ANOVA Calculator: One-Way ANOVA Table and F-Test
This ANOVA calculator runs a one-way analysis of variance to test whether two or more group means differ. Type each group's values in its own box, separated by commas or spaces; empty boxes are ignored. The calculator builds the complete ANOVA table with the between-groups and within-groups sums of squares, degrees of freedom, mean squares, the F statistic and the p-value. It also reports eta squared as an effect size, each group's mean and standard deviation, and a plain-English decision at your significance level.
One-Way ANOVA Calculator
Compare the means of 2 to 6 groups with a one-way ANOVA table, F statistic and p-value.
How to use the One-Way ANOVA Calculator
- Type the values for each group in separate boxes.
- Pick a significance level ฮฑ.
- Read the ANOVA table, F and the p-value.
- Check eta squared for the size of the effect.
ANOVA formulas
SSB = ฮฃ nแตข(x̄แตข − x̄)² · SSW = ฮฃฮฃ (x − x̄แตข)² · F = (SSB ÷ (k − 1)) ÷ (SSW ÷ (N − k))
Features
- One-way ANOVA for 2 to 6 groups
- Full ANOVA table (SS, df, MS, F)
- p-value and critical F
- Eta squared effect size
- Group means and standard deviations
Frequently asked questions
What is a one-way ANOVA?
A one-way ANOVA tests whether the means of three or more independent groups are equal, using the ratio of between-group to within-group variance.
What does the F statistic mean?
F = MS between ÷ MS within. An F near 1 means the group means differ about as much as chance would predict; a large F suggests a real difference.
How do I read the ANOVA p-value?
If p is below ฮฑ, such as 0.05, at least one group mean is different. ANOVA does not say which one; use a post-hoc test such as Tukey's HSD for that.
What are the assumptions of ANOVA?
Independent observations, roughly normal data in each group, and similar variances across groups.
What is eta squared?
Eta squared = SS between ÷ SS total, the share of total variation explained by the groups. About 0.01 is small, 0.06 medium and 0.14 large.