One-Way ANOVA calculator

Compare means across three or more independent groups. Get full ANOVA table, F-statistic, p-value, and eta-squared effect size online.

What it does

Tests whether the means of three or more independent groups differ, by comparing variation between groups against variation within them.

When to use it

One categorical grouping variable with three or more levels, and a roughly symmetric continuous outcome with comparable spread across groups.

Cautions

• A significant F only says some group differs. It does not say which — that needs post-hoc pairwise tests with a multiplicity correction (Tukey after ANOVA).
• Equal variances is an assumption, not a formality. When it fails, Welch's ANOVA is the fix rather than proceeding regardless.
• Report an effect size (η² or ω²) beside the F: with a large sample a trivial difference is still significant.

Alternatives

• Welch's ANOVA — group variances differ or group sizes are very unequal — the safer default in practice
• Kruskal-Wallis — the outcome is skewed, ordinal, or dominated by outliers
• Repeated-measures ANOVA — the same subjects appear in every condition

How to read the output

F-statistic and df

The spread between the group means measured against the spread within them. The two df are the number of groups minus one, and the leftover observations.

p-value

How surprising a difference at least this large would be IF the groups really were identical on this measure. A small p means the data would be surprising under that assumption. It is not the probability that the result is due to chance, and not the probability that the groups are the same — those read the conditional backwards. It also answers 'would this be surprising?', never 'is this big enough to matter?': with a large sample a trivial difference returns a small p, and the result looks identical to an important one.

What a significant F does and does not say

It says the groups are not all the same. It does not say which ones differ. The pairwise question is answered by the Tukey HSD table beneath the result, which is already corrected for making several comparisons. Reading the raw group means and picking the biggest gap is the multiplicity error the correction exists to prevent.

Tukey HSD (post-hoc)

Every pair of groups compared, with intervals and p-values adjusted so the whole family of comparisons keeps a 5% error rate. A significant overall F with no significant pair afterwards is a real and reportable outcome — the evidence supports 'they are not all equal' but not any specific pair.

How this calculator is validated · Which statistical test should I use?