Multivariate analysis of variance (MANOVA) is an extension of analysis of variance (ANOVA) to deal with two or more continuous outcomes or dependent variables. This technique is used to determine whether multiple levels of independent variables on their own or in combination with one another have an effect on the outcome variables.
Dr Joanna Dipnall is an applied statistician with interests in the advanced statistical methods, including machine learning and deep learning techniques. She completed her Honours in Econometrics with Monash University and her PhD with IMPACT SRC, School of Medicine, Deakin University. Joanna works extensively with registry and linked medical data and collaborates extensively with the Faculty of IT at Monash to supervise Masters and PhD students to integrate artificial intelligence within health research. Joanna teaches within the Monash Biostatistics Unit and is the Unit Co-coordinator for the Monash Masters of Health Data Analytics course. Joanna has taught advanced statistical methods for many years at universities and for ACSPRI.
One-way MANOVA compares two or more outcomes. For example, consider the outcome variables of Maths, Chemistry, Biology, and Physics test scores and a single factor variable of school type. A hypothesis could be that the four test scores together are affected by differences in school type. A MANOVA could be used to test this hypothesis. Instead of a univariate F value, we would obtain a multivariate test statistic based on a comparison of the error variance/covariance matrix and the effect variance/covariance matrix. Since the outcome measures are most likely correlated, this correlation needs to be taken into account when performing the significance test. Testing the multiple outcome variables is accomplished by creating new outcome variables that maximize group differences, whereby these new variables are linear combinations of the measured outcome variables. To extend MANOVA further, a two-way MANOVA could be performed to compare the four test outcome scores against two (or more) factor variables such as school type and region.
MANOVA is used when there are several reasonably correlated outcome variables, measuring a coherent theme (e.g. scientific achievement), and the researcher desires a single, overall statistical test on this set of variables instead of performing multiple individual tests. The researcher can use the covariance structure of the data between the outcome variables to test the equality of means at the same time. If the outcome variables are correlated, then this additional information can help detect differences too small to be detected through individual ANOVAs.
MANOVA is used to explore how factor variables influence some patterning of response on the outcome variables. Contrast codes on the outcome variables are then used to test hypotheses about how the independent variables differentially predict the dependent variables. MANOVA is often more powerful than ANOVA as there is a greater chance to detect effects and MANOVA reduces the Type I error problem with multiple ANOVA testing.
Several research questions can be answered using MANOVA:
- What are the main effects of the independent variables?
- What are the interactions among the independent variables?
- What is the importance of the outcome variables?
- What is the strength of association between outcome variables?
- What are the effects of covariates? How may they be utilized?
MANOVA requires that the dependent variables meet parametric assumptions and there needs to be an adequate sample size.
This course is suitable for early career researchers as well as other researchers with a good understanding of basic statistics and hypothesis testing. They should understand correlation and have performed simple tests such as t-tests.
- Review of ANOVA/ANCOVA
- One-way MANOVA
- Two-way MANOVA
- MANOVA assumptions
- MANCOVA
- MANOVA for Latin-square designs
- MANOVA for nested designs
- MANOVA for mixed designs
- MANOVA for repeated measures
By the end of the master-class students will be able to:
- Identify when it is appropriate to use MANOVA
- Establish the best MANOVA test to use
- Understand the theory, rationale, assumptions and restrictions associated with the tests
- Perform analyses using SPSS, and explore outcomes identifying the multivariate effects, univariate effects and interactions
- Be able to measure effect size and power
- Learn how to present the data and report the findings
The course will be run in an interactive workshop format using SPSS software. Participants can bring their own data in SPSS to experiment, but data files will be provided for class exercises.
This course is suitable for early career researchers as well as other researchers with a good understanding of basic statistics and hypothesis testing. They should understand correlation and have performed simple tests such as t-tests.
Course Notes will be provided.