Hypothesis testing · Comparing several means
One-Way ANOVA Calculator
Compare the means of three or more groups at once. You get the F statistic, df, p-value and the η² effect size, the full ANOVA table, and a reminder of what a significant F does — and doesn't — tell you about which groups differ.
Add or remove lines to change the number of groups.
Result
In plain English
ANOVA is a t-test stretched to three or more groups at once. It checks whether at least one group's average stands apart from the rest, while keeping false alarms under control (running lots of separate t-tests would not).
- F statistic
- The spread between the group averages divided by the noise within the groups. A big F means the groups differ by more than random scatter would explain.
- p-value
- How often you'd see group gaps this large if every group truly had the same average.
- η² (eta-squared)
- The share of the total variation that's explained by which group something is in — an effect size.
- post-hoc test
- ANOVA only says some group differs. A follow-up test (e.g. Tukey HSD) tells you which pairs differ, without cheating by peeking first.
Frequently asked
What does ANOVA tell me that several t-tests don't?
One-way ANOVA tests whether any of several group means differ, in a single test, without inflating the false-positive rate the way many pairwise t-tests would. A significant F means “at least one group differs” — not which one.
What's the difference between eta-squared and omega-squared?
Both measure how much of the variation the groups explain. Eta-squared (η²) is simple but biased upward in small samples; omega-squared (ω²) corrects that bias and is the more honest effect size to report.
ANOVA was significant — which groups differ?
ANOVA alone can't say. You need a post-hoc comparison (such as Tukey's HSD) that controls for multiple testing. A significant F only licenses you to look further.
What are the assumptions of ANOVA?
Independent observations, roughly normal residuals within each group, and similar variances across groups (homogeneity of variance). One-way ANOVA is fairly robust to mild departures when the groups are equal in size, but unequal variances combined with unequal group sizes can distort the F-test. When variances clearly differ, Welch’s ANOVA is safer; when the data are markedly skewed, ordinal or outlier-ridden, a Kruskal–Wallis test is the better choice.