ANCOVA
Stands for Analysis of Covariance
This is a multivariate means test.
It is just like the ANOVA 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 ≠ mean 2 ≠ 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 ≠ 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.
Example 2: Do on the Computer
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 ≠ 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).
Example 3: In Class 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.
3 variables: DV = hours worked (continuous), IV = social class (categorical), CV = number of children (continuous)
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
Answers:
Analysis = Multivariate Means test (ANCOVA), DV = continuous, IV = categorical, CV = continuous
Hypotheses
Ho: Social class does not
influence the number of hours worked controlling for number of children. Mean1
= mean2 = mean3 = mean4
or Mean Hours Worked of Lower class = Mean Hours Worked of Working
class = Mean Hours Worked of Middle class = Mean Hours Worked of Upper class
H1: Social class does influence the number of hours worked controlling for number of children. Mean1 ≠ mean2 ≠ mean3 ≠ mean4
or Mean Hours Worked of Lower class ≠ Mean Hours Worked of Working class ≠ Mean Hours Worked of Middle class ≠ Mean Hours Worked of Upper class
Results: F = 2.96, p = .02, Reject null
Interpretation: Social class does influence the number of hours worked controlling for number of children. People in the lower class work the least at about 36 hours a week, controlling for the number of children. People in the working and middle classes work the most at about 42 hours a week, controlling for the number of children.
Example 4: Take Home Exercise
Does wearing a condom influence the number of children that people have, controlling for income?
Answers:
DV = number of children, continuous
IV = condom use (yes, no the last time respondent had sex), categorical
CV = income in dollars, continuous
Analysis = multivariate means test (ANCOVA)
Hypotheses:
Ho: Wearing a condom does not influence the number of children that people have, controlling for income. Mean1 = Mean2, or Mean # of children among people who did not use a condom = Mean # of children among people who did use a condom
H1: Wearing a condom does influence the number of children that people have, controlling for income. Mean1 ≠ Mean2, or Mean # of children among people who did not use a condom ≠ Mean # of children among people who did use a condom
Results: F = 22.76, p = .000, Reject null
Interpretation: Wearing a condom does influence the number of children that people have, controlling for income. People who did not use a condom the last time they had sex have more children (1.72 on average) than people who did use a condom the last time they had sex (1.11 children on average).