Calculator Inputs
Use balanced data with equal replications in every cell.
Example Data Table
This example matches the default dataset inside the calculator.
| Factor A | Factor B | Value |
|---|---|---|
| Method A | Morning | 52 |
| Method A | Morning | 49 |
| Method A | Morning | 51 |
| Method A | Evening | 60 |
| Method A | Evening | 58 |
| Method A | Evening | 61 |
| Method B | Morning | 55 |
| Method B | Morning | 57 |
| Method B | Morning | 56 |
| Method B | Evening | 64 |
| Method B | Evening | 63 |
| Method B | Evening | 62 |
| Method C | Morning | 59 |
| Method C | Morning | 60 |
| Method C | Morning | 58 |
| Method C | Evening | 68 |
| Method C | Evening | 67 |
| Method C | Evening | 69 |
Formula Used
Grand mean: GM = Σy / N
Factor A sum of squares: SSA = b×n×Σ(ȳi.. − GM)²
Factor B sum of squares: SSB = a×n×Σ(ȳ.j. − GM)²
Interaction sum of squares: SSAB = n×ΣΣ(ȳij. − ȳi.. − ȳ.j. + GM)²
Error sum of squares: SSE = ΣΣΣ(yijk − ȳij.)²
Mean square: MS = SS / df
F statistic: F = MSeffect / MSerror
Eta squared: η² = SSeffect / SStotal
This calculator uses balanced two-factor ANOVA with replication.
How to Use This Calculator
- Name both factors and the response variable.
- Choose the significance level and decimal precision.
- Paste balanced rows in the format Factor A, Factor B, Value.
- Ensure each factor combination has equal replications.
- Click Calculate ANOVA to view the summary above the form.
- Review the ANOVA table, cell means, and interaction graph.
- Use Download CSV for spreadsheet work.
- Use Download PDF for a clean report snapshot.
FAQs
1. What does this calculator test?
It tests whether Factor A, Factor B, and their interaction significantly affect one continuous response variable in a balanced replicated design.
2. Does this calculator require balanced data?
Yes. Every Factor A and Factor B combination must contain the same number of observations. Unequal cells can distort the standard balanced ANOVA formulas.
3. Why are replications needed?
Replications let the calculator estimate the within-cell error term. Without replication, the interaction and residual structure cannot be separated cleanly here.
4. What does a significant interaction mean?
A significant interaction means the effect of one factor changes across levels of the other factor. Main effects should then be interpreted carefully.
5. What does eta squared show?
Eta squared estimates how much of the total variation is explained by a factor or interaction. Larger values suggest stronger practical impact.
6. What file format should I paste?
Paste plain comma-separated rows as Factor A, Factor B, Value. A header row is allowed because the calculator skips the first nonnumeric value row.
7. What does the Plotly graph show?
The graph plots cell means across Factor B levels, using one line for each Factor A level. Diverging slopes suggest interaction patterns.
8. Can I export the results?
Yes. The page can export a CSV summary for analysis and a PDF snapshot for reporting, review, or sharing.