Hi Mike,
The short answer to your question is that a higher order interaction tells
you that lower order interactions and main effects may be misleading. That
is, if you have a significant AxB interaction and a significant AxBxC
interaction, the 3-way tells you that the size of the AxB interaction
depends on the level of C. An AxB interaction may not even exist at some
level of C, even though the overall AxB interaction is statistically
significant. Hence, it would be misleading to report the AxB interaction as
if it described your data well overall.
If you have a 3-way interaction between AxBxC, there are three ways to
interpret these results. They look quite different, but in fact are only
different ways to say the same thing. The three interpretations are as
follows:
the BxC interaction depends on the level of A;
the AxC interaction depends on the level of B;
the AxB interaction depends on the level of C.
Sometimes one way of looking at these interactions makes more sense than
another. It may be helpful to plot the results in each of the three ways.
Again, these are the same results, so you don't need to report all three
interpretations. (If you do, be sure to acknowledge that you have an
alternate way to look at the same data, rather than a new finding.)
You may wish to follow up on the three-way interaction with 'simple-effects'
tests, whereby you test the BxC interaction at each level of A separately,
etc. The significant three-way interaction already established that these
BxC interactions differ from each other, but the simple effects tests can
help describe the size and direction of each of the simple 2-way BxC
interactions at each level of A.
Similarly, you can follow a 2-way BxC interaction at one level of A with
simple effects tests whereby you test the effects of B at each level of C or
vice versa. If the BxC interaction is significant, that tells you that the
effects of B are not the same at each level of C, and vice versa. As
before, one interpretation may make more sense than the other. Again, this
gives you a chance to talk about the size and direction of effects.
In general, statistical tests in ANOVA are most interpretable when you have
only one df in the numerator for the F test. Abelson calls tests with more
than one df in the numerator a 'blob' test, because the test does not tell
you where the differences are. You can construct contrasts of interest to
provide unambiguous tests.
Another caution: The full 3-way ANOVA design may not be the best way to look
at your data. It may be that the mean for one cell is quite different from
all of the others. That could produce all sorts of significant tests in the
ANOVA, including main effects, 2-way and 3-way interactions, which obscure
the fundamental pattern in the data.
Final advice: plot the data and verify the quality of your data and the
appropriateness of your statistical model.
Good luck,
Dale Berger
Professor and Dean, Psychology
Claremont Graduate University
123 East Eighth Street
Claremont, CA 91711
FAX: 909-621-8905
Phone: 909-621-8084
http://www.cgu.edu/faculty/bergerd.html
----- Original Message -----
From: Mike Hewitt <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Saturday, July 22, 2000 5:54 PM
Subject: interaction effects
> This is a multi-part message in MIME format.
> --------------1EB6033EF40E264F6048C4E4
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>
> Members,
>
> I am looking for assistance in interpreting results of a study. It
> involved the testing of three different music practicing conditions. I
> performed a GLM-repeated measures with three factors (modeling,
> self-listening, self-evaluation) in addition to a repeated measure
> (test). There was a significant interaction for test x modeling x
> self-evaluation. There was also a significant result for test x
> modeling. Does the higher-order interaction negate the results the
> "main effects" or lower-order interaction?
>
> Specifically, musicians who listened to "model" performance improved
> their performance more than those that did not listen to a model.
> Great. For the interaction (test x modeling x self-evaluation), the
> modeling/self-evaluation group improved more than did the no
> modeling/self-evaluation group (reinforcing the results for modeling
> only). HOWEVER, the same result did not occur for the groups that did
> not self-evaluate. They improved similarly to each other.
> So...listening to a model is more effective than not listening to one
> when there is no-self-evaluation.
>
> What then does this mean as far as the results for the test x modeling
> result? I guess my question is does a higher-level interaction
> "overrule" a lower-level interaction?
>
> I appreciate your help!
>
> TIA
>
>
> --------------1EB6033EF40E264F6048C4E4
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> begin:vcard
> n:Hewitt;Michael
> tel;work:301 405 5504
> x-mozilla-html:FALSE
> url:www.umd.edu
> org:University of Maryland;School of Music
> adr:;;Clarice Smith Performing Arts Center;College Park;MD;20742;
> version:2.1
> email;internet:[EMAIL PROTECTED]
> title:Assistant Professor of Music Education
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