ANCOVA

Stands for Analysis of Covariance

This is a multivariate means test.

It is just like the ANOVA (aka multiple group means test) you learned in the last section. But it enables you to add a control variable.

Used when:

DV = continuous

IV = categorical with 2 or more categories (nominal or ordinal)

CV = continuous

You write the same hypotheses as with ANOVA , do the test the same way, and interpret the results the same way.

Null: There is no relationship between the IV and the DV, controlling for the CV. The means are equal. Mean 1 = mean 2 = mean 3 ..... F = 0.

Research: There is a relationship between the IV and the DV, controlling for the CV. The means are not equal. Mean 1 NE mean 2 NE mean 3 .... F ? 0.

*Write in the names of the variables. And write out a mean for each category in the IV.

Example 1:

Dependent Variable = SEI; measured on a scale of 0-100.

Independent Variable = sex; measured as men and women

Control Variable (CV) = number of hours usually worked weekly (hrs2); measured as # of hours

Hypotheses:

Null: There is no relationship between sex and SEI, controlling for the number of hours worked per week. Mean SEI for women = mean SEI for men.

Research: There is a relationship between sex and SEI, controlling for the number of hours worked per week. Mean SEI for women NE mean SEI for men.

Using the GSS2000, we find:

Mean SEI men, controlling for the number of hours worked = 50.37, s = 20.05

Mean SEI women, controlling for the number of hours worked = 47.36, s = 16.35

F = 1.48, p = .24

We would accept the null hypothesis and conclude that there is no difference in the mean SEI for men and for women controlling for the influence of the number of hours worked. Men and women's SEI, on average, is somewhere between 47 to 50 (about halfway on the scale of 0-100), holding the number of hours worked per week constant.

DO THIS AGAIN WITH GSS2006 DATA


Example 2:

DV = Education

IV = Race

CV = Age

Ho: There is no relationship between race and education, controlling for age. Mean Education of Whites = Mean Education of Blacks = Mean Education of "Others"

H1: There is a relationship between race and education, controlling for age. Mean Education of Whites ? Mean Education of Blacks NE Mean Education of "Others"

Mean Education of Whites, Holding Age Constant = 13.43
Mean Education of Blacks, Holding Age Constant = 12.33
Mean Education of "Others", Holding Age Constant = 13.42

F=46.00, p = .000

Reject Null.

There is a relationship between race and education, controlling for age. The mean education of African Americans (12.33 years) is lower than that of Whites and people of other races (about 13.43 years).

DO THIS AGAIN WITH GSS2006 DATA


Example 3: Take Home Exercise

Does social class influence the number of hours worked controlling for number of children?

Social class (class) = lower class, working class, middle class, and upper class

Number of hours worked last week (hrs1) is measured in hours and ranges from 3 to 89.

Number of children (childs) is measured in numbers. It ranges from 0 -8 kids.

Average number of hours worked, holding number of children constant
Lower class: 36.18
Working class: 42.01
Middle class: 42.24
Upper class: 40.47

F = 2.96, p = .02


Example 4: Take Home Exercise

Does wearing a condom (yes/no) influence the number of children (measured in numbers) that people have, controlling for income (in dollars)?


Results: F = 22.76, p = .000

Mean # of children among those who usually wear a condom, controlling for income: 1.11 children on average

Mean # of children among those who usually do not wear a condom, controlling for income: 1.72 on average