The Accompanying Data Resulted from A $2^3$ Experiment with Three Replications Per Combination of Treatments Designed to Replications

question 15

Essay

The accompanying data resulted from a $2^3$ experiment with three replications per combination of treatments designed to study the effects of concentration of detergent (A), concentration of sodium carbonate (B), and concentration of sodium carboxymethyl cellulose (C0 on cleaning ability of a solution in washing tests (a larger number indicates better cleaning ability than a smaller number). $$\begin{array} { c c c c c c } \hline \text { Factor Levels } \\A & B & C & \text { Condition } & \text { Observations } \\\hline 1 & 1 & 1 & ( 1 ) & \begin{array} { c } 106,93 , \\116\end{array} \\\hline 2 & 1 & 1 & a & 198,200,214 \\\hline 1 & 2 & 1 & b & 197,202 , \quad 185 \\\hline 2 & 2 & 1 & a b & 329,331,307 \\\hline 1 & 1 & 2 & c & 149 , \quad 169 , \quad 135 \\\hline 2 & 1 & 2 & a c & 243,247,220 \\\hline 1 & 2 & 2 & b c & 255,230,252 \\\hline 2 & 2 & 2 & a b c & 383,360,364 \\\hline\end{array}$$
a. After obtaining cell totals
compute estimates of $\beta _ { 1 } , \gamma _ { 11 } ^ { λ c } , \text {and } \gamma^ { λ c } _ { \mathbf {210 } }$
b. Use the cell totals along with Yate's method to compute the effect contrasts and sums of squares. Then construct an ANOVA table and test all appropriate hypotheses using $\alpha = .05$

---

Definitions:

Unpleasant Stimulus

A negative or adverse stimulus that causes discomfort or aversion in individuals.

Classical Conditioning

A learning process that occurs when two stimuli are repeatedly paired; a response that is initially elicited by the second stimulus is eventually elicited by the first stimulus alone.

Treatment Alcoholism

Various therapeutic methods aimed at helping individuals overcome dependence on alcohol, including counseling, medication, and support groups.