ANOVA for paired data

Question

I'm asking just of curiosity.

If I have, for example, paired data and 3 groups (for example, baseline, 1 week, 2 weeks of treatment: I mean we take some samples at the baseline, then we apply some treatment and take the samples after the 1st and the 2nd week), in order to find out whether there is a difference in the effect of the treatment, may I use instead of one-way repeated measures ANOVA the following scheme:

1. to create new variable by making the difference between all possible paires (in this case I will have new groups notated as: 1 week - baseline, 2 weeks - baseline, 2 weeks - 1 week).

2. to apply normal one-way ANOVA using this new feature.

In addition I will update my question:

If I have the same data table but the study design was a bit different:

1) There is a nutritional study. There is baseline group. We take some samples from this group;

2) For one week this group eats some special food and we take samples after this week (1st week group).

3) There is a wash-out period for another week when people eat their normal food (we don't take the samples; we assume that the group will become baseline again).

4) For another week this group eats another special food and we take samples after this week (2nd week group).

The question: In this case, in order to check is there a difference in effects, can I build the groups as (2 week - baseline) and (1 week - baseline) and apply normal t-test for independent samples?

Answer 1

I changed my mind from my original answer. The differences do remove the additive variations among subjects. But using ANOVA would be comparing one set of changes with another - not comparing one week with another.

If you test the mean of (1 weeks - baseline) against zero, that would be the equivalent of the paired t test for comparing 1 weeks with baseline. Similarly, test (2 weeks - baseline) against zero and (1 weeks - 2 weeks) against zero. That seems more like the tests of greater interest, not comparing them with one another using ANOVA. And anyway, comparing all 3 sets of change scores using ANOVA would be a no-no because of dependence. For example, (2 weeks - baseline) - (1 weeks - baseline) = (1 weeks - 2 weeks).