Kruskal–Wallis H: what it means and how to read it
In the report: Kruskal-Wallis H — How far the mean ranks of the groups are apart, with the tie correction.
How to read it
The rank-based counterpart of the ANOVA F: the larger H, the more the groups differ. Read Asymp. Sig.; in a report: H(2) = 1.71, p = .425.
In plain words
A teacher compared three classes in a reading contest and wanted to know whether they read at the same level. A few scores were very high, so she did not trust the averages. She put all pupils in one line from best to worst and looked at the average place of each class. The Kruskal-Wallis H came out 8.4. The bigger H is, the further apart the average places of the classes are. The chance column next to it said the gap was hard to put down to chance alone. Now she can say the three classes did not read at the same level, though H does not tell which class differs.
How it is computed
H = (12 / (N(N + 1)) · Σ Rᵢ²/nᵢ − 3(N + 1)) / (1 − Σ (t³ − t) / (N³ − N))Example
The cell with Kruskal-Wallis H is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — three groups
=STATS_KRUSKAL(Data!A1:T51, "x,x1,x2")
Where you see it
STATS_KRUSKAL— Kruskal–Wallis test for two or more independent groups (usually three or more; for two it agrees with STATS_MANN_WHITNEY) — the rank replacement for STATS_ANOVA when the data are not normal, or are ranks or rating scales. Each selected column is a group, as in STATS_ANOVA; no column is dropped.
Related values
- Statistic — The test statistic.
- Pearson chi-square — Pearson's chi-square: how far the observed counts are from those expected if the two variables were unrelated. No continuity correction.
- Pearson Chi-Square — The same test as the chi2 at the top of the report, in the SPSS table: value, df and the asymptotic p from the chi-square distribution. No continuity correction.
- Continuity Correction (Yates) — Pearson's chi-square with the Yates correction, for a 2 × 2 table only; the row is absent for larger tables.
- Likelihood Ratio — The likelihood-ratio chi-square (G²) of the table with the same df as Pearson's; p from the chi-square distribution.
Get it in your sheet
One formula in a cell gives the whole report, Kruskal–Wallis H included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)