Enter Nested ANOVA Data
Paste three columns: outer factor, nested factor, and numeric response.
Formula Used
Model Structure
Yijk = μ + Ai + Bj(i) + εk(ij)
The outer factor is A. The nested factor B exists only inside each A level.
Sums of Squares
SSTotal = Σ(Yijk − Ȳ)2
SSOuter = Σni..(Ȳi.. − Ȳ)2
SSNested(Outer) = ΣΣnij.(Ȳij. − Ȳi..)2
SSError = ΣΣΣ(Yijk − Ȳij.)2
Degrees of Freedom and F Tests
dfOuter = a − 1
dfNested(Outer) = b − a
dfError = N − b
FOuter = MSOuter / MSNested(Outer)
FNested(Outer) = MSNested(Outer) / MSError
This page uses weighted group means and standard nested ANOVA mean-square ratios. Balanced designs usually provide the cleanest interpretation.
How to Use This Calculator
- Label your outer factor, nested factor, and numeric response.
- Paste your dataset with exactly three columns.
- Choose alpha, decimal places, and delimiter detection.
- Click the calculate button to generate the nested ANOVA table.
- Review sums of squares, F ratios, p-values, and cell summaries.
- Use the Plotly chart to inspect mean patterns across nested groups.
- Download the result as CSV or PDF for reporting.
Example Data Table
This example uses schools as the outer factor, teachers nested inside schools, and scores as the response.
| School | Teacher | Score |
|---|---|---|
| School A | Teacher A1 | 78 |
| School A | Teacher A1 | 82 |
| School A | Teacher A1 | 80 |
| School A | Teacher A2 | 74 |
| School A | Teacher A2 | 76 |
| School A | Teacher A2 | 75 |
| School B | Teacher B1 | 88 |
| School B | Teacher B1 | 90 |
| School B | Teacher B1 | 87 |
| School B | Teacher B2 | 84 |
| School B | Teacher B2 | 85 |
| School B | Teacher B2 | 83 |
| School C | Teacher C1 | 92 |
| School C | Teacher C1 | 94 |
| School C | Teacher C1 | 91 |
| School C | Teacher C2 | 89 |
| School C | Teacher C2 | 90 |
| School C | Teacher C2 | 88 |
FAQs
1. What is nested ANOVA used for?
Nested ANOVA tests hierarchical designs where one factor exists only inside another factor. It separates variation from outer groups, inner subgroups, and residual error.
2. When should I use nested ANOVA instead of two-way ANOVA?
Use nested ANOVA when subgroup labels are unique only within a parent group. If factors cross each other fully, then a crossed two-way ANOVA is more appropriate.
3. Can the calculator handle unbalanced data?
Yes. It calculates weighted sums of squares for unequal cell sizes. Still, balanced data usually produces cleaner inference and easier interpretation.
4. What do the p-values mean here?
Each p-value estimates how likely the observed F statistic would be under the null hypothesis. Smaller values indicate stronger evidence against no effect.
5. Why is the outer factor tested against the nested factor mean square?
In nested ANOVA, subgroup variation inside each outer level acts as the correct error term for testing the outer factor. That is why the denominator changes.
6. What happens if I have only one observation per nested group?
You lose pure within-cell error estimation. Reliable testing becomes limited because the residual mean square cannot be estimated properly from replication.
7. Does the nested factor need unique names across all outer groups?
No. Nested labels can repeat, because their identity is defined within the parent level. The calculator combines both columns to preserve structure.
8. What should I inspect besides significance?
Check effect sizes, cell means, balance, replicate counts, and the graph. Statistical significance alone does not explain practical importance or design quality.