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Montgomery DOE Example 5.1: battery life, material × temperature two-way ANOVA
| Tool | ANOVA and DOE |
| Source | Montgomery, D. C. (2013). Design and Analysis of Experiments, 8th ed. Wiley, Hoboken, NJ. Example 5.1, Tables 5.1 and 5.5, Section 5.3.2. |
| Level | Undergraduate |
Problem
Three plate materials are tested at three temperatures (15, 70, 125 °F) with four batteries per cell, 36 observations in all. Do material, temperature and their interaction affect battery life, and at 70 °F which materials differ?
Inputs to Enter
- Analysis 'Two-way ANOVA with replication' (loads the Table 5.1 data: lines 'material temperature y y y y')
- Factor names 'Material Temperature'; α 0.05
Answers
- SS: Material 10,683.72, Temperature 39,118.72, Interaction 9,613.78, Error 18,230.75, Total 77,646.97
- MS: 5,341.86 / 19,559.36 / 2,403.44 / 675.21; F = 7.91, 28.97, 3.56; P = 0.0020, < 0.0001, 0.0186
- Cell mean material 1 at 15 °F 134.75; material means 83.17, 108.33, 125.08; temperature means 144.83, 107.58, 64.17; grand mean 105.53
- Tukey at 70 °F: T0.05 = q(3, 27) √(MS_E/4) = 45.47 (book q 3.50); materials 2 and 3 do not differ (26 < 45.47), material 1 differs from 2 (62.5)
Notes
Choosing the two-way analysis in the Analysis select loads this example into the data box through set_input_values; not the default selection.