05 / 06 · Two-way ANOVA
Teaching example. Synthetic data.
Does a coating behave the same under different loads?
Compare two coatings under three load levels. Is the difference between coatings constant, or does it depend on the load?
24 specimens · 2 × 3 design
- Coating effect: p
- 1.102e-8
- Load effect: p
- 4.037e-8
- Factor interaction, p
- 0.1607
Inspect the original observations
| Coating | Load | Specimen | Value |
|---|---|---|---|
| Coating A | Low | 1 | 9 |
| Coating A | Low | 2 | 10.4 |
| Coating A | Low | 3 | 11.2 |
| Coating A | Low | 4 | 9.4 |
| Coating A | Medium | 5 | 11 |
| Coating A | Medium | 6 | 12.4 |
| Coating A | Medium | 7 | 13.2 |
| Coating A | Medium | 8 | 11.4 |
| Coating A | High | 9 | 13 |
| Coating A | High | 10 | 14.4 |
| Coating A | High | 11 | 15.2 |
| Coating A | High | 12 | 13.4 |
| Coating B | Low | 13 | 12 |
| Coating B | Low | 14 | 13.4 |
| Coating B | Low | 15 | 14.2 |
| Coating B | Low | 16 | 12.4 |
| Coating B | Medium | 17 | 15 |
| Coating B | Medium | 18 | 16.4 |
| Coating B | Medium | 19 | 17.2 |
| Coating B | Medium | 20 | 15.4 |
| Coating B | High | 21 | 18 |
| Coating B | High | 22 | 19.4 |
| Coating B | High | 23 | 20.2 |
| Coating B | High | 24 | 18.4 |
Calculated by the Linza engine from this example’s data. Opening it in the editor runs a fresh calculation.
Why this method
Two-way ANOVA separates coating, load and their interaction. Each cell contains four different specimens, making this an independent rather than repeated design. The model assumes independent errors, normal residuals and a common variance.
Explore the theory: Two factors and repeated measures →Work through it in Linza
In Data, check six factor combinations and distinct specimen IDs. In Analyses, read the three effects separately. The coating effect averages over loads; interaction asks a different question: does the coating difference change with load?
Open a copy and recalculateTry changing one condition
Add 2 to every coating B observation at every load. Does the pattern of differences across loads change?
Show the explanation
The gaps become 5, 6 and 7. The overall coating gap increases, but its change across loads stays the same. A constant shift does not introduce a new interaction. Read the inference for each effect separately.
Data and reproducibility
Teaching studies with synthetic data. The scenarios reflect practical questions, but do not report real experimental findings.