The ANOVA F-Value Calculator performs a one-way analysis of variance for three groups from summary statistics — means, sizes, and variances — without raw data. Returns the F-statistic, p-value, and ANOVA table for quick hypothesis testing in biology, medicine, and research.
6.98
34.9
5
2
27
6.98
34.9
5
2
27
Sometimes you are working from a published paper, a lab report, or a dataset where you only have the group summary statistics — means, sample sizes, and variances — rather than the raw observations. The calculator for ANOVA F-value computes the complete one-way ANOVA from these summary statistics, giving you the F-statistic and p-value without needing individual data points.
Given k groups with means x̄ⱼ, sizes nⱼ, and variances sⱼ², the F-statistic is computed as:
Grand mean: x̄ = Σ(nⱼ × x̄ⱼ) / N where N = Σnⱼ
SS_between = Σ nⱼ(x̄ⱼ − x̄)²
SS_within = Σ (nⱼ − 1) × sⱼ²
F = [SS_between / (k−1)] / [SS_within / (N−k)]
The p-value is then read from the F-distribution with df₁ = k−1 and df₂ = N−k degrees of freedom. This online calculator applies these formulas for three groups — the most common case in biological and clinical research. The ANOVA calculator handles raw data entry when individual observations are available.
The F-statistic is a ratio of two variance estimates under the null hypothesis that all group means are equal. When H₀ is true, F follows an F-distribution with its expected value close to 1.0. As the between-group differences grow relative to within-group variation, F increases. Critical F values at α = 0.05 for df₁ = 2 (three groups) and common df₂:
F values exceeding the critical threshold yield p below 0.05, supporting rejection of the null hypothesis. Effect size (η² = SS_between / SS_total) quantifies the practical magnitude of the group differences independently of sample size.
The three-group ANOVA is the workhorse of comparative biology and clinical pharmacology:
The chi-square test handles the equivalent comparison for categorical (count) data. The biology statistics calculators category provides the complete toolkit for biological data analysis.
Computing ANOVA from summary statistics assumes that the variances reported are sample variances (divided by n−1, not n). Using population variance estimates inflates SS_within and produces a conservative (lower) F value. Additionally, this approach cannot verify normality from summary statistics alone — if original data is available, normality checks and the full ANOVA with raw data are always preferable. For unequal variances across groups, Welch's ANOVA (which uses separate variance estimates per group rather than a pooled estimate) is more appropriate than the standard F-test.
ANOVA partitions total variance into between-group and within-group components:
Inputs
Results
F(2,27) = 6.88 exceeds the critical value. At least one dosage group differs significantly.
Inputs
Results
F(2,21) = 0.42 is not significant. No difference in plant growth between soil types.
Always use ANOVA when comparing three or more groups to control the familywise error rate.
Independent observations, normally distributed data within groups, and homogeneity of variances across groups.
F is the ratio of between-group variance to within-group variance. F much greater than 1 suggests real differences between groups.
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