91Ó°ÊÓ

The following data are obtained from a \(2^{3}\) factorial experiment replicated three times. Evaluate the sums of squares for all factorial effects by the contrast method. Draw conclusions. $$ \begin{array}{cccc} \text { Treatment } & & & \\ \text { Combination } & \text { Rep 1 } & \text { Rep 2 } & \text { Rep 3 } \\\ \hline(1) & 12 & 19 & 10 \\ a & 15 & 20 & 16 \\ b & 24 & 16 & 17 \end{array} $$ $$ \begin{array}{cccc} \text { Treatment } & & & \\ \text { Combination } & \text { Rep } 1 & \text { Rep } 2 & \text { Rep } 3 \\\ \hline a b & 23 & 17 & 27 \\ c & 17 & 25 & 21 \\ a c & 16 & 19 & 19 \\ b c & 24 & 23 & 29 \\ a b c & 28 & 25 & 20 \end{array} $$

Seven factors are varied at, two levels in an experiment involving only 16 trials. A \(\frac{1}{8}\) fraction of a \(2^{-}\) factorial experiment is used with the defining contrasts being \(A C D, B E F,\) and \(C E G .\) The data are as follows: $$ \begin{array}{lc|lc} \text { Treat. } & & \text { Treat. } & \\ \text { Comb. } & \text { Response } & \text { Co mb. } & \text { Response } \\\ \hline(1 & 31.6 & \text { acg } & 31.1 \\ \text { MI } & 28.7 & \text { cdg } & 32.0 \\ \text { abce } & 33.1 & \text { beg } & 32.8 \\ \text { cdef } & 33.6 & \text { adefg } & 35.3 \\ \text { acef } & 33.7 & \text { efg } & 32.4 \\ \text { bade } & 34.2 & \text { abdeg } & 35.3 \\ \text { abdf } & 32.5 & \text { bcdf } g & 35.6 \\ \text { b. } & 27.8 & \text { abc } \int g & 35.1 \end{array} $$ Perform an analysis of variance em all seven main effects, assuming that interactions are negligible. Use a 0.05 level of significance.