When is the Wilcoxon p-value exact?

With 1 to 30 nonzero paired differences, the calculator enumerates the conditional sign distribution using doubled midranks and a rank-sum dynamic program. Tied absolute differences are included exactly. Larger samples use an explicitly labeled tie-corrected normal approximation, with small tails evaluated directly. Probabilities below the representable floating-point range are disclosed as below 5e-324 instead of an exact zero.

How are missing values, zeros and ties handled?

Paired rows need two comma- or tab-separated numeric cells without a header. A missing cell excludes the pair and retains its physical source row and any supplied finite partner value. Malformed nonempty cells are rejected. Zero adjusted differences are excluded before ranking. Exact numeric ties receive midranks; values are not rounded to create ties.

What does the expected difference change?

The signed difference is after minus before minus your expected difference. Greater and less refer to this adjusted difference. A location interpretation assumes symmetric paired differences; the calculation does not establish a causal effect.

What does Kruskal-Wallis test?

The independent-group calculation pools ranks and reports tie-corrected H with a chi-square p-value. A median interpretation requires comparable distribution shapes. Groups with fewer than five observations are flagged, and no automatic posthoc comparisons are performed.

Can I see and export every row?

Yes. The rank table is paginated in groups of 50, while CSV and text reports include the complete result. The worksheet accepts up to 10,000 source rows or observations, 2 to 20 independent groups, and one million input characters. Input numbers use finite-precision arithmetic. CSV and full text reports retain the complete parsed numeric values, while summary statistics use readable formatting. Processing stays in a local browser worker.

Why can a result be undefined?

All-zero complete paired differences contain no nonzero ranks. If every independent observation is identical, the Kruskal-Wallis tie correction is zero. Both cases retain the rank data and show no invented statistic or p-value.

Rank Test Calculator

Compare paired observations with Wilcoxon signed ranks or independent groups with Kruskal-Wallis. Inspect every source row, excluded pair, midrank and method before exporting a complete local report.

Your observations

TestPaired columns: before, after

One pair per line, comma or tab separated, without a header. A missing cell excludes that pair explicitly. Blank lines are ignored; physical source row numbers remain visible.

Expected after − beforeAlternative

Continuity correction for the normal approximationAlpha

At most 10,000 source rows or observations and one million input characters. Exact numeric equality defines ties; values are never rounded before ranking. Paired differences should be symmetric for a location interpretation.

Ranks and inference

Your complete rank table and method appear here after analysis. All supplied values stay in this browser.

Supply paired columns or independent groups, then analyze their ranks.

Wilcoxon drops zero differences, uses midranks and assumes symmetric paired differences for a location interpretation; independent-group ranks do not prove median differences without shape assumptions. Exact conditional sign enumeration via rank-sum DP for≤30nonzero pairs; explicitly labeled tie-corrected normal approximation otherwise. Kruskal uses chi-square approximation and flags any group under5. No causal/clinical advice or automatic posthoc claims.

Common questions

When is the Wilcoxon p-value exact?: With 1 to 30 nonzero paired differences, the calculator enumerates the conditional sign distribution using doubled midranks and a rank-sum dynamic program. Tied absolute differences are included exactly. Larger samples use an explicitly labeled tie-corrected normal approximation, with small tails evaluated directly. Probabilities below the representable floating-point range are disclosed as below 5e-324 instead of an exact zero.
How are missing values, zeros and ties handled?: Paired rows need two comma- or tab-separated numeric cells without a header. A missing cell excludes the pair and retains its physical source row and any supplied finite partner value. Malformed nonempty cells are rejected. Zero adjusted differences are excluded before ranking. Exact numeric ties receive midranks; values are not rounded to create ties.
What does the expected difference change?: The signed difference is after minus before minus your expected difference. Greater and less refer to this adjusted difference. A location interpretation assumes symmetric paired differences; the calculation does not establish a causal effect.
What does Kruskal-Wallis test?: The independent-group calculation pools ranks and reports tie-corrected H with a chi-square p-value. A median interpretation requires comparable distribution shapes. Groups with fewer than five observations are flagged, and no automatic posthoc comparisons are performed.
Can I see and export every row?: Yes. The rank table is paginated in groups of 50, while CSV and text reports include the complete result. The worksheet accepts up to 10,000 source rows or observations, 2 to 20 independent groups, and one million input characters. Input numbers use finite-precision arithmetic. CSV and full text reports retain the complete parsed numeric values, while summary statistics use readable formatting. Processing stays in a local browser worker.
Why can a result be undefined?: All-zero complete paired differences contain no nonzero ranks. If every independent observation is identical, the Kruskal-Wallis tie correction is zero. Both cases retain the rank data and show no invented statistic or p-value.