Multivariate analysis of variance (MANOVA)is an extension of the univariateanalysis of varianceLinks to an external site.(ANOVA). In an ANOVA, we examine for statistical differences on one continuous dependent variable by an independent grouping variable. The MANOVA extends this analysis by considering multiple continuous dependent variables, and bundles them together into a weighted linear combination or composite variable. The MANOVA will compare whether or not the newly created combination differs by the different groups, or levels, of the independent variable. In this way, the MANOVA essentially tests whether or not the independent grouping variable simultaneously explains a statistically significant amount of variance in the dependent variable.

Questions answered:

• Do the various school assessments vary by grade level?
• Do the rates of graduation among certain state universities differ by degree type?
• Which diseases are better treated, if at all, by either X drug or Y drug?

Assumptions:

• Independent Random Sampling:MANOVA assumes that the observations are independent of one another, there is not any pattern for the selection of the sample, and that the sample is completely random.
• Level and Measurement of the Variables:MANOVA assumes that the independent variables are categorical and the dependent variables are continuous or scale variables.
• Absence of multicollinearity:The dependent variables cannot be too correlated to each other. Tabachnick & Fidell (2012) suggest that no correlation should be abover= .90.
• Normality:Multivariate normality is present in the data.
• Homogeneity of Variance:Variance between groups is equal.

Note that the best way to learn and develop skills in applying statistical techniques is by doing. To this end, lab/practice exercise is intended to aid you in applying the techniques of MANOVA by doing it.

Action Items

An investigator is interested on the effect of homeless status on quality of life and general health status. Homeless status is coded as 1, 2, and 3, which stand for Currently NOT Homeless, Acute, and Chronic respectively. The quality of life and general health status are measured on a scale of (1-5). The investigators collected data and presented you with the following dataset for analysis:

https://docs.google.com/spreadsheets/d/1wBUyjAerXPEpU3iZc44QxhmS5FiCbd9J/edit?usp=sharing&ouid=107160787338985820879&rtpof=true&sd=true

Based on the dataset, address the following.

1. Run a MANOVA analysis and review the resulting output.
2. What is the potential multivariate null hypothesis? Write it in symbolic form
3. Is there sufficient correlation among the dependent variables to justify the use of MANOVA?
4. Was the assumption of Equality of Covariance Matrices violated? Why or why not?
5. Is there a statistically significant multivariate effect of homeless status on the dependent variate?
6. Which of the dependent variables achieved statistically significant differences among the groups?
7. What would be the proper post hoc analyses for any statistically significant univariate effects. Provide rationale for your answer.
8. Why would a researcher conduct a MANOVA instead of several ANOVAs?
9. Write one to two paragraphs of how you will report this results in finding section of a dissertation or a journal article.