|Date: ||Fri, 11 Feb 2005 08:02:03 -0500|
|Reply-To: ||Yiftach Gordoni <gordoni@POST.TAU.AC.IL>|
|Sender: ||"SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>|
|From: ||Yiftach Gordoni <gordoni@POST.TAU.AC.IL>|
|Subject: ||marginal means' comparison and main effects' test in anova|
In the SAS onlinedoc on chapter 12, pp. 168 it is written that: "for models
involving interactions..., in the absence of a priori parametric
restrictions, it is not possible to obtain a test of a hypothesis for the
main effect free of parameters of higher-level effects with which the main
effect is involved".
But, as I understand it, in a 2x2 design, for example, despite the infinite
mathematical solutions for the interaction effects (and also for the main
effects), most of these solutions cannot be treated as a possible solutions
because, by definition, the interaction effects must be independent from
the main effects of each of the two variables, and the only pattern for the
interaction effects that fits this statistical demand is one in which the
two effects on the main diagonal have the same value, and the two other
effects, on the minor diagonal, have the same value. only patterns of this
kind can fulfill the demand for zero correlations between the interaction
and main effects, and can be consider as a possible solutions.
So if we take, for example, the following four means: 14,17,19,28, we can
say that a possible population's parameters for them can be: 16 for the
constant, -3,-3,5,5 for A, -2,4,-2,4 for B, and 3,0,0,3 for the
interaction. for this reasons, the estimates we gets from sas (which use
the "set to zero" constraints): 28 for the constant, -11 -11 0 0 for A, -9
0 -9 0 for B, and 6 0 0 0 for the interaction, cannot be consider a
possible solution, because the interaction effects in it correlates with
the main effects (r=-.577 with both main effects).
If the plausible patterns for the interaction parameters are as I mentioned
above (same for main diagonal, same for minor diagonal) they cancel each
other if we are using the estimable function comparing the two marginal
means for either one of the variables (A or B), in a way that makes this
marginal means' comparison an estimate of the two main effects' comparison.
Isn't because of all the above that we can interpret the marginal means'
comparison as a main effects' comparison?
thanks for your help