Tools › Quality › Design of Experiments › ANOVA and DOE › Example
Box, Hunter and Hunter Table 5.2: pilot plant 2³ factorial, temperature, concentration and catalyst
| Tool | ANOVA and DOE |
| Source | Box, G. E. P., Hunter, J. S., and Hunter, W. G. (2005). Statistics for Experimenters: Design, Innovation, and Discovery, 2nd ed. Wiley, Hoboken, NJ. Tables 5.2 and 5.3. |
| Level | Undergraduate |
Problem
A pilot plant experiment varies temperature (T, 160/180 °C), concentration (C, 20/40 %) and catalyst (K, A/B) in a 2³ design with yields 60, 72, 54, 68, 52, 83, 45, 80 in standard order. Compute the main effects and interactions and judge which matter.
Inputs to Enter
- Analysis '2^k factorial'; data typed as eight lines '- - - 60', '+ - - 72', '- + - 54', '+ + - 68', '- - + 52', '+ - + 83', '- + + 45', '+ + + 80'
- Factor names 'T C K'; α 0.05
Answers
- Average 64.25
- Effects T 23.0, C −5.0, K 1.5, TC 1.5, TK 10.0, CK 0.0, TCK 0.5 (Table 5.3)
- Lenth (single replicate): s0 = 2.25, PSE = 2.25; T and TK active, CK not
Notes
Type the eight runs in place of the loaded factorial example (− and + are read as −1 and +1). The book judges the effects by eye and by a replicate variance; the tool applies Lenth's PSE. Not the default case.