One-Way ANOVA Calculator
Compare the means of three or more groups with a one-way analysis of variance. Get the full ANOVA table, the F statistic, and the p-value, with a shaded F-distribution chart.
One group per line; separate values with commas or spaces.
| Source | SS | df | MS |
|---|---|---|---|
| Between | 392.6667 | 2 | 196.3333 |
| Within | 72.2500 | 9 | 8.0278 |
| Total | 464.9167 | 11 | — |
F distribution (2, 9)
p = 0.0002How to use this calculator
- Enter each group on its own line, with the values separated by commas or spaces.
- Use two or more groups; they can have different sizes.
- Read the F statistic and p-value, and the full ANOVA table of sums of squares.
What is one-way ANOVA?
One-way analysis of variance (ANOVA) tests whether the means of three or more independent groups differ. The null hypothesis is that all group means are equal. Rather than comparing groups two at a time, ANOVA compares the variation between groups to the variation within groups using a single F test.
Reading the ANOVA table
- Between-groups SS measures how far the group means are from the grand mean.
- Within-groups SS measures the variation of values around their own group mean.
- Each SS is divided by its degrees of freedom to give a mean square (MS).
- F is the ratio of the two mean squares; a large F gives a small p-value.
Interpreting the result
If the p-value is below your significance level (often 0.05), at least one group mean differs from the others. ANOVA does not tell you which groups differ — a post-hoc test (such as Tukey’s HSD) is used for that.
ANOVA in Excel
Enable the Analysis ToolPak, then use Data → Data Analysis → Anova: Single Factor. Excel outputs the same ANOVA table, F statistic, and p-value.
Frequently asked questions
When should I use ANOVA instead of a t-test?
Use a two-sample t-test to compare two groups, and one-way ANOVA to compare three or more groups at once. Running many t-tests inflates the chance of a false positive, which ANOVA avoids.
What does a significant ANOVA result tell me?
It tells you that at least one group mean is different from the others, but not which one. A post-hoc test such as Tukey’s HSD is needed to identify the specific differences.
What are the assumptions of one-way ANOVA?
ANOVA assumes the observations are independent, the groups are approximately normally distributed, and the group variances are roughly equal (homogeneity of variance).