Wilcoxon Signed-Rank Test calculator

Run a non-parametric Wilcoxon signed-rank test online for paired differences. Safe for skewed or ordinal data.

What it does

The rank-based counterpart to the paired t-test: ranks the within-pair differences by size and asks whether positive differences outweigh negative ones.

When to use it

Two measurements on the same subjects where the differences are skewed, ordinal, or contain outliers that would dominate a mean.

Cautions

• It assumes the distribution of differences is symmetric. When it is badly asymmetric, the sign test is the more honest choice.
• Pairs with zero difference are dropped, which reduces the effective sample size — check how many.
• Report a rank-biserial correlation or the median difference: a p-value alone says nothing about size.

Alternatives

• Paired t-test — the differences are roughly symmetric — it is more powerful when that holds
• Sign test — you can only trust the direction of each change, not its magnitude

How to read the output

W statistic and Z

W sums the ranks of the differences in one direction; Z is its normal approximation, used for the p-value on samples large enough to support it. The test assumes the differences are symmetric about their centre. It is not assumption-free — it drops the normality requirement, not every requirement.

N (non-zero pairs)

Pairs with a difference of exactly zero carry no directional information and are dropped, so this is smaller than your number of subjects. Many dropped zeros means most subjects did not change at all — worth reporting in its own right, and a signal that the measurement may be too coarse.

p-value

How surprising a difference at least this large would be IF the groups really were identical on this measure. A small p means the data would be surprising under that assumption. It is not the probability that the result is due to chance, and not the probability that the groups are the same — those read the conditional backwards. It also answers 'would this be surprising?', never 'is this big enough to matter?': with a large sample a trivial difference returns a small p, and the result looks identical to an important one.

How this calculator is validated · Which statistical test should I use?