Calculator Input
Paste three columns only: parent group, nested group, and numeric response. Nested labels are interpreted within each parent group.
Example Data Table
| Parent Group | Nested Group | Response |
|---|---|---|
| Model A | Run 1 | 0.812 |
| Model A | Run 1 | 0.805 |
| Model A | Run 2 | 0.842 |
| Model B | Run 1 | 0.781 |
| Model B | Run 2 | 0.804 |
| Model C | Run 1 | 0.861 |
| Model C | Run 2 | 0.874 |
| Model C | Run 2 | 0.877 |
Formula Used
yijk = μ + αi + βj(i) + εk(ij)
SSTotal = Σ(yijk − ȳ...)²
SSA = Σ ni(ȳi.. − ȳ...)²
SSB(A) = Σ Σ nij(ȳij. − ȳi..)²
SSError = Σ Σ Σ(yijk − ȳij.)²
MS = SS / df
FA = MSA / MSB(A)
FB(A) = MSB(A) / MSError
η² = SSsource / SSTotal
ω² adjusts η² by the comparison mean square.
This calculator supports balanced and unbalanced inputs. Classical nested ANOVA interpretation is strongest for balanced designs with clearly nested structure and repeated observations.
How to Use This Calculator
- Enter labels for the parent factor, nested factor, and response field.
- Choose the delimiter that matches your pasted dataset.
- Paste exactly three columns of data into the textarea.
- Keep the header option checked when the first row contains column names.
- Set alpha and display precision, then run the calculation.
- Review the ANOVA table, effect sizes, descriptives, and Plotly graph.
- Use the export buttons to save the results as CSV or PDF.
Frequently Asked Questions
1) What is hierarchical ANOVA?
Hierarchical ANOVA studies variation across levels that are nested inside other levels. It separates top-level differences, within-parent subgroup differences, and leftover random error.
2) When should I use this calculator?
Use it when each lower-level unit belongs to only one higher-level unit, such as runs within models, students within classes, or sensors within machines.
3) Can it handle unbalanced data?
Yes. The calculator accepts unequal subgroup sizes and unequal subgroup counts. Still, exact textbook testing assumptions are strongest when the design is balanced.
4) What does the top-level F test compare?
It compares the parent-group mean square against the nested-group-within-parent mean square. That checks whether top groups differ beyond lower-level subgroup variation.
5) Why are repeated observations required?
Residual error is estimated from repeated values inside each nested group. Without replication, the calculator cannot estimate the within-subgroup error term properly.
6) Can the same nested label appear under different parent groups?
Yes. A nested label is interpreted within its parent group. For example, Run 1 inside Model A is treated separately from Run 1 inside Model B.
7) What do eta squared and omega squared mean?
Eta squared shows the proportion of total variation attributed to a source. Omega squared is a more conservative effect-size estimate that reduces upward bias.
8) When should I move to mixed-effects modeling?
Move to mixed-effects models when your hierarchy is deeper, covariance matters, missingness is complex, or you need flexible random-effect structures and robust inference.