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I have the next problem:

I need to compare three treatments $A, B$ and $C$ for a type of pain. Every treatment has been used in 10 different patients. and every treatment is measured with two techniques. T1 and T2 Both techniques have a measure before the treatment and a measure after the treatment (a measure of pain).

$T1$ is measured before and after, i.e $T1_{before}, T1_{after}$

$T2$, is measured in four parts of the body, before and after the treatment using an special device for instance:

$T2_{before_i}, T2_{after_i}$, $i\in\{1,2,3,4\}$

What kind of statistical technique could I use to decide which treatment A,B or C performs better?

I have been reading about ANOVA but I am not sure about how to use technique 2, because it has measures in four parts of the body.

Moreover, I read that ANOVA only helps to see if the means are equal or different but not to see which one is better.

I hope an explanation or any good reference to read.

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A few ideas come to mind. For all of them, I would create change scores from the pre and post measures and then perform all analysis on these.

You could try multivariate ANOVA, aka MANOVA, which is like an ANOVA with multiple outcomes. You could test whether the means of the measures are jointly different across the treatment conditions.

You could try a simple structural equation model (SEM) with a latent variable that is measured by your measures. In a latent variable model, you assume there is a latent (unobserved) variable that is measured (imperfectly) by several measures, or indicators. You can then test whether the treatment variable explains variance in the latent variable using a SEM. An issue with this method is that it requires that the indicators are uncorrelated conditional on the latent variable, which I don't know will be true in your scenario, but is testable. If this assumption is true, this would be the most sophisticated and, in my opinion, the most valid way to estimate the treatment effects of interest.

Finally, a simple method would be to create a composite score from all the methods and then just run an ANOVA on the composite score. A major problem would be justifying the method of creating the composite, but demonstrating that you get similar results regardless of how you create the composite would be an effective sensitivity analysis. This method is essentially the same as the SEM method, which can be thought of as implictly creating a composite score form the measures.

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  • $\begingroup$ I have been thinking about ANOVA, but is not clear because I will test if there is a significative difference between the means However how to decide which method is much better? How to test that? $\endgroup$ – Boris Oct 24 '18 at 3:54
  • $\begingroup$ I will use the ANOVA considering for instance the compound score as the average of the change scores, the using the ANOVA I will test that the means of the three treatments are different. But If the methods are different I dont know which one is much better. $\endgroup$ – Boris Oct 24 '18 at 3:56
  • $\begingroup$ After rejecting the null hypothesis of the model F-test, you can probe further to see which groups differ from each other using post-hoc analyses like Scheffe's test. For significant differences between pairs of groups, you can just look at the means of the outcome in each group to descriptively order the conditions, relying on the hypothesis tests to make a generalizable conclusion. $\endgroup$ – Noah Oct 24 '18 at 3:57
  • $\begingroup$ I have an additional question, in my case technique $T1_after$ and $T1_{before}$ are discrete, because is a pain scale from $1$ to $10$. The anova is still a good choice to compare the three treatments A,B,C with these discrete data? because defining a change scare it will be also a discrete value. $\endgroup$ – Boris Oct 24 '18 at 19:44
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    $\begingroup$ You should consult a statistician with a problem this detailed. You shouldn't try to do an analysis that's inappropriate just because it's one you understand. You have a complicated problem that requires a complicated solution, one you probably won't find here but would find getting tailored help from a statistician. I honestly think a latent variable analysis would be perfect here (it would be able to handle discrete and continuous outcomes), so if you don't know how to do that you should get help with it. $\endgroup$ – Noah Oct 24 '18 at 21:12

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