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Calculation Machine

ANOVA Calculator (One-Way)

Compare three groups at once with F, p and eta squared.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
F statistic
61.5385
p-value
< 0.0001
Verdict
p < 0.001 — very strong evidence
Eta squared (effect size)
0.911
df (between, within)
2, 12
Group means
6.4 | 10.4 | 14.4

Working

  1. 1SS between = 160
  2. 2SS within = 15.6
  3. 3F = (160/2) ÷ (15.6/12) = 61.538

Quick answer

One-way ANOVA splits total variation into between-group and within-group parts; F = MS between ÷ MS within, and a large F means the group means differ.

The formula

F = MS_between ÷ MS_within

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Group 1 values5, 7, 6, 8, 6
  • Group 2 values9, 11, 10, 12, 10
  • Group 3 values (optional)14, 13, 15, 16, 14

Result

  • F statistic61.5385
  • p-value< 0.0001
  • Verdictp < 0.001 — very strong evidence
  • Eta squared (effect size)0.911
  • df (between, within)2, 12
  • Group means6.4 | 10.4 | 14.4

How to use the ANOVA Calculator (One-Way)

  1. 1Enter each group's raw values on its own line of inputs.
  2. 2Leave group 3 blank if you only have two groups.
  3. 3Read F and p, then use eta squared to see how much variation the grouping explains.

Frequently asked questions

What does a significant ANOVA tell me?

That at least one group mean differs — not which one. Follow up with pairwise t-tests and a correction such as Bonferroni.

What is a good eta squared?

Roughly 0.01 small, 0.06 medium, 0.14 large as a share of total variance explained.

About this calculator