Which test to choose when Wilcoxon test and McNemar's test are different? I have paired data.The response variable is categorical with levels 1-5.
And I have used both McNemar's test and Wilcoxon rank sign test and I get different p-values. For McNemar's test a p-value of 0.0396; and for Wilcoxon rank sign test a p-value of 0.538. 
before=c(4,3, 5, 3, 5, 4, 3, 3, 3, 5, 5, 4, 5, 4, 5, 5, 5, 5, 5, 5, 5, 5)
after=c(4, 4, 5, 5, 4, 3, NA, 5, 3, 4, 5, 3, 4, 4, 5, 5, 5, 4, 4, 5, 4, 5)

 A: Wilcoxon's signed rank test checks if the values after are systematically higher or lower compared to those before, while the chi-squared symmetry test (aka McNemar's test in the binary case) checks for any difference in distribution, not just a shift.
So, if the true distributions before and after would differ mainly in a shift, then Wilcoxon's signed-rank test would have higher power to detect this difference in a random sample. Otherwise (e.g. if there is a tendency for values before of 3 to become 5 and vice versa), then the symmetry test would have higher power.
The problem here is: you should choose the right test before looking at the p values, simply based on the research question and the type of data you got. So it would be a bit funny to write now: 

We were interested in any distributional change, so we performed a chi-squared test of symmetry and reached a significant result at the 5% level.

but actually mean: 

I want to provide my readers a significant result, thus we have chosen the chi-squared test".

A: McNemar's is for nominal variables so it's not a proper test in this case. Wilcoxon signed rank is more appropriate.
