ANOVA Calculator
Calculate a one-way ANOVA F statistic for three groups.
One-way ANOVA
ANOVA compares variation between group means with variation inside the groups. A larger F statistic indicates stronger separation relative to within-group variability.
How One-Way ANOVA Works
One-way ANOVA compares the means of three or more independent groups by separating variation between groups from variation within groups. The resulting F statistic indicates whether group-level differences are large relative to ordinary within-group variability.
ANOVA Example
Imagine comparing average test scores from three teaching methods. If the group means differ substantially while scores within each group are relatively consistent, the F statistic becomes larger and the evidence against equal group means increases.
What to Check Before Interpreting
ANOVA assumes independent observations and is most reliable when group variances are reasonably similar and residuals are not severely non-normal. A significant result tells you that at least one mean differs, but not which specific groups differ.
Frequently Asked Questions
Does ANOVA compare more than two groups?
Yes. It is commonly used when three or more means need to be compared in one overall test.
What happens after a significant ANOVA?
Post-hoc comparisons are often used to identify which groups differ.
Is a large F statistic always significant?
Significance depends on the F value together with degrees of freedom and the selected significance level.
What One-Way ANOVA Tests
One-way ANOVA compares variation between group means with variation within groups to test a common-mean null hypothesis. A significant result indicates evidence that not all group means are equal, but it does not identify which groups differ. Post-hoc comparisons and checks of assumptions may be needed.
Methodology, Assumptions and Interpretation
One-way ANOVA compares between-group variability with within-group variability through an F statistic. A significant result indicates that not all group means are equal, but post-hoc comparisons are needed to identify which groups differ; independence and variance assumptions should also be checked.