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Free one-way ANOVA calculator for comparing group means using F-test methodology. Input multiple data groups to compute between-group variation, within-group variation, F-statistic, and statistical significance.
Last updated: April 20, 2026
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Use commas/spaces within a group and semicolons between groups.
F-statistic
38.4000
Critical F
4.2600
df between
2
df within
9
SS between
128.0000
SS within
15.0000
Decision: Reject H0
Reject the null hypothesis at alpha = 0.05. At least one group mean differs significantly.
Group means
ANOVA assumptions:
SS between
nᵢ( x̄ᵢ - x̄ )² aggregation
SS within
Σ(x - x̄ᵢ)² across groups
Decision rule
Reject H0 when F > Fcritical
Groups: [8,9,6,7], [12,11,13,10], [15,16,14,17]
F-statistic
38.4000
Critical F (alpha 0.05)
4.2600
This tool partitions total variability into between-group and within-group components, then computes F = MS_between / MS_within to evaluate whether group means differ more than random sampling variation would predict.
F = (SS_between / df_between) / (SS_within / df_within)Degrees of freedom are df_between = k - 1 and df_within = N - k, where k is number of groups and N is total sample size across all groups.
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