Wilcoxon Signed-Rank Test Calculator

In short The Wilcoxon signed-rank test is the non-parametric partner of the paired t-test: it takes the difference within each pair, ranks those differences by SIZE, and then asks whether the positive ones outweigh the negative ones. The six pairs loaded above give W⁺ = 21 and W⁻ = 0 — every pair moved the same way — with z = 2.1260 and p = 0.0335. The two rank sums always add to n(n+1)/2, which is 21 for six pairs, and that identity is the fastest way to check the working. What separates this from a simple sign test is that it uses the SIZE of each change and not merely its direction, so a few large improvements outweigh many trivial declines. That extra information is where the extra power comes from. Pairs with a difference of exactly zero are dropped before ranking, which is standard and is why the effective n can be smaller than the number of pairs you entered. Use it for before-and-after measurements on the same subjects, matched pairs, or repeated ratings — particularly when the differences are skewed or the scale is ordinal, such as a five-point satisfaction score where the numbers have order but no meaningful spacing. The assumption people forget is symmetry: it assumes the differences are distributed symmetrically about their centre.