I am working on comparisons between two time points 2013 and 2019, I have 180 subjects. I have a numeric "score" from 2013 and 2019. I calculated the average score at both time points and would like to assess significance. I've run a paired T-test on this, however when I check the normality assumption it is not there. So I moved onto using the Wilcoxon test for non parametric data. I suppose my main question is, reading a few things online it appears the T-test tests if the average score from 2013 is significantly different from the 2019 average. Does the Wilcoxon test do the same? A few of the things I've read seem to indicate it compares median?
Wilcoxon rank test tells you whether there is a location shift between two samples. Wilcoxon signed-rank test tests is for one sample only and tests the null hypothesis $\mu = \mu_0$ for $\mu_0$ of your choice
So, if you wanted to run Wilcoxon rank test on your sample then you can see if the samples are shifted positively or negatively