# Fisher's exact test for results of Wilcoxon-Mann-Whitney

I have two groups of subjects (9 and 13 people). And data from two condition for this groups. In each condition for each subjects I have some measurements. But number of measurements are different for conditions (for second condition more then for first). First I use Wilcoxon-Mann-Whitney test for every subject to find subjects with significant difference between conditions. Second I use Fisher's Exact Test for understand is there significant difference in numbers of subjects with difference between condition for my two groups. Say, in first group 4 subjects show significant difference, and 3 in second. So my fisher's table is [[4,5],[3,10]]. Is this make any sense? and if so, Shall I use any correction for multiple comparisons?

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Perhaps adding some more details and context would make this question clearer. For example, do you have repeated measures on each subject? How many Mann-Whitney tests did you do? –  Joel W. Oct 14 '12 at 13:40
Yes I have repeated measures on each subject. But in second condition there are more measurements for each subject than in the first. I do 1 Mann-Whitney test for each subject. So it 9 for first group and 13 for second. –  sviter Oct 14 '12 at 13:57
Can you tell us more about your research design? Is the following example more or less what you are doing? You have two groups, say men and women. You have two types of data for the men, say height and weight. You have the same two types of data for the women. You want to know which are heavier, men or women. You also want to know which are taller, men or women. Or is your design something different? –  Joel W. Oct 14 '12 at 15:19
First of all, thank you for your attention. In term of your example, yes I have two groups - man and women. But I have one type of data, say blood pressure. I measured blood pressure n times for each subject. Then, say, they did physical exercises. And after it I again measured blood pressure for each subject, but m times. So m>n. I want to know in what group - man or women - chance of significant increase of blood pressure is more. –  sviter Oct 14 '12 at 15:56

I assume you measured blood pressure (BP) multiple times before the physical exercise because you thought the BP measure is somewhat variable. If so, you could average all the pre-exercise BP measures and get one more reliable value for each person. As to the post-exercise measures of BP, you might do the same thing. If you think the post-exercise measures of BP will slowly return to baseline, you might average the first few post BP measures for each person to get one, more reliable post-exercise BP value for each person. At that point you will have one pre-exercise BP value (i.e., the before average) and one post-exercise BP value (i.e., the after average) for each person. Then you can analyze the data in various ways. One simple but effective approach is to calculate a before-after difference score for each person. Then you can do a Mann-Whitney test between men and women on these difference scores. (You could also consider using a t-test because it might have higher power, especially with your sample size.) Good luck.

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Thanks, but I already did so. What I am interesting is MU+Fisher approach. Is this method make any sense? –  sviter Oct 15 '12 at 8:24
What are you hoping to learn with that approach? What is your research question? –  Joel W. Oct 15 '12 at 10:03
My research question is: how BP is changed and is any difference in this change between groups. But I want to use all data not just average. Because this approach yielded interesting, and slightly different results, and I try to understend is this method make any sense, or it is just an accident. –  sviter Oct 15 '12 at 10:23
If you have a reason for not wanting to use average before and after scores, what is that reason? Do you think you will get more power by using a Fisher Exact Test to detect higher rate of significant multiple Mann-Whitney tests? I think it is likely that such a two stage approach has lower power than just doing a t-test on the before and after averages. In any case, if you want to "use all the data" have you considered doing an AVOVA with subjects as blocks? –  Joel W. Oct 15 '12 at 12:17