Understand the hypothesis test
How rank-based inference works
Kruskal–Wallis Test. Rank procedures use relative order instead of the original numerical distances. This changes both robustness and the population statement being tested.
1Pool or pair the observations2Assign ranks with declared tie handling3Compare rank sums, signs, or concordance
Test statistic and reference model
H=[12/(N(N+1))]Σ(Ri²/ni)−3(N+1), corrected for ties.
A significant result indicates some stochastic group difference, not which pairs differ.
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: Groups must be independent with ordinal or numeric observations; median language requires comparable distribution shapes.
Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- 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 kruskal–wallis test calculator works
H=[12/(N(N+1))]Σ(Ri²/ni)−3(N+1), corrected for ties.
A significant result indicates some stochastic group difference, not which pairs differ.
Worked example
Kruskal–Wallis Test example
Three groups entered on separate lines are ranked together before group rank sums are compared.
H=[12/(N(N+1))]Σ(Ri²/ni)−3(N+1), corrected for ties.
Supported inputs
Precision and limits
Model and design
Groups must be independent with ordinal or numeric observations; median language requires comparable distribution shapes.
Input scope
Category lists accept up to 10,000 nonblank observations and render up to 200 distinct labels. Matching trims outer whitespace but remains case-sensitive; no numeric ordering or distance is inferred.
Interpretation
A significant result indicates some stochastic group difference, not which pairs differ.
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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