II.3 An Example and II.3 An Example and Analyzing InteractionsAnalyzing Interactions

Emergency Room ExampleEmergency Room Example Interaction Plots and TablesInteraction Plots and Tables

Emergency Room ExampleEmergency Room Example

Quality of Care Index (10 to 50)Quality of Care Index (10 to 50) Design factors:Design factors:

– FactorFactor Levels (Lo,Hi)Levels (Lo,Hi)A: Lab CoatA: Lab Coat White, Green White, Green

B: Patient GenderB: Patient Gender Female, MaleFemale, Male

C: Caregiver GenderC: Caregiver Gender Male, FemaleMale, Female

The 8 Standard Runs of the 2The 8 Standard Runs of the 233 Design Were Design Were Randomly Randomly Ordered, and Each Combination of Ordered, and Each Combination of Factors was Factors was observedobserved

Emergency Room ExampleEmergency Room ExampleReport FormReport Form

Run Order Standard

Order Trial Number

Lab Coat A

Patient Gender B

Caregiver

Gender C

Quality of

Care Y

1 4 Green M M 40 2 7 White M F 36 3 1 White F M 37 4 8 Green M F 33 5 3 White M M 43 6 2 Green F M 33 7 5 White F F 44 8 6 Green F F 42

Emergency Room ExampleEmergency Room ExampleStandard OrderStandard Order

StdOrder A-Coat B-Patient C-Caregiver y 1 -1 -1 -1 37 2 1 -1 -1 33 3 -1 1 -1 43 4 1 1 -1 40 5 -1 -1 1 44 6 1 -1 1 42 7 -1 1 1 36 8 1 1 1 33

Emergency Room ExampleEmergency Room ExampleCube PlotCube Plot

Emergency Room Emergency Room ExampleExample

Estimated EffectsEstimated Effects

Term Effect Coef Constant 38.500 A-Coat -3.000 -1.500 B-Patient -1.000 -0.500 C-Caregiver 0.500 0.250 A-Coat*B-Patient 0.000 0.000 A-Coat*C-Caregiver 0.500 0.250 B-Patient*C-Caregiver -7.500 -3.750 A-Coat*B-Patient*C-Caregiver -0.500 -0.250

Emergency Room ExampleEmergency Room ExampleEffects Probability PlotEffects Probability Plot

Effect

Perc

ent

0.0-2.5-5.0-7.5

99

95

90

80

70605040

30

20

10

5

1

F actor NameA A -C oatB B-PatientC C -C aregiver

Effect TypeNot SignificantSignificant

BC

A

Normal Probability Plot of the Effects(response is y, Alpha = .05)

Lenth's PSE = 0.75

Emergency Room ExampleEmergency 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 The Presence of a Strong Interaction Causes Some Interpretation Problems - the Interacting Factors B Interpretation Problems - the Interacting Factors B and C Must be Discussed as a "Team".and C Must be Discussed as a "Team".

Interaction Plots and TablesInteraction Plots and TablesInteraction PlotsInteraction Plots

A Tool for Aiding Interpretation of A Tool for Aiding Interpretation of Two-Way Interactions.Two-Way Interactions.

Interaction Plots and TablesInteraction Plots and TablesInteraction PlotsInteraction Plots

ConstructionConstruction

1. For a Given Pair of Factors Find 1. For a Given Pair of Factors Find the Average Response at Each of the Average Response at Each of Their Four Level Combinations.Their Four Level Combinations.

2. Plot These with Response on the 2. Plot These with Response on the Vertical Axis, Using One of the Vertical Axis, Using One of the Factor’s Levels on the Horizontal Factor’s Levels on the Horizontal Axis. Connect and Label the Axis. Connect and Label the Averages with the Same Level of the Averages with the Same Level of the Other Factor.Other Factor.

Interaction Plots and TablesInteraction Plots and TablesInteraction PlotsInteraction PlotsInterpretationInterpretation

1. If the Lines are 1. If the Lines are RoughlyRoughly Parallel, Parallel, There is No Strong Interaction.There is No Strong Interaction.

