1. Confounded Predictors
ANCOV
Confounded Predictors

2. Confound.sas
data confound; input gender courses aptitude pair apt1 apt2 diff; interaction = gender*courses; cards; …………….. Data here Follow the Link …………. proc corr; var gender courses aptitude; Courses = number of literature courses taken Aptitude = verbal aptitude Gender 1 = female, 2 = male Contrived data.

3. Significant gender difference on number of courses and reading aptitude.
Significant correlation between verbal aptitude and number of literature courses taken.

4. Courses: Independent Samples t
proc ttest; class gender; var courses aptitude;
Women took significantly more courses than did men, t(32) = 4.05, p < .001
gender N
Mean
Std Dev
Std Err
Minimum
Maximum 1 17
7.0000
2.2079
0.5355
4.0000 2
3.9412
2.1929
0.5319
Diff (1-2)
3.0588
2.2004
0.7547

5. Aptitude
Women had significantly greater verbal aptitude, t(32) = 2.68, p = .012
gender N
Mean
Std Dev
Std Err
Minimum
Maximum 1 17
2.6912 2
2.7437
Diff (1-2)
3.8432

6. Match Subjects on # Courses
Match subjects on number of lit courses taken.
Conduct matched-pairs t test comparing the two genders
Data from many of the highest scoring women dropped due to lack of men that score so high.
Data from many of the lowest scoring men dropped due to lack of women that score so low.

7. Matched Pairs t proc means mean stddev n t prt; var apt1 apt2 diff;
Now the men score significantly higher than do the women, t(9) = 5.93, p < .001.

8. ANCOV Using All Data
After showing that the Gender x Aptitude interaction is not significant, do ANCOV
proc glm; class gender;
model aptitude = courses gender / ss1;
means gender; lsmeans gender;
Source DF
Type I SS
Mean Square
F Value
Pr > F
courses 1
632.65
<.0001
gender
18.26
0.0002

9. Least Squares Means
After holding constant the effect of number of literature courses taken, men have verbal aptitude that is significantly greater than that of women, F(1, 31) = 18.26, p < .001
gender
aptitude LSMEAN 1 2

10. Weights.sas proc format; value gen 1='Female' 2='Male'; data weights;
input gender height weight;
interaction = gender*height;
format gender gen. ;
cards;
…………….. Rest of Data ……………

11. Zero-Order Corrs proc corr; var gender height weight;
These are from PDS data, subjects are grad students.

12. Heights proc ttest; class gender; var height weight;
Men are significantly taller than women, t(47) = 8.00, p < .001.
Men are 5.68 inches taller than women.
gender N
Mean
Std Dev
Std Err
Minimum
Maximum
Female 28
2.6011
0.4916
Male 21
2.2488
0.4907
Diff (1-2)
2.4574
0.7094

13. Weights
gender N
Mean
Std Dev
Std Err
Minimum
Maximum
Female 28
123.4
2.7652
101.0
165.0
Male 21
163.8
3.8520
130.0
205.0
Diff (1-2)
4.6150
Men weigh significantly more than do women, t(47) = 8.76, p < .001.
The mean difference is 40.4 pounds.

14. ANCOV proc glm; class gender; model weight= height gender / ss1;
means gender; lsmeans gender;
There was no significant Gender x Height interaction.
If men and women did not differ on height, would they differ on weight?

15. gender weight LSMEAN Female 125.568794 Male 160.813037
Source DF
Type I SS
Mean Square
F Value
Pr > F
height 1
52.80
<.0001
gender
24.63
gender
weight LSMEAN
Female
Male
Men weigh significantly more than women even when controlling for height.
Do note that the difference has been reduced from 40.4 pounds to pounds