Wilcoxon Signed-Rank Calculator

What is the Wilcoxon Signed-Rank Test?

The Wilcoxon signed-rank test is a non-parametric test for comparing two related samples. Unlike the paired t-test, it does not assume the differences are normally distributed. It tests whether the median difference between pairs is zero.

How it works:

1. Calculate the difference for each pair (Sample 1 - Sample 2)
2. Discard pairs with zero difference
3. Rank the absolute differences (average ranks for ties)
4. Sum the ranks of positive differences (W+) and negative differences (W-)
5. T = min(W+, W-)
6. Compare T to the sampling distribution (or use the normal approximation for n > 10)

Normal Approximation (n > 10):

• E(T) = n(n+1)/4
• SD(T) = sqrt(n(n+1)(2n+1)/24)
• z = (T - E(T)) / SD(T)

When to use Wilcoxon:

• Paired or matched data (before/after, pre/post)
• Data that is ordinal or not normally distributed
• Small samples where normality is difficult to check
• You want to test the median difference rather than the mean