One-Way ANOVA Test Calculator
Compare the means of 2 or more independent groups. Enter one group per line. You can optionally label each group using a colon.
What this one-way ANOVA calculator does
A one-way ANOVA (Analysis of Variance) tests whether at least one group mean is different from the others. It is commonly used when you have one categorical factor (for example, treatment type) and one continuous outcome (for example, blood pressure, test scores, or reaction time).
This calculator gives you:
- Group-level summary statistics (sample size, mean, standard deviation)
- ANOVA table values (SS, df, MS, and F-statistic)
- p-value for the F-test
- Eta-squared effect size (η²)
- A plain-language interpretation at your chosen alpha level
How to use the calculator
Step 1: Enter your groups
Type each group on its own line. Values can be separated by commas, spaces, or semicolons. Labels are optional.
- With labels:
Diet A: 4, 5, 6, 7 - Without labels:
4 5 6 7
Step 2: Choose alpha
Most studies use α = 0.05. If your p-value is below alpha, you reject the null hypothesis that all group means are equal.
Step 3: Click “Calculate ANOVA”
The calculator will instantly compute your test results and interpretation.
Understanding the ANOVA output
ANOVA partitions variability into two parts:
- Between Groups: variation explained by group differences
- Within Groups: variation inside each group
The core test statistic is:
F = MSbetween / MSwithin
A larger F value suggests stronger evidence that the means are not all equal.
Assumptions for one-way ANOVA
- Independent observations
- Approximately normal outcome distribution in each group
- Homogeneity of variances across groups (similar spread)
If assumptions are strongly violated, consider alternatives such as Welch’s ANOVA or Kruskal–Wallis.
If your ANOVA is significant, what next?
A significant ANOVA tells you that at least one mean differs, but not which pairs differ. Follow up with post-hoc tests (such as Tukey HSD) for pairwise comparisons while controlling error rates.
Quick FAQ
Can group sizes be unequal?
Yes. One-way ANOVA works with unequal sample sizes, though severe imbalance can reduce robustness.
What if p is not significant?
You fail to reject the null hypothesis. That means your data do not provide strong enough evidence of mean differences at your chosen alpha.
What is eta-squared (η²)?
η² measures effect size: the proportion of total variance explained by group membership. Larger values indicate stronger group effects.