ANOVA Calculator - One-Way Analysis of Variance with F Statistic and p-Value
ANOVA Calculator
Do these groups have the same average?
Any Number of Groups
Compare two, three or many groups at once instead of running many pairwise tests.
Full ANOVA Table
See the sums of squares, mean squares, degrees of freedom, F and p, plus the effect size.
Group Summary
Each group’s size, mean and standard deviation are listed so you can see what drives the result.
Private
Your data stays in your browser.
What a One-Way ANOVA Tells You
Analysis of variance compares the averages of several groups at once. It splits the total variation in the data into the part between the groups, which reflects real differences between group means, and the part within the groups, which is just natural scatter. The F statistic is the ratio of the two: if the groups really have the same average, F should be near 1, and a much larger F means the means are probably not all equal.
The p-value is the probability of seeing an F this large if all the group means were in fact equal. A p-value below your chosen significance level, often 0.05, is called significant. ANOVA only says that at least one mean differs. To find which, run a follow-up such as Tukey’s test. The method assumes the observations are independent, the groups are roughly normally distributed and their spreads are similar. With very unequal group sizes or spreads, Welch’s ANOVA is safer.
Key Takeaways
- Checked against SciPy: F statistics and p-values match scipy.stats.f_oneway, including very small p-values.
- Effect size matters: Eta squared is the share of total variation explained by the groups. A significant result can still be a small effect.
- Related calculators: See also the t-Test Calculator for two groups and the Standard Deviation Calculator.