main effect
**A main effect** in DOE is the **direct impact of changing a single factor** on the response variable, averaged across all levels of the other factors. It answers the question: "What happens to the output when I change this one input from low to high?"
**How Main Effects Are Calculated**
For a factor with two levels (− and +):
$$\text{Main Effect of A} = \bar{y}_{A+} - \bar{y}_{A-}$$
The average response when A is at its high level minus the average response when A is at its low level.
**Example: Etch Process DOE**
- **Factor A**: RF Power (200W vs. 400W)
- **Factor B**: Pressure (20 mTorr vs. 50 mTorr)
- **Response**: Etch Rate (nm/min)
| Run | Power (A) | Pressure (B) | Etch Rate |
|-----|-----------|-------------|----------|
| 1 | 200W (−) | 20 mT (−) | 100 |
| 2 | 400W (+) | 20 mT (−) | 180 |
| 3 | 200W (−) | 50 mT (+) | 120 |
| 4 | 400W (+) | 50 mT (+) | 160 |
- **Main Effect of Power**: $\frac{(180+160)}{2} - \frac{(100+120)}{2} = 170 - 110 = 60$ nm/min.
- **Main Effect of Pressure**: $\frac{(120+160)}{2} - \frac{(100+180)}{2} = 140 - 140 = 0$ nm/min.
- **Interpretation**: Power has a large effect (+60 nm/min); Pressure has no main effect on average.
**Main Effect Plots**
- A **main effect plot** shows the average response at each factor level, connected by a line.
- A steep line indicates a **large main effect** — the factor strongly influences the response.
- A flat (horizontal) line indicates **no main effect** — the factor has little or no influence.
**Important Cautions**
- **Interactions Can Mislead**: If a strong **interaction effect** exists between two factors, the main effect of each factor depends on the level of the other. In such cases, the main effect (averaged across the other factor) may not tell the full story.
- **Effect Hierarchy**: In most processes, main effects are larger than two-factor interactions, which are larger than three-factor interactions. This principle justifies focusing on main effects first.
- **Statistical Significance**: Use ANOVA (Analysis of Variance) to determine whether a main effect is **statistically significant** or just due to experimental noise.
Main effects are the **first thing to examine** in any DOE analysis — they identify which process knobs have the biggest impact on the response and guide where to focus optimization effort.