# Interpretation of Wilcoxon Rank Sum test results

I compared the two distributions shown below using a Wilcoxon Rank Sum test (two-sided) using R. The p-value of the test was highly significant (as shown on the plot) and is based on 1,320 observations for each set

Although the overall distribution of Set 2 is shown to be lower than Set 1, the median of Set 2 is higher than the median of Set 1. Given this difference, how should the test results be interpreted?

Can it be stated that the values of Set 2 are significantly lower than those of Set 1? (even though the median of Set 2 is higher than the median of Set 1)

The rank sum test (Wilcoxon-Mann-Whitney test, U test) considers whether $$P(X>Y)$$ differs from $$\frac12$$ (X being a random value from the first population and Y being a random value from the second, assuming continuity), and is effectively based on a sample equivalent of that (the proportion of cross-pair samples for which it is the case, compared to 1/2).