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Montgomery DOE Example 3.1: plasma etching, one-way ANOVA with Tukey and LSD
| Tool | ANOVA and DOE |
| Source | Montgomery, D. C. (2013). Design and Analysis of Experiments, 8th ed. Wiley, Hoboken, NJ. Examples 3.1, 3.3, 3.4, 3.7 and 3.8, Tables 3.1, 3.4 and 3.6. |
| Level | Undergraduate |
Problem
An engineer tests four RF power settings (160, 180, 200, 220 W) on the etch rate of a plasma etching tool, five wafers at each setting. Test whether power affects the etch rate, give a confidence interval on the 160 W mean, check the equal-variance assumption and find which pairs of means differ.
Inputs to Enter
- Analysis One-way ANOVA; α 0.05
- 160 W: 575 542 530 539 570 / 180 W: 565 593 590 579 610 / 200 W: 600 651 610 637 629 / 220 W: 725 700 715 685 710 (loaded by default)
Answers
- Means 551.2, 587.4, 625.4, 707.0; grand mean 617.75
- SS_Treatments 66,870.55, SS_E 5,339.20, SS_T 72,209.75; MS_Treatments 22,290.18, MS_E 333.70; F0 = 66.80, P < 0.01; R² = 0.9261
- 95 % CI on μ1: 533.88 to 568.52 (Example 3.3); Bartlett χ0² = 0.43 (Example 3.4), variances homogeneous
- Tukey T0.05 = 4.05 √(333.70/5) = 33.09 (Example 3.7); LSD = 24.49 (Example 3.8); every pair differs
- Residual e11 = 23.8 (Table 3.6)
Notes
The tool's default inputs are this example; press Submit.