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II.2 Four Factors in Eight Runs Demonstrating the Effects of Confounding*

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 (25 o C, 45 o C)

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II.2 Four Factors in Eight Runs Demonstrating the Effects of Confounding*

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  1. II.2 Four Factors in Eight RunsDemonstrating 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

  2. 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)

  3. II.2 Four Factors in Eight Runs: A Demonstration • 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) • Significant Effects • A, B, AB • C, CD

  4. II.2 Four Factors in Eight Runs: A DemonstrationHalf-Fraction Signs Tables • 24 DOE EstimatedSignificant 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 DemonstrationHalf-Fraction Probability Plots

  6. II.2 Four Factors in Eight Runs: A DemonstrationSequential 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

  7. II.2 Four Factors in Eight Runs: A DemonstrationSequential 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.

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