The article “Factorial Experiments in the Optimization of Alkaline Wastewater Pretreatment” (M. Prisciandaro. A. Del Borghi, and F. Veglio, Industrial Engineering and Chemistry Research, 2002:5034–5041) presents the results of several experiments to investigate methods of treating alkaline wastewater. One experiment was an unreplicated 24 design. The four factors were A: concentration of sulfuric acid. B: temperature. C: time, and D: concentration of calcium chloride. The outcome variable is the amount of precipitate in kg/m3 The results are presented in the following table.
- a. Estimate all main effects and interactions.
- b. Which effects seem to be larger than the others?
- c. Assume that all third-and higher-order interactions are equal to 0, and add their sums of squares. Use the result in place of an error sum of squares to compute F statistics and P-values for the main effects. Which factors can you conclude to have an effect on the outcome?
- d. The article described some replicates of the experiment, in which the error mean square was found to be 1.04, with four degrees of freedom. Using this value, compute F statistics and P-values for all main effects and interactions.
- e. Do the results of part (d) help to justify the assumption that the third-and higher-order interactions are equal to 0? Explain.
- f. Using the results of part (d), which factors can you conclude to have an effect on the outcome?
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