Question 9.13: The design suggested in Example 9. 12 has been adopted, and ...

Principles of Statistics for Engineers and Scientists

The design suggested in Example 9. 12 has been adopted, and the experiment has been carried out. The results (from MTNITAB) follow. Does the output indicate any violation of necessary assumptions? What do you conclude regarding the effect of drill speed on excess diameter?

Two-way ANOVA: Excess Diameter versus Block, Speed

\begin{array}{lrrrrr}\text{Source}& \text{DF}& \text{SS}& \text{MS}& F & P \\\text{BTock}& 5 & 0.20156 & 0.0403117 & 1.08 & 0.404 \\\text{Speed}& 2 & 0.07835 & 0.0391750 & 1.05 & 0.370 \\\text{Interaction}& 10 & 0.16272 & 0.0162717 & 0.44 & 0.909 \\\text{Error}& 18 & 0.67105 & 0.0372806 & & \\\text{Tota1}& 35 & 1.11368 & & &\end{array}

S = 0.1931 R-Sq = 39 .74% R-Sq(adj) = 0 .00%

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In a randomized complete block design, there must be no interaction between the treatment factor and the blocking factor, so that the main effect of the treatment factor may be interpreted. The P-value for interactions is 0.909, which is consistent with the hypothesis of no interactions. Therefore there is no indication in the output of any violation of assumptions. The P-value for the main effect of speed is 0.370, which is not small. Therefore we cannot conclude that excess hole diameter is affected by drill speed.

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