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I have had a particular problem that I haven't been able to solve.

Here is the scenario: I would like to perform a paired t-test of sorts on multiple groups. Instead of before and after conditions, there are multiple conditions (ex: treatment 1, treatment 2, treatment 3 etc). Each subject appears in each 'group'. I have tried to use ANOVA, but this method averages data of all subjects within each condition, then compares their means. However, I would like to look at the differences of individual subjects between the conditions, and compare those between subjects. To me, it sounds like a paired t-test for of 2+ groups. I am using n=4. I hope that makes sense.

thanks for any input

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    $\begingroup$ Can you describe the study design better? Is this a cross-over design? An AB design? Pre-post randomized design for differences in differences? $\endgroup$ – AdamO Dec 20 '16 at 2:41
  • $\begingroup$ Have you heard of MANOVA (multivariate analysis of variance. For each subject you have a k dimensional vector k=4 in your case. I think this will let you include all the results for the patients in a single vecotr. $\endgroup$ – Michael Chernick Dec 20 '16 at 2:46
  • $\begingroup$ Thanks for the reply. I'm not sure what the proper terminology is. Currently, it is two sets of paired t-tests, but using the same n=4 overall. It compares scores of conditions A vs B and C vs D (all using the same unit of measurements). But now I want to compare A & D and C & B as well. My options as far as I can see are reusing the data two make four graphs (I'm hesitant about this) or perhaps combining all 4 sets on the same graph (but I'm not sure how to mathematically compare them). $\endgroup$ – new2stats Dec 20 '16 at 2:51
  • $\begingroup$ In the usual ANOVA that sounds like testing contrasts. This can be done but whenever you do this you need to take account of the multiple testing and adjust p-values. $\endgroup$ – Michael Chernick Dec 20 '16 at 3:12
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The test you are looking for is one-way repeated measures ANOVA. That is equivalent to two-way ANOVA, with repeated measures in one factor, with no replication. Following the ANOVA, you'll want to run followup tests to make the comparisons you are asking for, while adjusting for multiple comparisons.

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