Confounded Predictors ANCOV Confounded Predictors

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.

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 3.9412 2.1929 0.5319 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 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 4562.985 632.65 <.0001 gender 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 LSMEAN 1 37.4319085 2 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 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 Men weigh significantly more than do women, t(47) = 8.76, p < .001. The mean difference is 40.4 pounds.

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?

gender weight LSMEAN Female 125.568794 Male 160.813037 Source DF Type I SS Mean Square F Value Pr > F height 1 13517.895 52.80 <.0001 gender 6307.040 24.63 gender weight LSMEAN Female 125.568794 Male 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