One Way ANOVA Calculator

Group 1

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Group 2

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Group 3

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Alpha Level (α)

Your risk tolerance for a false positive. Leave blank to default to 0.05.

About This Test

What Is One-Way ANOVA?

One-way ANOVA (Analysis of Variance) tests whether the means of three or more independent groups differ significantly from one another. Instead of running many separate t-tests — which stacks up your risk of a false positive — ANOVA compares all groups in a single test.

When to Use It

Comparing average scores across three or more teaching methods
Comparing average yield across three or more fertilizer treatments
Comparing average response time across three or more software versions
Any comparison of means across three or more independent groups

The Formula

\[ F = \frac{MSB}{MSW} = \frac{SSB / df_B}{SSW / df_W} \]

Worked Example

Three training programs, three employees tested each. At α = 0.05, is there a real difference in average performance?

Group 1: 5, 7, 6 (mean = 6) Group 2: 9, 11, 10 (mean = 10) Group 3: 13, 15, 14 (mean = 14)
Grand mean = 10, SSB = 96, SSW = 6
dfₖ = 2, df𝑖 = 6 → MSB = 48, MSW = 1
F = 48/1 = 48, which gives a very small p-value
Since p < 0.05, we reject H₀ — at least one program's average performance is genuinely different.

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