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Two Level Factorial Design |
This example validates the calculation of the two level factorial design.
Reference Case
Data is from an example on page 223 in book “Design and Analysis of Experiments” by Douglas C. Montgomery, John Wiley & Sons, 2001.
Data
| Factor | Treatment Combination | Replicate | |||
|---|---|---|---|---|---|
| A | B | 1 | 2 | 3 | |
| - | - | A low, B low | 28 | 25 | 27 |
| + | - | A high, B low | 36 | 32 | 32 |
| - | + | A low, B high | 18 | 19 | 23 |
| + | + | A high, B high | 31 | 30 | 29 |
Result Table 6-1 from the book shows the ANOVA table for this experiment.
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F value | P-Value |
|---|---|---|---|---|---|
| A | 208.33 | 1 | 208.33 | 53.15 | 0.0001 |
| B | 75.00 | 1 | 75.00 | 19.13 | 0.0024 |
| AB | 8.33 | 1 | 8.33 | 2.13 | 0.1826 |
| Error | 31.34 | 8 | 3.92 | ||
| Total | 323.00 | 11 |
Results in DOE++
The results from the software are same with the results from the book, which shows that A and B are significant factors.
