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Montgomery DOE Example 6.2: filtration rate, unreplicated 2⁴ factorial with Lenth's method
| Tool | ANOVA and DOE |
| Source | Montgomery, D. C. (2013). Design and Analysis of Experiments, 8th ed. Wiley, Hoboken, NJ. Example 6.2, Tables 6.10, 6.12 and 6.13, Section 6.5; Lenth, R. V. (1989). "Quick and Easy Analysis of Unreplicated Factorials." Technometrics, Vol. 31, No. 4, pp. 469–473. |
| Level | Graduate |
Problem
A single replicate of a 2⁴ design studies temperature (A), pressure (B), formaldehyde concentration (C) and stirring rate (D) on the filtration rate of a chemical product. Estimate the fifteen effects, decide which are active without a replicate error estimate, and fit the regression model in coded units.
Inputs to Enter
- Analysis '2^k factorial' (loads the 16 runs of Table 6.10: four −1/+1 columns then the response)
- Factor names 'A B C D'; α 0.05
Answers
- Grand mean 70.06; effects A 21.625, B 3.125, C 9.875, D 14.625, AB 0.125, AC −18.125, AD 16.625, BC 2.375, BD −0.375, CD −1.125, ABC 1.875, ABD 4.125, ACD −1.625, BCD −2.625, ABCD 1.375 (Table 6.12)
- SS_A 1870.56, SS_AC 1314.06, SS_AD 1105.56, SS_D 855.56, SS_C 390.06; SS_T 5730.94; A contributes 32.64 %, AC 22.93 %
- Lenth: s0 = 3.9375, PSE = 2.625, ME = 2.571 × 2.625 = 6.75, SME = 13.70; active set {A, C, D, AC, AD}
- Model: 70.06 + 10.81 x1 + 4.94 x3 + 7.31 x4 − 9.06 x1 x3 + 8.31 x1 x4
- Projection onto A, C, D (Table 6.13): MS_E 22.44 on 8 df; F_A 83.36, F_C 17.38, F_D 38.13, F_AC 58.56, F_AD 49.27
Notes
Choosing the factorial analysis in the Analysis select loads this example; the pooled-error ANOVA on the page pools the ten inactive effects, while Table 6.13 is the projection the test script reproduces by choosing the terms. Not the default selection.