An analyst desk with three sample containers and a magnifying glass over a blank report. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
The omnibus question comes first
One-way ANOVA tests the null hypothesis that all modeled population group means are equal. A rejection says the equal-means model does not fit the observed between-group variation as well as expected under the assumptions. It does not tell you that every mean differs, or identify which particular pair differs. Those are additional questions.
Read the table through a worked dataset
For groups [1,2,3], [4,5,6] and [7,8,9], the grand mean is 5. Between-group SS is 54 and its two degrees of freedom give MS = 27. Within-group SS is 6 with six degrees of freedom, giving MS = 1. The ratio is F = 27. The upper-tail probability under F(2,6) is 0.001. At a prespecified 5% significance level, the ordinary test rejects the equal-means null.
| Source | SS | df | MS |
|---|---|---|---|
| Between groups | 54 | 2 | 27 |
| Within groups | 6 | 6 | 1 |
A small p-value does not measure the size of an effect
The example has eta squared = 54/(54+6) = 0.9, the fraction of observed total squared variation assigned to group differences in this sample decomposition. This is not a causal fraction, an unbiased population effect estimate or a universal label such as “large.” Report group means in their original units and consider uncertainty and practical consequences. The p-value is not the probability that the null hypothesis is true.
Plan what follows the global test
If specific pairwise comparisons matter, choose a suitable comparison procedure and account for multiplicity. This calculator does not silently perform a post-hoc test. A non-rejection likewise does not prove equality; equivalence needs its own margin and analysis. Use the ANOVA Calculator for the table and read the independent-group preparation guide before accepting the test interpretation. The site's existing confidence interval tool addresses estimation questions under its own stated scope, rather than replacing ANOVA or post-hoc comparisons.
Check the model behind your result
Use the ANOVA Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26