Definition: Multivariate Analysis of (Co)Variance (MANCOVA) is used to explore the relationship between multiple dependent variables(2DVs), and two independent variables of categorical and one continuous explanatory variable.
Assumptions: normally distributed within groups, homogeneity of variance (intercorrelation matrix between DVs must be equal), significant of linear relationship between dependent variables and covariate variable
Application: comparing the effectiveness of two different teaching methodology on multiple measures of academic achievement performance and school leadership, while controlling for the effect of student’s age.
Real Life example: We want to know how a student’s level of education and their gender impacts both their annual income and amount of student loan debt. However, we want to account for the annual income of the students’ parents as well. In this case, we have two factors (level of education and gender), one covariate (annual income of the students parents) and two dependent variables (annual income of student and student loan debt). IV DV Level of Education Annual Income Gender Students Loan debt Annual Income of parents ( Covariates)
# two-way mancova
annualincome <- c(50, 100, 120, 70, 250)
studentsloan <- c(200, 300, 350, 120, 100)
educationlevel <- c(2, 3, 2, 1, 2)
gender <- c(1, 2, 2, 1, 1)
parentincome <- c(80, 120, 100, 80, 90, 200, 250, 300, 350, 400)
data <- data.frame(group=c(annualincome, studentsloan), educationlevel=educationlevel, gender=gender, parentincome=parentincome)
manova <- manova(cbind(educationlevel, gender) ~ group + parentincome, data=data)
summary(manova)## Df Pillai approx F num Df den Df Pr(>F)
## group 1 0.197487 0.73826 2 6 0.5168
## parentincome 1 0.043389 0.13607 2 6 0.8754
## Residuals 7