# The article “Anodic Fenton Treatment of Treflan MTF” describes a two-factor experiment designed to study the sorption of the herbicide trifluralin.

The article “Anodic Fenton Treatment of Treflan MTF” describes a two-factor experiment designed to study the sorption of the herbicide trifluralin. The factors are the initial trifluralin concentration and the $$\displaystyle{F}{e}^{{{2}}}\ :\ {H}_{{{2}}}\ {O}_{{{2}}}$$ delivery ratio. There were three replications for each treatment. The results presented in the following table are consistent with the means and standard deviations reported in the article. $$\begin{array}{|c|c|}\hline \text{Initial Concentration (M)} & \text{Delivery Ratio} & \text{Sorption (%)} \\ \hline 15 & 1:0 & 10.90 \quad 8.47 \quad 12.43 \\ \hline 15 & 1:1 & 3.33 \quad 2.40 \quad 2.67 \\ \hline 15 & 1:5 & 0.79 \quad 0.76 \quad 0.84 \\ \hline 15 & 1:10 & 0.54 \quad 0.69 \quad 0.57 \\ \hline 40 & 1:0 & 6.84 \quad 7.68 \quad 6.79 \\ \hline 40 & 1:1 & 1.72 \quad 1.55 \quad 1.82 \\ \hline 40 & 1:5 & 0.68 \quad 0.83 \quad 0.89 \\ \hline 40 & 1:10 & 0.58 \quad 1.13 \quad 1.28 \\ \hline 100 & 1:0 & 6.61 \quad 6.66 \quad 7.43 \\ \hline 100 & 1:1 & 1.25 \quad 1.46 \quad 1.49 \\ \hline 100 & 1:5 & 1.17 \quad 1.27 \quad 1.16 \\ \hline 100 & 1:10 & 0.93 \quad 0.67 \quad 0.80\\ \hline \end{array}$$ a) Estimate all main effects and interactions. b) Construct an ANOVA table. You may give ranges for the P-values. c) Is the additive model plausible? Provide the value of the test statistic, its null distribution, and the P-value.

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Bentley Leach

Step 1 Given: $I=3$
$J=4$
$K=3$ a) The mean is the sum of all values divided by the number of data values: ${\stackrel{―}{X}}_{1.}=3.6992$
${\stackrel{―}{X}}_{2.}=2.6492$
${\stackrel{―}{X}}_{3.}=2.575$
${\stackrel{―}{X}}_{.1}=8.2011$
${\stackrel{―}{X}}_{.2}=1.9656$
${\stackrel{―}{X}}_{.3}=0.9322$
${\stackrel{―}{X}}_{.4}=0.7989$
${\stackrel{―}{X}}_{11}=10.6$
${\stackrel{―}{X}}_{12}=2.8$
${\stackrel{―}{X}}_{13}=0.7967$
${\stackrel{―}{X}}_{14}=0.6$
${\stackrel{―}{X}}_{21}=7.1033$
${\stackrel{―}{X}}_{22}=1.6967$
${\stackrel{―}{X}}_{23}=0.8$
${\stackrel{―}{X}}_{24}=0.9967$
${\stackrel{―}{X}}_{31}=6.9$
${\stackrel{―}{X}}_{32}=1.4$
${\stackrel{―}{X}}_{33}=1.2$
${\stackrel{―}{X}}_{34}=0.8$
$\stackrel{―}{X}=2.9744$ Step 2 The main effects are the difference of the mean of the values in the category decreased by the overall mean. $\text{Main effects concentration}$

$\text{Main effects delivery ratio}$