# One-Way ANOVA Calculator

Free one-way ANOVA calculator. Test if group means differ significantly using summary statistics. Get F-statistic, degrees of freedom, and p-value.

## What this calculates

Perform a one-way analysis of variance (ANOVA) to test whether the means of three groups are statistically different. Enter the mean, standard deviation, and sample size for each group.

## Inputs

- **Group 1 Mean**
- **Group 1 Std Dev** — min 0.0001
- **Group 1 Size** — min 2
- **Group 2 Mean**
- **Group 2 Std Dev** — min 0.0001
- **Group 2 Size** — min 2
- **Group 3 Mean**
- **Group 3 Std Dev** — min 0.0001
- **Group 3 Size** — min 2

## Outputs

- **F-Statistic** — The ratio of between-group variance to within-group variance.
- **df (Between Groups)** — Degrees of freedom between groups (k - 1).
- **df (Within Groups)** — Degrees of freedom within groups (N - k).
- **Mean Square (Between)** — Mean square between groups.
- **Mean Square (Within)** — Mean square within groups.
- **Approximate P-Value** — Approximate p-value from the F-distribution.
- **Significant at α = 0.05?** — formatted as text — Whether the result is statistically significant.

## Details

ANOVA tests whether there is a statistically significant difference among group means.

Key Components

- SSB (Sum of Squares Between): Variation due to differences between group means

- SSW (Sum of Squares Within): Variation within each group

- F = MSB / MSW: Ratio of between-group to within-group variance

If the F-statistic is large enough (p < 0.05), at least one group mean is significantly different. ANOVA does not tell you which groups differ -- use post-hoc tests for that.

## Frequently Asked Questions

**Q: What is the difference between ANOVA and a t-test?**

A: A t-test compares the means of exactly two groups, while ANOVA compares the means of three or more groups simultaneously. Running multiple t-tests increases the risk of Type I error; ANOVA controls this by testing all groups at once.

**Q: What assumptions does ANOVA make?**

A: One-way ANOVA assumes: (1) independence of observations, (2) normal distribution within each group, (3) homogeneity of variances (equal variances across groups). Moderate violations of normality are tolerable with large sample sizes.

**Q: What should I do after a significant ANOVA result?**

A: A significant ANOVA only tells you that at least one group differs, not which ones. Use post-hoc tests like Tukey's HSD, Bonferroni correction, or Scheffé's test to determine which specific pairs of groups differ.

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Source: https://vastcalc.com/calculators/statistics/anova
Category: Statistics
Last updated: 2026-04-21