Analgesic Study with Three Treatments Crossed with Gender
Analgesic study with three treatments crossed with gender.
1
Data on pain and factor levels
male
C
12.4
female
A
7.69
male
C
14.0
female
A
9.69
male
C
11.6
female
A
8.89
female
A
6.94
female
A
2.13
female
A
7.26
female
A
5.87
male
B
12.9
female
C
12.2
female
A
7.20
male
C
13.9
male
A
8.18
male
B
16.6
female
C
9.41
male
C
11.2
female
B
8.35
male
A
7.24
female
A
6.81
male
B
9.81
female
A
6.67
female
A
6.98
female
A
7.07
female
C
2.40
male
B
7.84
female
B
3.84
male
B
9.42
male
A
7.00
male
A
7.00
female
A
5.00
male
A
8.00
2
Factors and Response Variable
Response variable, Y, is Pain index
Gender is one factor (sometimes called independent
variable)
Drug (type of analgesic agent) is the other factor
All factor combinations are considered
3
Statistical Model
So that Pain level is modeled as a linear function of
Factor levels.
4
ANOVA table
Source
DF Sum of Squares F Ratio Prob > F
gender
1
73.8082
12.6378 0.0014*
drug
2
51.0591
4.3713
0.0227*
drug*gender 2 30.5427
2.6148 0.0916
5
What if we had dropped the interaction from the
model since it was not significant?
The Drug Effect is now close to being not significant. Why?
Because we have inflated our MSE. In ANOVA, the model you
originally fit is generally the model you use for reporting significance.
6
Main Effect of Gender
7
Range Test on Main Effect of Drug
Level
Least Sq Mean
C
A
10.316622
B
A
B
8.710767
A
B
7.134856
Levels not connected by same letter are significantly
different.
8
Effect of Drug
9
What did Interaction term test?
The interaction tests whether an “Additive Model” is
adequate. The Additive model only contains Main
Effects and has the form:
Another way to think about Interaction is to look at
Interaction Plots.
10
Interaction plots
11
Alternate Interaction Plot
12
Residual Plot
13
Residual by Predicted
14
Normal Plot
15
Goodness of Fit
Goodness-of-Fit Test
Shapiro-Wilk W Test
W
Prob<W
0.970483
0.4936
Note: Ho = The data is from the Normal distribution. Small
p-values reject Ho.
16
Box-Cox Transformation
(lambda which minimizes SSE is optimal)
17
This study explores the effects of analgesic treatments crossed with gender on pain levels. The data analysis includes factors such as gender and drug type, and the statistical model examines pain index as a linear function of factor levels. The ANOVA results indicate significant effects of gender, drug, and their interaction on pain levels. Dropping the insignificant interaction term may inflate the Mean Squared Error (MSE) and affect the significance of the drug effect. Main effects of gender and drug are analyzed, including a range test and interpretations of the drug effect. The significance of interaction terms is discussed in relation to additive models and interaction plots.
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Presentation Transcript
Analgesic study with three treatments crossed with gender. 1
Data on pain and factor levels male female male female male female female female female female male female female male male C A C A C A A A A A B C A C A 12.4 7.69 14.0 9.69 11.6 8.89 6.94 2.13 7.26 5.87 12.9 12.2 7.20 13.9 8.18 male female male female male female male female female female female male female male male male female male B C C B A A B A A A C B B B A A A A 16.6 9.41 11.2 8.35 7.24 6.81 9.81 6.67 6.98 7.07 2.40 7.84 3.84 9.42 7.00 7.00 5.00 8.00 2
Factors and Response Variable Response variable, Y, is Pain index Gender is one factor (sometimes called independent variable) Drug (type of analgesic agent) is the other factor All factor combinations are considered 3
Statistical Model = + + + + * Y Gender Drug Gender Drug ( ) ij k ijk i j ij So that Pain level is modeled as a linear function of Factor levels. 4
ANOVA table Source DF Sum of Squares F Ratio Prob > F gender 1 73.8082 drug 2 51.0591 drug*gender 2 30.5427 12.6378 0.0014* 4.3713 0.0227* 2.6148 0.0916 5
What if we had dropped the interaction from the model since it was not significant? The Drug Effect is now close to being not significant. Why? Because we have inflated our MSE. In ANOVA, the model you originally fit is generally the model you use for reporting significance. 6
Range Test on Main Effect of Drug Level C A B A A Least Sq Mean 10.316622 B 8.710767 B 7.134856 Levels not connected by same letter are significantly different. 8
What did Interaction term test? The interaction tests whether an Additive Model is adequate. The Additive model only contains Main Effects and has the form: = + + + Y Gender Drug ( ) ij k ijk i j Another way to think about Interaction is to look at Interaction Plots. 10
Normal Plot 15
Goodness of Fit Goodness-of-Fit Test Shapiro-Wilk W Test W 0.970483 Prob<W 0.4936 Note: Ho = The data is from the Normal distribution. Small p-values reject Ho. 16
Box-Cox Transformation (lambda which minimizes SSE is optimal) 17
