1. 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

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)
Poor choice of D’s level (D=122.64)

3. 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 to first 8 runs, subtract to second 8 runs (difference of is changed to difference of 0). Then subtract grand mean (74.88).

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

5. 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?

6. 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
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
The estimate of the effect of D for the concentration (not CC) would have been
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.