ANOVA Calculator

One-way ANOVA tests whether the means of several groups differ, such as marks under three teaching methods, more safely than running many t-tests.

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Results update as you type.

F statistic

2.35753

Not significant at α = 0.05: p ≥ 0.05

p-value
0.113848
Critical F at α = 0.05
3.35413F(2, 27)
Effect size (η²)
0.14867share of variation explained by the groups
Grand mean
85.8

Group summary

Group summary
GroupnMeanStd dev
Group 11083.48.43538
Group 21089.34.80856
Group 31084.75.29255

About this calculator

It compares the variation between group means with the variation inside the groups.

How to use it

  1. Enter each group’s values.
  2. Choose the significance level.
  3. Read F, the p-value and the conclusion.

The formula

F = MS between ÷ MS within; MS = SS ÷ df
SS between
Σ nᵢ(x̄ᵢ − x̄)²
SS within
Σ Σ(x − x̄ᵢ)²
df
k − 1 and N − k

Worked example

Three groups of 10 scores

  1. F(2, 27) = 2.358, p = 0.114.
  2. p is above 0.05, so the means are not significantly different.

What the result means

A significant result says that not all means are equal. It does not say which ones differ; a post-hoc test does that.

Assumptions

  • Independent groups, roughly normal data and similar spreads.

Limitations

  • For very unequal spreads, Welch’s ANOVA is more reliable.

Frequently asked questions

What is the F statistic?

The ratio of between-group to within-group variance. Large values suggest the means differ.

Why not use several t-tests?

Each test adds a chance of a false positive; ANOVA keeps it at α overall.

What is η²?

The share of total variation explained by the groups.

Last reviewed on 6 October 2026. Found a mistake? Tell us.