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Statistics · Hypothesis testing

Wilcoxon Signed-Rank Test Calculator

Test the symmetry-centered location of paired differences using signed absolute ranks.

Statistics · Hypothesis testing

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Private in-browser calculation · explicit assumptions
Rank procedures replace raw magnitudes with ordered positions, then compare rank patterns under the stated design.
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  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Understand the hypothesis test

How rank-based inference works

Wilcoxon Signed-Rank Test. Rank procedures use relative order instead of the original numerical distances. This changes both robustness and the population statement being tested.

Test statistic and reference model

W+ sums positive-difference ranks; normal variance includes tie corrections.

The test concerns a symmetric distribution of differences, not merely equality of marginal medians.

Responsible interpretation

A rank test is not automatically a test of medians. Median language generally needs comparable distribution shapes and a design that supports that interpretation.

Required assumption: Pairs must align and be independent across units; zero differences are removed and inference uses a tie-corrected normal approximation.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the wilcoxon signed-rank test calculator works

W+ sums positive-difference ranks; normal variance includes tie corrections.

The test concerns a symmetric distribution of differences, not merely equality of marginal medians.

Worked example

Wilcoxon Signed-Rank Test example

Aligned before-and-after data are reduced to nonzero signed differences and ranked by magnitude.

W+ sums positive-difference ranks; normal variance includes tie corrections.

Supported inputs

Precision and limits

Model and design

Pairs must align and be independent across units; zero differences are removed and inference uses a tie-corrected normal approximation.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

The test concerns a symmetric distribution of differences, not merely equality of marginal medians.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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