DB said:
"Possibly somewhat more to the point (or at least
differently...), Art's question might have been
asked in a multiple-regression (MR) context; in
which case, however <d*g> were constructed, it would
only be
represented with one d.f. in an analysis predicting
a dependent variable
(Y?) from <d*g>."
And since I always think about anova from a contrast
coding point of view this seemed to me the way to do
it. In a simple 2x2 balanced design using contrast
codes the only change between an analysis with and
without the main effects is in the dferror and so
the power.
While I am stumped for a reason to test the
interaction term absent the main effects the only
negative side effect I see is the lost of power.
What confuses me is how one gets from a 1 df
interaction to a 3 df interaction by deleting the
main effect terms from the analysis. Clearly these
are not tests of the same thing.
Michael
****************************************************
Michael Granaas [EMAIL PROTECTED]
Assoc. Prof. Phone: 605 677 5295
Dept. of Psychology FAX: 605 677 3195
University of South Dakota
414 E. Clark St.
Vermillion, SD 57069
*****************************************************
----- Original Message -----
From: Donald Burrill <[EMAIL PROTECTED]>
Date: Tuesday, February 17, 2004 1:17 am
Subject: Re: [edstat] Main Effects and Interactions
> I found Art's question ambiguous in a number of
senses: see below,
> in my
> comments on his post.
>
> Karl's example does not, it seems to me, entirely
address the question
> being asked. For one thing, it depends much on
how the interaction
> predictor (which I'll call d*g) is actually
constructed. If <d*g> is
> obtained by multiplying <d> by <g> and no
adjustments are made to the
> product, <d*g> may (but need not) end up with four
different values;
> and if it is used alone in an ANOVA context, of
course it will
> take 3 df
> to account for its effects.
> (E.g., if <d> = 1 or 2 and <g> = 1 or 3, <d*g> =
1, 2, 3, or 6.)
> But <d*g> might have only two values (e.g., if
both <d> and <g> are
> coded {+1, -1}, then <d*g> = +1 or -1), and in
that case an ANOVA
> usingonly <d*g> would find only 1 df for the <d*g>
effect. (I
> suspect this
> would have happened in Karl's example had he used
data with balanced
> frequencies; but whether that suspicion be
correct depends on
> what SAS
> actually does in computing <d*g>.)
>
> Possibly somewhat more to the point (or at least
differently...),
> Art'squestion might have been asked in a
multiple-regression (MR)
> context;in which case, however <d*g> were
constructed, it would
> only be
> represented with one d.f. in an analysis
predicting a dependent
> variable(Y?) from <d*g>.
>
> Whether such an analysis be useful or not depends
on a whole lot of
> context: things that Art hasn't told us about his
problem, e.g.
> why (or
> perhaps if?) he wants to ignore any main effects
that may (but
> need not)
> be present, and whether the interaction variable
<d*g>, _as_used_
> in_the_analysis_, be correlated with either main
effect.
>
> (One could have constructed <d*g> to be orthogonal
to both <d> and <g>
> -- see my White Paper on interactions in MR, on
the MINITAB web site
> www.minitab.com for an example and description of
how to do that -
> - so
> that <d*g> represents what one might call the
"pure interaction"
> effect,uncontaminated with main effects; for this
variable in
> Karl's example,
> used as a predictor all by itself (in MR, not
ANOVA), the SS would be
> rather more like 15.9 than 1312.3.)
>
> On Mon, 16 Feb 2004, Karl L. Wuensch wrote:
>
> > Here is SAS GLM output for a 2x2 ANOVA,
unequal cell sizes, type
> > III sums of squares. First the full factorial
design:
> > Source DF Type III SS
> > deattr 1 1286.325649
> > gender 1 3.955131
> > deattr*gender 1 15.873457
> >
> > Now I drop the two main effects and run the
analysis again:
> > Source DF Type III SS
> > deattr*gender 3 1312.292621
> >
> > As you can, both the sums of squares and the
df previously
> assigned> to the main effects are now assigned to
the interaction
> term.>
> > ----- Original Message -----
> >
> > From: "Arthur Tabachneck" <[EMAIL PROTECTED]>,
Fri Feb 13:
> >
> > Is it legal to test for an interaction without
testing for the main
> > effects of the variables included in those
interactions. And,
> in the
> > case it is (which I recall it isn't), does one
still have to account
> > for the degrees of freedom used by the
non-tested main effects?
>
> Depends on what you mean by "legal". Can one do
such a thing? Yes.
> But it _also_ depends on what you mean by
"interaction". One
> meaning is
> "an effect attributable to a combination of two
(?) variables,
> above and
> beyond the effects attributable to the two
variables separately" --
> that
> is, what I've called "pure interaction" above and
elsewhere. Another
> meaning is "an effect attributable to the product
of two (?)
> variables",and this effect does depend heavily on
(1) how the
> "product" is
> constructed (see my notes above) and (2) whether
the "main
> effects" are
> also being separately accounted in this analysis.
As Karl's analyses
> showed, the "interaction" might only contain the
"pure interaction"
> information (as in his first analysis), or it
might contain ALL the
> effects due to interaction AND main effects (as in
his second
> analysis).
> You ask about "accounting for the degrees of
freedom used by the
> non-tested main effects"; you didn't ask about
"accounting for
> the sums
> of squares explained by the non-tested main
effects". But I cannot
> think of a context in which one wouldn't want so
to account (which
> doesn't mean you don't have such a context -- I
may not be
> sufficientlyimaginative, is all), because if you
don't as it were
> extract the SS due
> to the main effects, you'll have an "error" SS
that includes all those
> systematic effects; so your analysis will be
relatively
> insensitive to
> the interaction effect (and any other effects that
may be retained in
> your model), due to the unnecessary inflation of
"error".
>
> > Hoping that was sufficiently clear,
> > Art
>
> Well, no, I didn't think it was. As I tried to
illustrate. There are
> lots of things more I can imagine saying about
your question, but I
> can't tell which of those things may be relevant
to your context.
> Good luck! -- DFB.
>
------------------------------------------------------------
> Donald F. Burrill
[EMAIL PROTECTED]
> 56 Sebbins Pond Drive, Bedford, NH 03110
(603) 626-0816
> .
> .
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