On Wed, 10 Jul 2002, Rob Briers wrote (to the MINITAB list):
> Dear All,
>
> More of a general statistical question rather than Minitab specific, but I
> have carried out a repeated measures ANOVA with two main effects and one
> within- subjects factor. The results indicate that one of the main effects
> is signficant, but that there is an interaction between that main effect and
> the within-subjects factor. In this case is it still valid to perform
> multiple comparisons between the levels of the significant main effect?
>
> Thanks in advance for any help,
>
> Rob Briers
> _________________________________
> Dr Rob Briers
> Institute of Biological Sciences
> University of Wales, Aberystwyth
> Ceredigion
> SY23 4NL
> http://users.aber.ac.uk/rob/
Essentially your problem now is to interpret the _pattern_ of results, in
the light of the significant main effect and the significant interaction.
The short answer to your question ("is it still valid...?") is, "Yes, it's
valid; but the result(s) may be misleading if you aren't careful."
It is in general impossible to give a useful answer without knowing what
the two-dimensional pattern of means is. (The two dimensions being the
significant factor and the repeated-measures factor; your third factor,
one gathers, shows no differences of any kind.)
An example may help. In a psycholinguistic Ph.D. thesis some years ago, a
3x5 subset of a design that had (I think) 5 factors all together showed a
highly significant interaction, along with even more highly significant
main effects. The 5-level (repeated-measures) factor entailed 5 different
tasks; the 3-level factor represented three groups of children (grade 8
good readers, grade 8 poor readers, grade 5 average readers -- the latter
two were of about the same reading skill). Of the five tasks, two
involved recognition of individual letters, and three involved complete
words. The dependent variable for the particular analysis of interest was
the "encoding time" required for processing the task. All three groups
showed nearly identical performance on the letter tasks (one could
interpret this as indicating that those tasks had been thoroughly mastered
by grade 5), and the letter tasks had distinctly shorter encoding times
(main effect!) than the word-level tasks. On the word tasks, however, the
encoding times for two groups was generally similar, and for the third
(grade 8 good readers) they were markedly shorter. All of which makes
quite reasonable sense when you think about the underlying meaning of the
results.
But for interpretation: it was in that case sensible to split the word-
level tasks from the letter-level tasks, almost as though they represented
two different experiments. For these two pieces (of course?) there were
no interactions -- no main effect of subpopulation for the letter tasks,
but a smallish (significant) difference between the tasks; no main effect
of tasks for the word tasks, but a strong effect of subpopulation.
Now that was what I consider a relatively simple instance of a two-way
interaction pattern: but it's taken me 20 or 25 lines to describe the
results and a (possibly reasonable) way of interpreting them. Your
patterns may be more (or perhaps less) complicated, and certainly some
post hoc tests are in order; but just which comparisons will make the
underlying structure perceived most clearly is hard to describe in general
(and is, in any case, a matter of artistry).
I hope this has been helpful.
-- Don.
-----------------------------------------------------------------------
Donald F. Burrill [EMAIL PROTECTED]
184 Nashua Road, Bedford, NH 03110 (603) 471-7128
.
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