One-Way ANOVA Calculator
The One-Way ANOVA Calculator tests whether the means of three groups differ more than you'd expect by chance. It compares the variation between group means with the variation within groups and returns the F-statistic, sums of squares, and degrees of freedom. The formula used is: F = (SS_between ÷ df_between) ÷ (SS_within ÷ df_within), with df_between = k − 1 and df_within = N − k.
Formula
F = (SS_between/df_between) / (SS_within/df_within) · df_between = k−1, df_within = N−k
Example Calculation
Inputs
- Group 1 (comma-separated): 85,87,90,88
- Group 2 (comma-separated): 78,82,80,76
- Group 3 (comma-separated): 92,95,90,94
With group means of about 87.5, 79, and 92.75, the variation between groups is large relative to the spread inside each group, giving a high F-statistic — evidence the group means genuinely differ.
Frequently asked questions
What does one-way ANOVA test?
It tests whether at least one group mean differs from the others by comparing the variance between group means to the variance within the groups.
What is the F-statistic?
F is the ratio of between-group mean square to within-group mean square. A large F suggests the group means differ more than random variation alone would produce.
How do I read the significance flag?
This tool flags F > 3.5 as potentially significant as a rough guide. For a proper decision, compare F against the critical value for your degrees of freedom and chosen significance level.
What are the degrees of freedom?
Between-groups df is k − 1 (groups minus one); within-groups df is N − k (total observations minus number of groups).
How do I enter my data?
Type the values for each group as comma-separated numbers. You can use two or three groups.