Wilcoxon Signed-Rank Test Calculator
Calculate signed-rank sums and a conditional exact two-sided sign-assignment p-value with explicit zero and tied-rank handling.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Omit exactly zero differences, average tied absolute ranks and enumerate the exact conditional sign-assignment distribution using doubled integer ranks.
W+=sum positive ranks; two-sided p=min(1,2×min(inclusive lower tail,inclusive upper tail))
Worked example
Five strictly positive nonzero paired differences give W−=0. Under the conditional symmetric-sign model, the two-sided tail probability is 2/2⁵=0.0625, including observed ties through their ranks.
Assumptions and input details
At most 50 nonzero differences among up to 500 entered pairs. Exactly zero differences use the Wilcox omission convention; tied absolute differences get average ranks. Unlike some software defaults, this page uses a conditional exact sign-randomization distribution even with tied ranks, rather than an asymptotic normal correction. Independent symmetric differences under the null are assumed. Measurement noise must be rounded by you if it should be treated as a tie.
References: NIST: signed-rank purpose and symmetry assumptions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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