Wilcoxon Signed Rank Test Calculator

Work out wilcoxon signed rank test instantly with clear inputs, formula shown and shareable results.

About Wilcoxon Signed Rank Test Calculator

The Wilcoxon signed-rank test ranks the absolute paired differences, then compares the total ranks of the positive and negative differences. Zero differences are discarded, reducing the effective sample size.

Formulas

Test statistic

W = min(W₊, W₋) over the ranks of |differences|

Normal approximation

z = (W − n(n+1)/4) / √(n(n+1)(2n+1)/24)

Worked example

With the default values below, Wilcoxon Signed Rank Test Calculator returns Wilcoxon W of 1.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Before values: 125, 132, 128, 140, 135, 142, 130
After values: 120, 128, 130, 132, 129, 138, 126

Results

Wilcoxon W: 1.0000
Sum of positive ranks: 1.0000
Sum of negative ranks: 27.0000
Two-tailed p value: 0.02799172

Step by step

1Values used
2Test statistic
3Normal approximation
4Wilcoxon W= 1.0000
5Sum of positive ranks= 1.0000
6Sum of negative ranks= 27.0000
7Two-tailed p value= 0.02799172

Assumptions and limits

The result is derived only from the 2 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 8 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

For the sample blood pressures?

Six of the seven differences are negative, so W₊ is small and the test suggests a real reduction.

How does it differ from the sign test?

The sign test uses only the direction of each difference; Wilcoxon also uses their relative magnitudes, giving more power.