2. If There is Interaction, the Plot Shows 2. If There is Interaction, the Plot Shows Clearly the Effect of a Factor at Each of Clearly the Effect of a Factor at Each of the Levels of the Other Factor.the Levels of the Other Factor.

3. Maximizing and Minimizing 3. Maximizing and Minimizing Combinations of the Factors are Easily Combinations of the Factors are Easily Identified on the Plot and in the Table.Identified on the Plot and in the Table.

Emergency Room ExampleEmergency Room ExamplePatient*Caregiver Interaction TablePatient*Caregiver Interaction Table

Let’s Construct an Patient*Caregiver Interaction Let’s Construct an Patient*Caregiver Interaction Table for the Emergency Room DataTable for the Emergency Room Data

Patient

Caregiver Female Male

Male373335

434041.5

Female444243

363334.5

Emergency Room ExampleEmergency Room Example Patient*Caregiver Interaction PlotPatient*Caregiver Interaction Plot

Emergency Room ExerciseEmergency Room ExerciseU-Do-It AC Interaction Table and PlotU-Do-It AC Interaction Table and Plot

Construct an AC interaction Table and Construct an AC interaction Table and Plot for the Emergency Room Data.Plot for the Emergency Room Data.

(Note in Practice We Would Not Do an (Note in Practice We Would Not Do an AC Interaction Analysis for This Data AC Interaction Analysis for This Data Because the Estimate AC is Small - Because the Estimate AC is Small - We Do It Here for Comparison We Do It Here for Comparison Purposes and Practice).Purposes and Practice).

InteractionsInteractionsMore on Expected ResponsesMore on Expected Responses

When there is Strong Interaction, we need a rule to When there is Strong Interaction, we need a rule to compute estimated responses. Suppose we want to compute estimated responses. Suppose we want to know the best expected response for Male Patientsknow the best expected response for Male Patients

We would want Male Doctors (C=-1) to administer to We would want Male Doctors (C=-1) to administer to the Male Patients (B=1) in White Lab Coats (A=-1)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:

EMR38.5

( 1)(.5) (1)( 1.0) ( 1)( 3.0) ( 1)(1)( 7.5) 2

38.5 9 2

43.0

InteractionsInteractions 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 Multiply each important effect by its sign. We find the

correct sign of interaction effects by multiplying together correct sign of interaction effects by multiplying together the signs of the main effects that comprise the interactionthe signs of the main effects that comprise the interaction

Add all the signed effects then divide by 2Add all the signed effects then divide by 2 Add to the overall meanAdd to the overall mean U-do-it: find the optimal estimated response for a female U-do-it: find the optimal estimated response for a female

patientpatient

Emergency Room ExerciseEmergency Room ExerciseResults of the ExperimentResults of the Experiment

The treatment factor under The treatment factor under study, lab coat design, had an study, lab coat design, had an effecteffect

An even stronger effect, the An even stronger effect, the gender preference interaction, gender preference interaction, was discoveredwas discovered

Emergency Room ExerciseEmergency Room ExerciseResults of the ExperimentResults of the Experiment

A recoding of the factors can A recoding of the factors can result in a simpler presentationresult in a simpler presentation—replace C with C*, Gender —replace C with C*, Gender Match (Lo=N, Hi=Y).Match (Lo=N, Hi=Y).

An interaction in the original An interaction in the original factors may simply be a main factors may simply be a main effects model in the effects model in the fundamentalfundamental factors. factors.

Emergency Room ExampleEmergency Room ExampleRecoding FactorsRecoding Factors

A-Coat B-Patient C-Caregiver C*-Gender Match

y

White F M N 37 Green F M N 33 White M M Y 43 Green M M Y 40 White F F Y 44 Green F F Y 42 White M F N 36 Green M F N 33

Emergency Room ExampleEmergency Room ExampleCube Plot for Recoded FactorsCube Plot for Recoded Factors

Emergency Room ExampleEmergency Room ExampleEffects Plot for Recoded FactorsEffects Plot for Recoded Factors