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Montgomery Example 3.1: one-way ANOVA of plasma etch rate at four RF power levels with Tukey HSD
| Tool | Hypothesis Tests |
| Source | Montgomery, D. C. (2013). Design and Analysis of Experiments, 8th ed. John Wiley and Sons, Hoboken, NJ. Example 3.1 and Table 3.1 (plasma etching experiment), Section 3.5.7 (Tukey's test), Appendix Table VII. |
| Level | Undergraduate |
Problem
An engineer etched five wafers at each of four RF power settings (160, 180, 200 and 220 W) and recorded the etch rate in Å/min. Test at α = 0.05 whether power affects the etch rate and determine which pairs of power levels differ by Tukey's HSD.
Inputs to Enter
- 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
- Test: One-way ANOVA (and Tukey HSD), α = 0.05; paste one group per row
Answers
- SS_Treatments = 66,870.55, SS_E = 5,339.20, SS_T = 72,209.75
- MS_E = 333.70, F = 66.80 on (3, 16) df, p = 2.88 × 10⁻⁹ (book: P < 0.01)
- η² = 66,870.55 / 72,209.75 = 0.926
- Tukey HSD T_0.05 = q_0.05(4,16) √(MS_E/n) = 33.09 with q = 4.05 (tool q = 4.046); all six pairs of means differ
Notes
Select the ANOVA test and paste the four rows of five values. Montgomery reads q_0.05(4,16) = 4.05 from his Table VII; the tool integrates the studentized range distribution (4.046), so its HSD differs from 33.09 in the third digit.