Jim's advice looks pretty good to me;  as he remarks, the particular
contrasts you choose to examine (among the five degrees of freedom
available from the six groups of difference scores) may depend on what
you think C, T, and M actually means.

There is another parallel analysis that might be of interest:  a similar
one-way ANOVA on the sums (w1+w2) rather than on the differences
[(w2-w1), presumably].  This would permit you to see whether the average
performance (if that's a reasonable term to use) differs (a) among the
three pairs and (b) by the order within pairs.  (Average performance
gets subtracted out when you take difference scores.)

It is entirely possible that a useful set of five orthogonal contrasts
among the six sums might not be the same as the set of five contrasts
you chose for the six differences...

On Fri, 20 Feb 2004, jim clark wrote in part:

> 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,

[Haven't seen any so far.  -- DFB.]

> 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.

  <snip, argument justifying differences>

> [Or,] 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.  [...]  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

<snip, the rest>

  Good luck!   -- Don Burrill.
 ------------------------------------------------------------
 Donald F. Burrill                              [EMAIL PROTECTED]
 56 Sebbins Pond Drive, Bedford, NH 03110      (603) 626-0816
.
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