1. II.3 An Example and Analyzing Interactions Emergency Room Example Emergency Room Example Interaction Plots and Tables Interaction Plots and Tables

2. Emergency Room Example Quality of Care Index (10 to 50) Quality of Care Index (10 to 50) Design factors: Design factors: –FactorLevels (Lo,Hi) A: Lab CoatWhite, Green B: Patient GenderFemale, Male C: Caregiver GenderMale, Female The 8 Standard Runs of the 2 3 Design Were Randomly Ordered, and Each Combination of Factors was observed The 8 Standard Runs of the 2 3 Design Were Randomly Ordered, and Each Combination of Factors was observed

3. Emergency Room Example Report Form

4. Emergency Room Example Standard Order

5. Emergency Room Example Cube Plot

6. Emergency Room Example Estimated Effects

7. Emergency Room Example Effects Probability Plot

8. Emergency Room Example What do you see in the effects probability plot? What do you see in the effects probability plot? –The Presence of a Strong Interaction Causes Some Interpretation Problems - the Interacting Factors B and C Must be Discussed as a "Team".

9. Interaction Plots and Tables Interaction Plots A Tool for Aiding Interpretation of Two- Way Interactions. A Tool for Aiding Interpretation of Two- Way Interactions.

10. Interaction Plots and Tables Interaction Plots Construction 1. For a Given Pair of Factors Find the Average Response at Each of Their Four Level Combinations. 1. For a Given Pair of Factors Find the Average Response at Each of Their Four Level Combinations. 2. Plot These with Response on the Vertical Axis, Using One of the Factor’s Levels on the Horizontal Axis. Connect and Label the Averages with the Same Level of the Other Factor. 2. Plot These with Response on the Vertical Axis, Using One of the Factor’s Levels on the Horizontal Axis. Connect and Label the Averages with the Same Level of the Other Factor.

11. Interaction Plots and Tables Interaction Plots Interpretation 1. If the Lines are Roughly Parallel, There is No Strong Interaction. 1. If the Lines are Roughly Parallel, There is No Strong Interaction. 2. If There is Interaction, the Plot Shows Clearly the Effect of a Factor at Each of the Levels of the Other Factor. 2. If There is Interaction, the Plot Shows Clearly the Effect of a Factor at Each of the Levels of the Other Factor. 3. Maximizing and Minimizing Combinations of the Factors are Easily Identified on the Plot and in the Table. 3. Maximizing and Minimizing Combinations of the Factors are Easily Identified on the Plot and in the Table.

12. Emergency Room Example Patient*Caregiver Interaction Table Let’s Construct an Patient*Caregiver Interaction Table for the Emergency Room Data Let’s Construct an Patient*Caregiver Interaction Table for the Emergency Room Data

13. Emergency Room Example Patient*Caregiver Interaction Plot

14. Emergency Room Exercise U-Do-It AC Interaction Table and Plot Construct an AC interaction Table and Plot for the Emergency Room Data. Construct an AC interaction Table and Plot for the Emergency Room Data. (Note in Practice We Would Not Do an AC Interaction Analysis for This Data Because the Estimate AC is Small - We Do It Here for Comparison Purposes and Practice). (Note in Practice We Would Not Do an AC Interaction Analysis for This Data Because the Estimate AC is Small - We Do It Here for Comparison Purposes and Practice).

15. Interactions More on Expected Responses When there is Strong Interaction, we need a rule to compute estimated responses. Suppose we want to know the best expected response for Male Patients When there is Strong Interaction, we need a rule to compute estimated responses. Suppose we want to know the best expected response for Male Patients We would want Male Doctors (C=-1) to administer to the Male Patients (B=1) in White Lab Coats (A=-1) We would want Male Doctors (C=-1) to administer to the Male Patients (B=1) in White Lab Coats (A=-1) The estimated response should be computed as: The estimated response should be computed as:

16. Interactions In general, we start with a set of signs for the factors, In general, we start with a set of signs for the factors, Multiply each important effect by its sign. We find the correct sign of interaction effects by multiplying together the signs of the main effects that comprise the interaction Multiply each important effect by its sign. We find the correct sign of interaction effects by multiplying together the signs of the main effects that comprise the interaction Add all the signed effects then divide by 2 Add all the signed effects then divide by 2 Add to the overall mean Add to the overall mean U-do-it: find the optimal estimated response for a female patient U-do-it: find the optimal estimated response for a female patient

17. Emergency Room Exercise Results of the Experiment The treatment factor under study, lab coat design, had an effect The treatment factor under study, lab coat design, had an effect An even stronger effect, the gender preference interaction, was discovered An even stronger effect, the gender preference interaction, was discovered

18. Emergency Room Exercise Results of the Experiment A recoding of the factors can result in a simpler presentation—replace C with C*, Gender Match (Lo=N, Hi=Y). A recoding of the factors can result in a simpler presentation—replace C with C*, Gender Match (Lo=N, Hi=Y). An interaction in the original factors may simply be a main effects model in the fundamental factors. An interaction in the original factors may simply be a main effects model in the fundamental factors.

19. Emergency Room Example Recoding Factors

20. Emergency Room Example Cube Plot for Recoded Factors

21. Emergency Room Example Effects Plot for Recoded Factors