Question 9.9: The article "Uncertainty in Measurements of Dennal Absorptio...
The article “Uncertainty in Measurements of Dennal Absorption of Pesticides” (W . Navidi and A. Bunge, Risk Analysis, 2002:11 75-1182) describes an experiment in which a pesticide was applied to skin at various concentrations and for various lengths of time. The outcome is the amount of the pesticide that was absorbed into the skin. The following output (from MINITAB) presents the ANOYA table. ls the additive model plausible? If so, do either the concentration or the duration affect the amount absorbed?
T’wo-way ANOVA: Absorbed versus Concentration. Duration
\begin{array}{lrrrrr}\text{Source}& \text{DF}& \text{SS}& \text{MS}& \text{F}& \text{P}\\\text{Concent}& 2 & 49.991 & 24.996 & 107.99 & 0.000 \\\text{Duration}& 2 & 19.157 & 9.579 & 41.38 & 0.000 \\\text{Interaction}& 4 & 0.337 & 0.084 & 0.36 & 0.832 \\\text{Error}& 27 & 6.250 & 0.231 & & \\\text{Total}& 35 & 75.735 & & &\end{array}| 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 | |||
The P-value for the interaction is 0.832, so we conclude that the additive model is plausible. The P-values for both concentration and dose are very small. Therefore we can conclude that both concentration and duration affect the amount absorbed.