Enter Data
Paste raw rows or upload a CSV file. Use five columns in this order: Factor A, Factor B, Factor C, Factor D, Response.
Example Data Table
The example below matches the sample dataset preloaded in the textarea. It uses a balanced two-level design with two replicates per cell.
| Factor A | Factor B | Factor C | Factor D | Response |
|---|---|---|---|---|
| A1 | B1 | C1 | D1 | 46.7 |
| A1 | B1 | C1 | D1 | 49.3 |
| A1 | B1 | C1 | D2 | 49.7 |
| A1 | B1 | C1 | D2 | 52.3 |
| A1 | B1 | C2 | D1 | 51.7 |
| A1 | B1 | C2 | D1 | 54.3 |
| A1 | B1 | C2 | D2 | 56.7 |
| A1 | B1 | C2 | D2 | 59.3 |
| A1 | B2 | C1 | D1 | 42.7 |
| A1 | B2 | C1 | D1 | 45.3 |
| A1 | B2 | C1 | D2 | 42.7 |
| A1 | B2 | C1 | D2 | 45.3 |
Formula Used
Model: Y = μ + A + B + C + D + AB + AC + AD + BC + BD + CD + ABC + ABD + ACD + BCD + ABCD + ε
Total sum of squares: SST = Σ(Yi − Ȳ)²
Residual sum of squares: SSE = Σ(Yi − Ŷi)²
Effect sum of squares: SS(effect) = RSS(reduced model) − RSS(full model)
Mean square: MS = SS / df
F statistic: F = MS(effect) / MSE
Effect size: Partial η² = SS(effect) / [SS(effect) + SSE]
This page fits a full factorial regression model with categorical predictors, then compares full and reduced models to obtain partial tests for each main effect and interaction.
How to Use This Calculator
- Label the four categorical factors and the numeric response field.
- Paste raw rows or upload a CSV file with five columns.
- Keep one observation per row and one response value per row.
- Use repeated measurements for each factor combination whenever possible.
- Click the calculate button to generate the ANOVA table, summaries, and graph.
- Review p values, F statistics, partial eta squared, and cell means.
- Download the ANOVA table as CSV or save the report as PDF.
FAQs
1. What does a 4 way ANOVA test?
It tests whether four categorical factors and their interactions explain meaningful differences in a numeric response. You get results for main effects, two-way, three-way, and four-way interactions.
2. Does this calculator need raw data?
Yes. It expects one row per observation with four factor columns and one numeric response column. Raw data allows the tool to estimate residual error, means, and interaction effects.
3. Can I use unequal group sizes?
Yes, but balanced replicated designs are easier to interpret. Very sparse or incomplete combinations can make the design matrix singular and stop the full factorial model from fitting.
4. Why are interactions important?
An interaction means the effect of one factor changes depending on another factor’s level. In four-way ANOVA, ignoring interactions can hide or distort the real pattern in the response.
5. What is partial eta squared?
Partial eta squared is an effect size measure. It estimates how much response variability is associated with a specific effect after accounting for residual variation.
6. Why might the model fail to run?
Failures usually happen when there are too few observations, missing factor combinations, or no replication left for residual error. Adding more rows often fixes the issue.
7. How should I read the p values?
Compare each p value with your alpha level. A p value below alpha suggests the effect is statistically significant under the fitted factorial model.
8. What should I report from this output?
Report the tested factors, ANOVA source, degrees of freedom, sum of squares, mean squares, F values, p values, and partial eta squared. Include design balance and replication notes.