Is it correct to use the Wilcoxon signed ranks test for relative differences $\frac{Wx-Wy}{Wy}$, instead of absolute differences $Wx-Wy$? In some cases the relative difference is more relevant, for example if we want to compare the change in house prices I would argue that the percentage difference is a much better indicator than the absolute difference.
I need to compare the reaction time of participants before/after, and some participants have a really slow reaction time, meaning that even a (relatively) small improvement has a huge impact (since the absolute difference is big) while if someone with a good reaction time improves by 30% it gets lost in the data.
My question is that what is the correct way to compare relative differences?
Best Answer
Yes, that's fine.
As long as you have one sample (either to begin with, or formed by taking differences between two columns of data, relative or otherwise), then the signed-rank test is appropriate. Usually the only assumptions of this single sample are that the r.v.s are iid and (usually) that they're continuous random variables. When these assumptions are satisfied, then you can find rejection regions by using quantiles of the asymptotic sampling distribution of the test statistic under the null hypothesis, or the from the exact sampling distribution.