Calculator inputs
Example data table
This sample matches the default values already loaded into the calculator.
| Group | Sample Size | Mean | Variance |
|---|---|---|---|
| Control | 12 | 48 | 25 |
| Variant A | 15 | 55 | 36 |
| Variant B | 14 | 61 | 30 |
Formula used
For grouped summaries, the calculator rebuilds one-way ANOVA fit statistics from group sizes, means, and within-group dispersion.
Grand Mean = Σ(nᵢ × meanᵢ) / N SS Between = Σ[nᵢ × (meanᵢ − grand mean)²] SS Within = Σ[(nᵢ − 1) × varianceᵢ] SS Total = SS Between + SS Within MS Between = SS Between / (k − 1) MS Within = SS Within / (N − k) F = MS Between / MS Within
Additional fit measures:
- R² = SS Between / SS Total
- Adjusted R² = 1 − (MS Within / (SS Total / (N − 1)))
- Eta² = SS Between / SS Total
- Omega² = (SS Between − (df_between × MS Within)) / (SS Total + MS Within)
- Cohen f = √(Eta² / (1 − Eta²))
- RMSE = √MS Within
How to use this calculator
- Enter a label for each group, or leave labels blank to auto-name them.
- Provide sample sizes, group means, and either variances or standard deviations.
- Select the matching dispersion type so the calculator interprets inputs correctly.
- Choose alpha and decimal precision to match your reporting standard.
- Click Calculate model fit to generate the ANOVA table, effect sizes, and chart.
- Use the CSV button for spreadsheet export and the PDF button for report-ready output.
FAQs
1. What does this calculator estimate?
It estimates one-way ANOVA fit quality from grouped summary statistics. You get sums of squares, mean squares, F statistics, p-values, variance explained, and practical effect measures without entering every raw observation.
2. Can I use standard deviations instead of variances?
Yes. Choose the standard deviation option in the dispersion field selector. The calculator squares those values internally before rebuilding within-group variance and the ANOVA table.
3. What does R squared mean here?
R squared shows the share of total variability explained by differences among group means. Larger values indicate that the grouping factor accounts for more of the observed outcome variation.
4. Why does the tool show both eta squared and omega squared?
Eta squared is a direct explained-variance estimate. Omega squared adjusts that estimate downward to reduce upward bias, so many analysts prefer it for practical interpretation of population-level effect strength.
5. When can the F statistic become very large?
The F value becomes very large when between-group separation is strong while within-group variability is very small. That pattern suggests the grouping structure explains outcome differences unusually well.
6. Does this replace a raw-data ANOVA workflow?
It works well for fast model fit review from summary statistics, but raw-data analysis remains better for residual checks, post hoc testing, assumption diagnostics, and plots based on individual observations.
7. What assumptions should I keep in mind?
Interpret results with the usual ANOVA assumptions in mind: independent observations, roughly normal residuals within groups, and similar variance across groups. The calculator does not test those assumptions automatically.
8. What should I download as CSV or PDF?
Use CSV when you want numeric output for spreadsheets or dashboards. Use PDF when you need a clean shareable report with summary metrics, the ANOVA table, group contributions, and the graph.