Wilcoxon Test Calculator

Perform a Wilcoxon signed-rank test for paired non-parametric data.

About Wilcoxon Test Calculator

The Wilcoxon signed-rank test replaces the paired t-test when differences are not normally distributed. It uses ranks of the absolute differences, so outliers have limited influence. It has about 95 per cent of the power of a paired t-test when normality does hold, which makes it a low-cost default for small samples.

Formula

Wilcoxon Test

E(W) = n(n+1)/4; SD(W) = √(n(n+1)(2n+1)/24); z = (W − E(W)) ÷ SD(W)

signed rank: Ranks of absolute differences, carrying the sign of the difference

Worked example

With the default values below, Wilcoxon Test Calculator returns Z Statistic of -2.38544. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sum of the smaller signed ranksminimum 0: 18
Number of non-zero pairsminimum 5: 15
Significance levelaccepts 0.1–20 %: 5 %

Results

Z Statistic: -2.38544
Expected W Under the Null: 60.000
Standard Deviation of W: 17.60682
Decision: Reject H0 — the paired difference is significant
Critical Z Value: 1.96039

Step by step

1Values used
2Wilcoxon Test
3Z Statistic= -2.38544
4Expected W Under the Null= 60.000
5Standard Deviation of W= 17.60682
6Decision= Reject H0 — the paired difference is significant
7Critical Z Value= 1.96039

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Wilcoxon Test calculated?

E(W) = n(n+1)/4; SD(W) = √(n(n+1)(2n+1)/24); z = (W − E(W)) ÷ SD(W) The Wilcoxon signed-rank test replaces the paired t-test when differences are not normally distributed. It uses ranks of the absolute differences, so outliers have limited influence.

Why does Wilcoxon Test matter?

It has about 95 per cent of the power of a paired t-test when normality does hold, which makes it a low-cost default for small samples.

What values do I need to enter?

This calculator takes 3 inputs: Sum of the smaller signed ranks, Number of non-zero pairs, Significance level. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.