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Probably a trivial questions, but I've been wrapping my head around it for a while...

I have a small sample (N=7) that performed a test in two conditions. No assumption can be made about the eventual normality of the population. I would like to test if the change in conditions significantly affected the results of the tests across subjects.

In this case a t-test on the means for the two conditions across subjects should not be applied. Am I right ?

Would a Mann U-test or Wilcoxon signed-rank test be more suitable ?

EDIT : (I am aware that these two test would compare the medians of the results)

Thanks

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About your first question, yeah, a (paired) t-test wouldn't do because of the sample size (assuming you are not willing to assume a normal distribution). – Néstor May 8 '12 at 5:54
thanks for pointing out that, in case of normality, a paired test would be needed. the U-test requires two independent samples so maybe it's not suitable for my case. Even though the order of the two conditions was randomly chosen for each element of the sample. – user11170 May 8 '12 at 6:34
Wilcoxon and Mann-U don't compare the median of the results. They test the hypothesis that the two distributions of the two samples are identical, and have better power when the alternative is a location shift. If you have paired samples, one approach is to compute the differences (Condition 1 - Condition 2) for each of the 7 samples, and do a Sign Test of the differences. Unless there is a very dramatic difference, this test (and any other) won't have much power, meaning that one should be careful not to over-interpret the results. – guest May 8 '12 at 7:40
Why was question titled ...and variance? The question itself doesn't show any intent to compare spreads of the distributions. – ttnphns May 8 '12 at 10:53
this is due mostly to my incompetence, i.e. I don't have a clear picture of what I should to analyze the role of the variance in my results, which is by the way fairly high in both conditions. @guest thanks for your very useful remarks! – user11170 May 8 '12 at 20:00

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