ANCOV

Confounded Predictors

Confound.sas

data confound;

input gender courses aptitude pair apt1 apt2 diff;

interaction = gender*courses;

cards;

…………….. Data here ………….

proc corr; var gender courses aptitude;

Courses = number of literature courses taken

Aptitude = verbal aptitude

Gender 1 = female, 2 = male

Contrived data.

• Significant gender difference on number of courses and reading aptitude.

• Significant correlation between verbal aptitude and number of literature courses taken.

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 12.0000

2 17 3.9412 2.1929 0.5319 0 7.0000

Diff (1-2)   3.0588 2.2004 0.7547    

Aptitude

• Women had significantly greater verbal aptitude, t(32) = 2.68, p = .012

gender N Mean Std Dev Std Err Minimum Maximum

1 17 45.0000 11.0962 2.6912 28.0000 66.0000

2 17 34.7059 11.3124 2.7437 15.0000 52.0000

Diff (1-2)   10.2941 11.2048 3.8432    

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.

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.

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 4562.985 4562.985 632.65 <.0001gender 1 131.6917 131.6917 18.26 0.0002

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 LSMEAN1 37.43190852 42.2739738

Weights.sas

proc format; value gen 1='Female' 2='Male';data weights;input gender height weight;interaction = gender*height;format gender gen. ;cards; 2 70 172 2 74 130

…………….. Rest of Data ……………

Zero-Order Corrs

• proc corr; var gender height weight;• These are from PDS data, subjects are grad

students.

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 64.8929 2.6011 0.4916 60.0000 70.0000

Male 21 70.5714 2.2488 0.4907 66.0000 74.0000

Diff (1-2)   -5.6786 2.4574 0.7094    

Weights

• Men weigh significantly more than do women, t(47) = 8.76, p < .001.

• The mean difference is 40.4 pounds.

gender N Mean Std Dev Std Err Minimum Maximum

Female 28 123.4 14.6318 2.7652 101.0 165.0

Male 21 163.8 17.6519 3.8520 130.0 205.0

Diff (1-2)   -40.4048 15.9869 4.6150    

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?

Source DF Type I SS Mean Square

F Value Pr > F

height 1 13517.895 13517.895 52.80 <.0001

gender 1 6307.040 6307.040 24.63 <.0001

gender weight LSMEANFemale 125.568794Male 160.813037

• Men weigh significantly more than women even when controlling for height.

• Do note that the difference has been reduced from 40.4 pounds to 35.24 pounds