Statistics

ANOVA Calculator

Run a one-way ANOVA on three group summaries.

Group 1 size

Group 1 mean

Group 1 SD

Group 2 size

Group 2 mean

Group 2 SD

Group 3 size

Group 3 mean

Group 3 SD

Calculated Output

F-statistic 7.219

df between 2

df within 27

Formula: F = (SSB/df_between) ÷ (SSW/df_within)

Step-by-Step Breakdown

1. Values used:

2. Group 1 size = 10

3. Group 1 mean = 20

4. Group 1 SD = 3

5. Group 2 size = 10

6. Group 2 mean = 24

7. Group 2 SD = 3.5

8. Group 3 size = 10

9. Group 3 mean = 19

10. Group 3 SD = 2.8

11.

12. F-statistic = 7.219

13. df between = Group 1 mean / Group 1 size = 20 / 10 = 2

14. df within = 27

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The math behind it

It compares between-group variance to within-group variance: F = MS_between ÷ MS_within. A large F suggests real differences.

Means 20/24/19 → F ≈ 6.4, df 2 and 27.

What does a big F mean?

Compare it to the F critical value; if larger, at least one group mean differs significantly.