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

2. Emergency Room Example
Quality of Care Index (10 to 50)
Design factors:
Factor Levels (Lo,Hi) A: Lab Coat White, Green B: Patient Gender Female, Male
C: Caregiver Gender Male, Female
The 8 Standard Runs of the 23 Design Were Randomly Ordered, and Each Combination of Factors was observed
Stat lab obtains examples like this from clinical faculty in School of Medicine (tie, glasses, tie color). STAT 706 project chat roulette example, too.

3. Emergency Room Example Report Form

4. Emergency Room Example Standard Order
Do this in Minitab. Runs AND effects.

5. Emergency Room Example Cube Plot

6. Emergency Room Example Estimated Effects

7. Emergency Room Example Effects Probability Plot
Move line in Minitab

8. Emergency Room Example
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.
Skim next three slides—we covered this in 6.3

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.
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.
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.

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

13. Emergency Room Example Patient*Caregiver Interaction Plot
Plots are quite similar

14. Emergency Room Exercise U-Do-It AC Interaction Table and Plot
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).
Interesting plots here—have students organize the tables only, rather than construct plots.

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
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:
Note that we need to include insignificant main effects when an interaction is present.

16. Interactions 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
Add all the signed effects then divide by 2
Add to the overall mean
U-do-it: find the optimal estimated response for a female patient
Female Doctor (C=1), Female patient (B=-1), White lab coat (A=-1). EMR is 44.5

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

18. Emergency Room Exercise Results of Reorganized Factors
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.
Show them: Create Custom Factorial Design

19. Emergency Room Example Recoding Factors
C* has the same sign as the BC interaction. We may not always have an orthogonal 2^3 design, which means we could start the experiment over..

20. Emergency Room Example Cube Plot for Recoded Factors
See how simple the structure is?

21. Emergency Room Example Effects Plot for Recoded Factors
C* is still 7.5!