Hi
On 19 Feb 2004, Kasper Hornbaek wrote:
> I have a question on how to analyse an exprimental design.
>
> We had three treatments (C, T, M) of which only two could be
> administred to each subject. The subjects receieved those treatments
> in two weeks following each other (W1, W2). I total there were six
> experimental groups, each defined by a treatment combination, i.e.
>
> grp w1 w2
> 1 C T
> 2 C M
> 3 T C
> 4 T M
> 5 M C
> 6 M T
>
> We are interested in comparing the effects of treatments, e.g. C vs M.
> Right now I am considering a repeated measures analysis, with week and
> grp as factors. However, I cannot figure out how to compose the
> contrasts that would answer our questions.
Others will probably come up with more sophisticated approaches,
but you might consider a simple two-stage analysis.
1. One-way ANOVA on the W1 scores comparing the 3 groups: C
(1&2), T (3&4), M (5&6), ideally with planned contrasts if you
had any predictions for the differences among the three
groups. Or pairwise comparisons if not. This analysis is
uncomplicated as the groups differ only on treatment, assuming
random assignment to groups.
2. The 2nd stage would involve 3 anovas to determine whether
order and prior treatment had any effect, one each for the C, T,
and M comparisons. For C, this would involve 1&2 vs. 3 vs. 5,
with an omnibus anova followed by planned comparisons for order
(-2 +1 +1) and prior treatment (0 -1 +1). Similar anova for the
other two treatments.
A major downside of this approach is that it ignores the within-s
comparisons, which could be more sensitive if the effects of
treatment are subtle. One way to attack this would be to compute
difference scores and do a one-way anova of the difference scores
on the 6 groups, with some meaningful planned comparisons across
the means. Could be tricky, although some possibilities seem
clear (e.g., does CT differ from TC, and similar for other 2
comparisons). If we assume C stands for control, for example,
then one meaningful pattern of 5 orthogonal contrasts would be:
1 2 3 4 5 6
CT CM TC TM MC MT
-1 -1 -1 +2 -1 +2
-1 +1 -1 0 +1 0
-1 0 +1 0 0 0
0 -1 0 0 +1 0
0 0 0 -1 0 +1
Contrast 1 would determine whether the differences involving the
C condition differ from the differences between T and M.
Contrast 2 would determine whether the differences between C and
T differed from those between C and M.
The remaining 3 contrasts test for order effects.
Whether these or other contrasts make sense would depend on what
C, T, and M actually represent.
You could do one more test of the difference scores, again
depending on whether it made sense. Specifically, you could ask
whether the mean of all the difference scores differed
significantly from 0 (i.e., equivalent to a paired-difference
t-test).
Actually, this last possibility raises the interesting question
of how you would compute the difference scores for the anova.
Would CT = C-T (i.e., w1 - w2), and TC = T-C (i.e., w1 - w2), or
would TC = C-T (i.e., w2 - w1)? Same for the other comparisons.
I suspect the 2nd approach might make the results of the anova
easier to interpret because CT and TC would be "oriented" in the
same direction and any difference would represent an order
effect rather than a treatment effect.
Best wishes
Jim
============================================================================
James M. Clark (204) 786-9757
Department of Psychology (204) 774-4134 Fax
University of Winnipeg 4L05D
Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED]
CANADA http://www.uwinnipeg.ca/~clark
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