How this calculation works
Partition variation around the grand mean into differences between group means and residual differences inside each group. Compare the corresponding mean squares using an F tail.
F = (between-group sum of squares / (g−1)) / (within-group sum of squares / (N−g))A worked example
Three groups [1,2,3], [4,5,6] and [7,8,9] have between SS 54 and within SS 6. Mean squares are 27 and 1, producing F = 27 with degrees of freedom 2 and 6.
Good to know
Classical fixed-effects independent-group ANOVA. Requires appropriate residual normality and common variance; no post-hoc comparisons, causal conclusion or automatic design validation.
Reference: NIST: one-way analysis of variance (opens in a new tab) ↗
Groups are sampling units, not separate columns of pairs
Each line is a separate independent group. Repeated measurements on the same subjects need a model that accounts for that dependence rather than this independent-groups calculation.
Unequal group sizes are supported, with the grand mean weighted by observation count rather than averaging group means equally.
The kruskal wallis ties calculator adds calculate pooled average ranks, a tie-corrected Kruskal–Wallis statistic and approximate chi-square p value, exposing rank sums by group.
Within-group variation is the reference spread
The numerator summarizes separation among group means. The denominator summarizes residual variation around each group’s own mean. Both sums are divided by their respective degrees of freedom.
If every within-group residual is zero, the ordinary finite F calculation is undefined. The page rejects that case rather than reporting a made-up probability.
A global test does not identify every differing pair
The global p value addresses the common-mean null under the model. It does not tell which pairs differ after accounting for multiple comparisons.
Eta-squared summarizes the observed variation partition. It is not a causal-effect guarantee or a substitute for checking practical importance and study assumptions.
Use the result with the next measurement
The Kruskal Wallis ties calculator compares pooled ranks with a tie correction. It has different assumptions and is not an automatic cure for every ANOVA design violation.
Classical fixed-effects independent-group ANOVA. Requires appropriate residual normality and common variance; no post-hoc comparisons, causal conclusion or automatic design validation.
A few questions, answered
Are post-hoc comparisons included?
No, the result is the global one-way test.
Can group sizes differ?
Yes, the calculations use each group’s actual count.
Does this model repeated measures?
No, observations and groups must fit an independent design.