log in to unmask]] On
Behalf Of Thomas Klausch
Sent: Thursday, August 28, 2008 11:05 AM
To: [log in to unmask]
Subject: [POLMETH] SPSS treatment of factors and covariates in UNIANOVA
(GLM) commands
Hello,
Recently, I encountered an interesting problem in SPSS, for which I
could not find any solution so far. Following a short problem
description. Any explanations would be greatly appreciated.
I am analyzing results of an experiment using one covariate. The
condition has only two steps and is coded dummy (0 - 1). The covariate
is assumed to be metric. Additionally an interaction effect between both
is to be modeled. For this I am using the UNIANOVA command syntax
specifying
"Dependent variable BY condition WITH covariate"
In order to model the interaction effect I furthermore specify
"Design = Condition covariate condition*covariate"
Now, I am interested in the results of the parameter estimates, which
are
Condition: b=.260 (n.s.)
Covariate: b=0.150 (n.s.)
Interaction: b=0.136 (p<.05)
This is the first part of the analysis. Consequently, and here the
problem starts, I thought that since I coded the condition as a dummy, a
regression analysis should yield the same results. Put differently,
using the condition as a covariate in the same model should yield the
same results. Thus I specified
UNIANOVA
Dependent variable WITH condition covariate.
In order to model the interaction effect, I specified again "Design =
Condition covariate condition*covariate"
Again, I am looking at the parameter estimates and their significance
levels. Now the results change 'significantly' in that
Condition: b=-0.260 (n.s.)
Covariate: b=0.150 (p<.01 !!!)
Interaction: b=-.136 (p<.05)
Please note that not only the level of significance but also all of the
parameter estimates change. It should be added that using the syntax
command REGRESSIONS and creating a new interaction variable
condition*covariate would yield the exact same results as the second
procedure.
I couldn't find an explanation for the deviation of the first and second
procedure. I actually believed that there shouldn't be any difference
between the two procedures. Could anybody please explain the statistical
/ mathematical difference between both procedures and why I arrive at
different results?
Thank you very much.
Kind regards
Thomas Klausch
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