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MANOVA (Multivariate Analysis of Variance) is a statistical method used to analyze the simultaneous effect of multiple independent variables on multiple dependent variables. It is commonly used in research to determine whether there are significant differences between groups on a combination of dependent variables. In Stata, MANOVA can be performed by using the “manova” command, which allows for the inclusion of multiple dependent variables and the specification of different types of MANOVA models such as Wilks’ Lambda, Pillai’s Trace, and Hotelling-Lawley Trace. Additionally, Stata provides various options for post-hoc tests and output interpretations to further analyze the results of a MANOVA. Overall, Stata offers a user-friendly and comprehensive approach to performing MANOVA, making it a popular choice for researchers in various fields.
Perform a MANOVA in Stata
A is used to determine whether or not different levels of an explanatory variable lead to statistically different results in some response variable.
For example, we might be interested in understanding whether or not three levels of education (Associate’s degree, Bachelor’s degree, Master’s degree) lead to statistically different annual incomes. In this case, we have one explanatory variable and one response variable.
- Explanatory variable: level of education
- Response variable: annual income
A MANOVA is an extension of the one-way ANOVA in which there is more than one response variable. For example, we might be interested in understanding whether or not level of education leads to different annual incomes and different amounts of student loan debt. In this case, we have one explanatory variable and two response variables:
- Explanatory variable: level of education
- Response variables: annual income, student loan debt
Because we have more than one response variable, it would be appropriate to use a MANOVA in this case.
Next, we’ll explain how to perform a MANOVA in Stata.
Example: MANOVA in Stata
To illustrate how to perform a MANOVA in Stata, we’ll use the following dataset that contains the following three variables for 24 individuals:
- educ: level of education (0 = Associate, 1 = Bachelor, 2 = Master)
- income: annual income
- debt: total student loan debt
You can replicate this example by manually entering the data yourself by going to Data > Data Editor > Data Editor (Edit) along the top menu bar.
To perform the MANOVA using education as the explanatory variable and income and debt as the response variables, we can use the following command:
manova income debt = educ
Stata produces four unique test statistics along with their corresponding p-values:
Wilks’ lambda: F-Statistic = 5.02, P-value = 0.0023.
Lawley-Hotelling trace: F-Statistic = 5.94, P-value = 0.0008.
Roy’s largest root: F-Statistic = 13.10, P-value = 0.0002.
For an in-depth explanation of how each test statistic is calculated, refer to from the Penn State Eberly College of Science.
The p-value for each test statistic is less than 0.05, so the null hypothesis will be rejected no matter which one you use. This means we have sufficient evidence to say that level of education leads to statistically significant differences in annual income and total student debt.
Note on p-values: The letter next to the p-value in the output table indicates how the F-statistic was calculated (e = exact calculation, a = approximate calculation, u = an upper bound).