Free statistics tool

One-Way ANOVA Calculator

A one-way ANOVA calculator tests whether the means of independent groups differ more than expected from random variation. Enter raw observations to get the F-statistic, p-value, ANOVA table, and a clear significance result.

Group data

Separate numbers with commas, spaces, semicolons, or new lines.

Group 1
Group 2
Group 3

ANOVA result

Conclusion at alpha = 0.05

Statistically significant

Reject the null hypothesis. At least one group mean differs; use a post-hoc test to find which pairs differ.

F-statistic
15.775862
p-value
0.000205
Groups
3
Observations
18

ANOVA table

SourceSum of squaresdfMean squareFp-value
Between groups142.3333271.166715.7758620.000205
Within groups67.6667154.5111--
Total21017---

Group statistics

Control
n: 6Mean: 74.8333SD: 2.3166Variance: 5.3667
Variant A
n: 6Mean: 81.6667SD: 2.1602Variance: 4.6667
Variant B
n: 6Mean: 77.5SD: 1.8708Variance: 3.5

Grand mean: 78. Statistical results are educational and should be reviewed alongside study design, assumptions, effect sizes, and domain context.

How the ANOVA calculation works

  1. 1. Summarize groups. The calculator finds each group mean, sample variance, and the grand mean.
  2. 2. Split variation. Total variation is separated into between-group and within-group sums of squares.
  3. 3. Compute F. Mean square between groups is divided by mean square within groups.
  4. 4. Find p. The right tail of the F distribution gives the probability of an F-statistic this large under equal means.
F = MS between / MS within

ANOVA assumptions

  • Independent observations: one measurement should not determine another.
  • Approximately normal outcomes: especially important with small samples.
  • Similar variances: group spreads should be reasonably comparable.
  • Numeric outcome: the dependent variable should be measured on an interval or ratio scale.

ANOVA calculator FAQ

What does a one-way ANOVA test?

A one-way ANOVA tests whether the means of three or more independent groups are all equal. A small p-value indicates that at least one group mean differs, but it does not identify which pair differs.

How do I interpret the ANOVA p-value?

Compare the p-value with your alpha level. If p is smaller than alpha, reject the null hypothesis and conclude that at least one group mean is statistically different.

What assumptions does one-way ANOVA make?

One-way ANOVA assumes independent observations, roughly normal outcomes within each group, and similar group variances. Severe violations can make the p-value unreliable.

What should I do after a significant ANOVA?

Run a post-hoc comparison such as Tukey's HSD to determine which group pairs differ. Adjusting for multiple comparisons helps control false positives.

Can I use ANOVA for only two groups?

Yes, a one-way ANOVA with two groups is mathematically equivalent to an independent two-sample t-test when the same variance assumptions are used. ANOVA is most useful for three or more groups.

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