One-Way ANOVA Calculator

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A one-way ANOVA tests whether three or more group means are all equal. It compares the spread between the group means with the spread within the groups: F = MS_between ÷ MS_within. A large F and a small p-value point to a real difference.

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Group 1

Group 2

Group 3

Group 4 (optional)

Group 5 (optional)

Significance level α

F(2, 15)

0.813

p = 0.462. Fail to reject H₀ at α = 0.05: the data do not show a difference between the means.

Groups
Group 1 (n = 6)	mean 84.3333, SD 6.8896
Group 2 (n = 6)	mean 88.6667, SD 3.8297
Group 3 (n = 6)	mean 86, SD 6.603
ANOVA table
Between groups	SS 57.3333, df 2, MS 28.6667
Within groups	SS 528.6667, df 15, MS 35.2444
Total	SS 586, df 17
Test
F statistic	0.8134
p-value	0.462
Critical F at α = 0.05	3.6823
Eta squared (η²)	0.0978

Show steps

Grand mean = 1,554 ÷ 18 = 86.3333.
SS between = Σ n(group mean − grand mean)² = 57.3333.
SS within = Σ (value − its group mean)² = 528.6667.
MS between = 57.3333 ÷ 2 = 28.6667; MS within = 528.6667 ÷ 15 = 35.2444.
F = 28.6667 ÷ 35.2444 = 0.8134, with df (2, 15).
p-value = area to the right of F = 0.462.

How to use the ANOVA calculator

Enter each group’s values in its own box, separated by commas or spaces. You can use two to five groups, and they can be different sizes.
Set the significance level (0.05 is common).
Press Calculate to get the ANOVA table, the F statistic, the p-value and eta squared.

What one-way ANOVA tests

The null hypothesis is H₀: μ₁ = μ₂ = … = μ_k. The alternative is that at least one mean is different. ANOVA uses one test for all the groups, instead of many t tests that would raise the chance of a false positive.

Source	SS	df	MS	F
Between groups	Σ n_j(x̄_j − x̄)²	k − 1	SS ÷ df	MS_B ÷ MS_W
Within groups	Σ (x − x̄_j)²	N − k	SS ÷ df
Total	Σ (x − x̄)²	N − 1

Assumptions

The observations are independent.
Each group comes from a roughly normal population. ANOVA copes well with mild departures when the groups are similar in size.
The groups have similar variances. A rule of thumb is that the largest standard deviation is less than twice the smallest.

Reading eta squared

Eta squared (η² = SS_between ÷ SS_total) is the share of the total variation explained by the groups. Common rough guides are 0.01 small, 0.06 medium and 0.14 large. A tiny p-value with a small η² can happen with very large samples.

ANOVA practice questions

Test yourself with 6 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.

Frequently asked questions

What does a one-way ANOVA tell you?

It tells you whether the means of three or more groups are all equal. A small p-value says at least one mean differs; a post-hoc test tells you which ones.

How is the F statistic calculated?

F is the mean square between groups divided by the mean square within groups. Each mean square is a sum of squares divided by its degrees of freedom.

Can I use ANOVA with two groups?

Yes. With two groups the one-way ANOVA gives the same p-value as a two-sample t test with equal variances, and F equals t².

Do the groups need to be the same size?

No. One-way ANOVA works with unequal group sizes, though equal sizes make it less sensitive to unequal variances.

Sources

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