One-Way ANOVA Calculator
Compare the means of three or more independent groups with a transparent one-way ANOVA table and model-based upper-tail F p-value.
ANOVA compares between-group variation with variation inside the groups
The F statistic grows when group means are far apart relative to the spread of observations inside those groups. Lynara exposes SS between, SS within, both degrees of freedom and eta squared so the result is not reduced to one p-value.
The omnibus p-value does not identify a particular pair of groups. If the assignment requires follow-up comparisons, choose a post-hoc method that matches the design instead of treating the largest and smallest sample means as automatically different.
Privacy: calculator inputs are processed in your browser; Lynara does not need to upload these values to calculate the result.
Formula
F = MS between ÷ MS within; p = P(F(df₁,df₂) ≥ observed F); η² = SS between ÷ SS total
Example
For group means 5, 9 and 10 in the sample data, F ≈ 9.2647 with df = (2, 15), p ≈ 0.002399 and η² ≈ 0.5526.
Useful for
- Intro statistics ANOVA homework
- Compare three or more independent group means
- Check an ANOVA F statistic and p-value
- Inspect between- and within-group sums of squares
Questions
Does ANOVA tell me which groups are different?
No. The omnibus F test evaluates whether the group means are all compatible with one common mean under the model. Identifying pairs requires a suitable post-hoc procedure.
Why require at least three groups?
Two-group mean comparison is already covered by the T-Test Calculator. This page stays focused on the distinct multi-group one-way ANOVA workflow.