Two-Way ANOVA
Analyse PhaseBBTest the effect of two categorical factors and their interaction on a continuous response. Identifies main effects (Factor A, Factor B) and the A×B interaction effect.
Data (12 rows)
| Factor A | Factor B | Value | |
|---|---|---|---|
| Machine A | Operator 1 | 12.3 | |
| Machine A | Operator 1 | 11.8 | |
| Machine A | Operator 2 | 14.1 | |
| Machine A | Operator 2 | 13.7 | |
| Machine B | Operator 1 | 10.2 | |
| Machine B | Operator 1 | 10.8 | |
| Machine B | Operator 2 | 15.3 | |
| Machine B | Operator 2 | 14.9 | |
| Machine C | Operator 1 | 11.5 | |
| Machine C | Operator 1 | 12 | |
| Machine C | Operator 2 | 13.2 | |
| Machine C | Operator 2 | 13.8 |
ANOVA Table
| Source | SS | df | MS | F | p-value |
|---|---|---|---|---|---|
| Factor A (e.g. Machine) | 0.2450 | 2 | 0.1225 | 0.955 | p = 0.4366 ns |
| Factor B (e.g. Operator) | 22.4133 | 1 | 22.4133 | 174.649 | p < 0.001 *** |
| Factor A (e.g. Machine) × Factor B (e.g. Operator) | 5.2317 | 2 | 2.6158 | 20.383 | p = 0.0021 ** |
| Error | 0.7700 | 6 | 0.1283 | — | — |
| Total | 28.6600 | 11 | — | — | — |
R² = 97.31% · Grand Mean = 12.8000
Cell Means Plot
- Operator 1
- Operator 2
Interpretation
Factor A (e.g. Machine): No significant main effect (p = 0.4366).
Factor B (e.g. Operator): Significant main effect (p = 0.0000). The levels of Factor B (e.g. Operator) produce significantly different means.
Interaction (Factor A (e.g. Machine) × Factor B (e.g. Operator)): Significant interaction (p = 0.0021). The effect of one factor depends on the level of the other. Interpret main effects with caution.
Model R² = 97.31% of total variation explained by the model.