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I have an experiment with one independent variable with 4 levels (4 different treatments) and 1 dependent variable which was measured twice - before and after the treatment (repeated measures).

I think there are at least two ways to analyze this:

  1. Mixed-design/Split-plot ANOVA:

    • Between-subject variable treatment (4 levels) with within-subject variable time (t1 & t2) and the dependent variable
  2. One-way ANOVA:

    • Between-subject variable treatment and delta values/change from time (t2-t1) as a dependent variable

What are the advantages and disadvantages of these methods? Which one has more power?

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    $\begingroup$ There is also the possibility of one-way anova at each time, which is one acceptable way of analysing repeated measures designs. Although less powerful than mixed models from what I currently know, it is however easier to explain (in my opinion). $\endgroup$ – Rodolphe Jun 15 '15 at 15:09
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This is a common question and there are variety of ways in which it can be tested. Most importantly, you have to ask yourself if you are interested in delta or in the post-treatment level. Secondly, do the pre-treatment level affect the post-treatment level or not? I personally feel comparing the delta values give very clear information as to the degree of benefit by each of the treatments. However, there are some cases where pre test is done only for detection of disease, e.g. blood sugar in diabetes, then treatment is given and much later the post-treatment blood sugar test is done. Here it may be sound reasonable to compare just the post-treatment values without taking pre- levels into consideration or by doing a regression analysis where post-level is the dependent variable and pre-level is a covariate. You need to ask yourself what exact question you want to answer and then pick the best approach. Another approach is to evaluate post/pre ratio, which in some cases may even be better than delta values.

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  • $\begingroup$ Thank you for your very interesting answer. In my case, the participants were randomly assigned to the 4 different treatments. This should ensure that the values of the dependent variable are equally distributed across the different treatments at t1. So I think I could just analyze the post-treatment levels, but I'm still wondering if this might reduce power. You mentioned post/pre ratio - when is it better to use ratio instead of delta values? $\endgroup$ – Florian Jun 16 '15 at 7:10
  • $\begingroup$ Post/pre ratio makes sense most of the time since it is easy to explain to others the percent change a treatment is making. If you think in your situation, it is easier to explain in terms of abdolute change you should use delta. When you want to report relative or percent change, use ratio. $\endgroup$ – rnso Jun 16 '15 at 8:18

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