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

2. II.2 Four Factors in Eight Runs: A Demonstration Full 2 4 Experiment Full 2 4 Experiment Response: Conductivity (milliohm/cm) Response: Conductivity (milliohm/cm) Factors (Lo, Hi) Factors (Lo, Hi) –A: Stirring Rate (Low, High) –B: Gas Bubbling (Off, On) –C: Solution Temperature (25 o C, 45 o C) –D: Solution Concentration (.076 M,.76 M NaOH) Full 2 4 Experiment Full 2 4 Experiment Response: Conductivity (milliohm/cm) Response: Conductivity (milliohm/cm) Factors (Lo, Hi) Factors (Lo, Hi) –A: Stirring Rate (Low, High) –B: Gas Bubbling (Off, On) –C: Solution Temperature (25 o C, 45 o C) –D: Solution Concentration (.076 M,.76 M NaOH)

3. II.2 Four Factors in Eight Runs: A Demonstration Response: Conductivity (milliohm/cm), Corrected for Concentration (CC) Response: Conductivity (milliohm/cm), Corrected for Concentration (CC) Factors (Lo, Hi) Factors (Lo, Hi) –A: Stirring Rate (Low, High) –B: Gas Bubbling (Off, On) –C: Solution Temperature (25 o C, 45 o C) –D: Solution Concentration (.076 M,.76 M NaOH) Response: Conductivity (milliohm/cm), Corrected for Concentration (CC) Response: Conductivity (milliohm/cm), Corrected for Concentration (CC) Factors (Lo, Hi) Factors (Lo, Hi) –A: Stirring Rate (Low, High) –B: Gas Bubbling (Off, On) –C: Solution Temperature (25 o C, 45 o C) –D: Solution Concentration (.076 M,.76 M NaOH) o Significant Effects – A, B, AB – C, CD o Significant Effects – A, B, AB – C, CD

4. II.2 Four Factors in Eight Runs: A Demonstration Half-Fraction Signs Tables o 2 4 DOE Estimated Significant Effects – A: -7.36 – B: -12.29 – C: 12.84 – AB: -8.01 – CD: 10.76 o 2 4 DOE Estimated Significant Effects – A: -7.36 – B: -12.29 – C: 12.84 – AB: -8.01 – CD: 10.76

5. II.2 Four Factors in Eight Runs: A Demonstration Half-Fraction Probability Plots

6. II.2 Four Factors in Eight Runs: A Demonstration Sequential Design Comments Suppose the ABCD = -I Half-Fraction Was Performed First 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 Suppose the ABCD = -I Half-Fraction Was Performed First 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

7. II.2 Four Factors in Eight Runs: A Demonstration Sequential Design Comments Suppose the ABCD = I Half-Fraction Were Performed First 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. Suppose the ABCD = I Half-Fraction Were Performed First 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.