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?
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.
If you're getting different answers with your approach versus a more traditional ANOVA, then it's probably because each subject brings their own variability to the BP measurements. ANOVA assumes homogeneous variances and lost information in your case. Unfortunately, the MU-FE approach is conditional upon the alpha-level you're using to test the conditional difference; if you had compared the before-after using alpha=0.25, would you get the same FE result? Your design appears to be a split-plot (whole plot=sex, subplot=before/after) aka repeated measures. And you are interested in testing to see if there is a significant interaction between the two factors. In this case, you maximize power by using all of the information. The suggestion of using the MU on the differences is a good step, but it assumes the differences across the subjects are measured with the same accuracy. Consider using a weighted t-test on the differences, where the weights are the sums of some (robust) measure of the before and after BP sample variabilities. If the number of measurements is the same across subjects, then just adding these measures of variability will incorporate the difference in number of observations between before and after. As long as the populations of differences are not too skewed, the t-test should provide a reasonably robust test.