Enter Factorial Data
Use balanced raw data. Each line must be: Factor A level, Factor B level, response. Include equal observations for every cell.
Example Data Table
| Teaching Method | Study Schedule | Score |
|---|---|---|
| Video | Daily | 78 |
| Video | Daily | 82 |
| Video | Daily | 80 |
| Video | Weekly | 69 |
| Video | Weekly | 72 |
| Video | Weekly | 71 |
| Text | Daily | 84 |
| Text | Daily | 88 |
| Text | Daily | 86 |
| Text | Weekly | 74 |
| Text | Weekly | 77 |
| Text | Weekly | 76 |
Formula Used
Total sum of squares: SST = Σ(yijk − ȳ···)2
Factor A sum of squares: SSA = bn Σ(ȳi·· − ȳ···)2
Factor B sum of squares: SSB = an Σ(ȳ·j· − ȳ···)2
Interaction sum of squares: SSAB = n Σ(ȳij· − ȳi·· − ȳ·j· + ȳ···)2
Error sum of squares: SSE = ΣΣΣ(yijk − ȳij·)2
Mean square: MS = SS ÷ df
F statistic: F = MS effect ÷ MS error
Eta squared: η² = SS effect ÷ SST
Partial eta squared: partial η² = SS effect ÷ (SS effect + SSE)
Omega squared: ω² = (SS effect − df effect × MS error) ÷ (SST + MS error)
This implementation is designed for balanced two-factor experiments with replication and fixed effects.
How to Use This Calculator
- Name your two categorical factors.
- Choose an alpha level and decimal precision.
- Paste raw data as Factor A, Factor B, response.
- Keep the design balanced across all combinations.
- Click the calculation button to generate the report.
- Review the ANOVA table, effect sizes, and means.
- Export the report as CSV or PDF when needed.
Frequently Asked Questions
1. What does this calculator test?
It tests two main effects and their interaction in a balanced factorial design with replication. You get sums of squares, F statistics, p-values, and effect sizes in one report.
2. Does it support unbalanced data?
No. This version expects equal observations in every factor combination. Unbalanced designs usually need more advanced model coding and sums-of-squares choices such as Type II or Type III.
3. Why are at least two observations per cell required?
Replication lets the calculator estimate within-cell error. Without replication, the error term cannot be separated cleanly from interaction and F testing becomes unreliable for this workflow.
4. What does the interaction row mean?
It shows whether the effect of one factor changes across levels of the other factor. A significant interaction means main effects should be interpreted with extra care.
5. What are eta squared and omega squared?
They are effect-size measures. Eta squared describes explained variance directly. Omega squared is more conservative and often preferred when you want a less biased population-level estimate.
6. Can I change the factor names?
Yes. Replace the default labels with names that match your study, such as machine type and operator shift, or campaign format and audience segment.
7. What format should the raw data follow?
Each line should contain three comma-separated entries: first factor level, second factor level, and the numeric response. Example: Video, Daily, 78.
8. When should I export the report?
Export after checking the ANOVA table and means. CSV works well for spreadsheets. PDF is useful for teaching notes, audit packs, and research summaries.