What is a multivariate analysis of variance MANOVA When is i

What is a multivariate analysis of variance (MANOVA)? When is it used? Give an example

Solution

Multivariate analysis of variance (MANOVA) is simply an ANOVA with several dependent variables. That is to say, ANOVA tests for the difference in means between two or more groups, while MANOVA tests for the difference in two or more vectors of means. For example, we may conduct a study where we try two different textbooks, and we are interested in the students\' improvements in math and physics. In that case, improvements in math and physics are the two dependent variables, and our hypothesis is that both together are affected by the difference in textbooks. A multivariate analysis of variance (MANOVA) could be used to test this hypothesis. Instead of a univariate F value, we would obtain a multivariate F value (Wilks\' ) based on a comparison of the error variance/covariance matrix and the effect variance/covariance matrix. Although we only mention Wilks\' here, there are other statistics that may be used, including Hotelling\'s trace and Pillai\'s criterion. The \"covariance\" here is included because the two measures are probably correlated and we must take this correlation into account when performing the significance test. Testing the multiple dependent variables is accomplished by creating new dependent variables that maximize group differences. These artificial dependent variables are linear combinations of the measured dependent variables.