In reply to Abi.

Thanks for writing. When I hear "difference in medians" I think of paired data. For paired data, you can compute the difference D[i] = x[i]-y[i] and report the median of the differences. This article does not consider that scenario. This article assumes that there are two groups, possibly from different distributions. It tests whether the median of the distribution for the first group is significantly different from the median of the distribution of the second group.