Response: Conductivity (milliohm/cm), Corrected for Concentration (CC)

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II.2 Four Factors in Eight Runs Demonstrating the Effects of Confounding* Response: Conductivity (milliohm/cm), Corrected for Concentration (CC) Factors (Lo, Hi) A: Stirring Rate (Low, High) B: Gas Bubbling (Off, On) C: Solution Temperature (25oC, 45oC) D: Solution Concentration (.076 M, .76 M NaOH) * Based on DOE study done by Kamal Jha, USC Statistics 506 and Chemical Engineering Student

II.2 Four Factors in Eight Runs: A Demonstration Full 24 Experiment Response: Conductivity (milliohm/cm) Factors (Lo, Hi) A: Stirring Rate (Low, High) B: Gas Bubbling (Off, On) C: Solution Temperature (25oC, 45oC) D: Solution Concentration (.076 M, .76 M NaOH) Poor choice of D’s level (D=122.64)

II.2 Four Factors in Eight Runs: A Demonstration Significant Effects A, B, AB C, CD Response: Conductivity (milliohm/cm) , Corrected for Concentration (CC) Factors (Lo, Hi) A: Stirring Rate (Low, High) B: Gas Bubbling (Off, On) C: Solution Temperature (25oC, 45oC) D: Solution Concentration (.076 M, .76 M NaOH) Add 61.32 to first 8 runs, subtract 61.32 to second 8 runs (difference of 122.64 is changed to difference of 0). Then subtract grand mean (74.88).

II.2 Four Factors in Eight Runs: A Demonstration Half-Fraction Signs Tables 24 DOE Estimated Significant Effects A: -7.36 B: -12.29 C: 12.84 AB: -8.01 CD: 10.76 Which fraction you select matters. AB=-8.01, CD=10.76

II.2 Four Factors in Eight Runs: A Demonstration Half-Fraction Probability Plots Graphs are interesting to interpret, but take a close look at the effects—what happened to AB-CD? A-BCD?

II.2 Four Factors in Eight Runs: A Demonstration Sequential Design Comments Suppose the ABCD = -I Half-Fraction Was Performed First The estimate of the effect of D for the concentration (not CC) would have been 123.125. This with the ABCD = -I probability plot would indicate that factors A, B, C, and D are significant if you assume that 3-way interactions are negligible. You would be unsure how to interpret the AB - CD. This ambiguity would be resolved by adding the half-fraction determined by ABCD = I. If the data were the same as given above for runs ABCD = I you would combine the data for the two half-fractions (two blocks) the estimated effects would be obtained from the 16-run signs table ABCD is confounded with the block effect

II.2 Four Factors in Eight Runs: A Demonstration Sequential Design Comments Suppose the ABCD = I Half-Fraction Were Performed First The estimate of the effect of D for the concentration (not CC) would have been 122.15. This with the ABCD = I probability plot would indicate that factors B, C, and D are significant if you assume that 3-way interactions are negligible. Based on this half-fraction, you would not detect the AB or CD interactions.