On Fri, 29 Sep 2000, Lu�s Silva wrote:
> For a certain variable I applied a Three Factor ANOVA and found a
> significant interaction between two factors.
Was this the only significant effect, or were there others?
Actually, it would be easier to address your question usefully if
you'd supply the eight means (and the ANOVA summary table).
> I have two levels for each factor. Then, I applied the HSD Tukey test
> for multiple unplanned comparisons, in order to detect what are the
> significantly different treatments.
OK so far, although "I applied the HSD Tukey test" is not very
informative. (One cannot tell whether you applied it correctly, for
example, let alone completely.)
> Since I detected an interaction between two factors, is it correct to
> apply Tukey test?
Sure. Why wouldn't it be? If the three factors are all fixed, there
isn't even any quibble to be made about what the proper error mean square
is for the test.
> If not, are there other type of unplanned comparisons that might be
> used?
The Scheffe' method comes to mind. For pairwise comparisons, Tukey's
method is said to yield narrower confidence intervals; for more complex
contrasts, Scheffe' intervals are narrower. (All other post hoc
comparison methods that I know of either are designed explicitly for
pairwise comparisons, or are customarily applied only to pairwise
comparisons (as is the case with Tukey's method). Pairwise comparisons,
in my experience, are often too simple-minded to convey a decently clear
picture of what's going on in the data.)
When you're dealing with an interaction, particularly in a 2**k
design, it may well be parsimonious to analyze the pattern of means in a
series of complex, preferably orthogonal, contrasts, rather than in terms
of the stereotypical main effects and interactions. Can't tell without
seeing the results.
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
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Department of Mathematics, Boston University [EMAIL PROTECTED]
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