Question 9.8: Use the preceding ANOVA table to determine whether the addit...
Use the preceding ANOVA table to determine whether the additive model is plausible for the yield data. If the additive model is plausible, can we conclude that either the catalyst or the reagent affects the yield?
| ANOVA table | |||||
| Source | DF | SS | MS | F | P |
| Material | 1 | 2352.0 | 2352.0 | 10.45 | 0.012 |
| Design | 1 | 3072.0 | 3072.0 | 13.65 | 0.006 |
| Interaction | 1 | 2700.0 | 2700.0 | 12.00 | 0.009 |
| Error | 8 | 1800.0 | 225.00 | ||
| Total | 11 | 9924.0 | |||
We first check to see if the additive model is plausible. The P-value for the interactions is 0.55, which is not small. We therefore do not reject the null hypothesis that all the interactions are equal to 0, and we conclude that the additive model is plausible. Since the additive model is plausible, we now ask whether the row or column factors affect the outcome. We see from the table that the P-value for the row effects (Catalyst) is approximately 0, so we conclude that the catalyst does affect the yield. Similarly, the P-value for the column effects (Reagent) is small (0.010), so we conclude that the reagent affects the yield as well.