## Multivariate Analysis of Variance

Let us first look at an example that will help us understand the application of MANOVA or Multivariate Analysis of Variance. Suppose we have a hypothesis that a new statistical training style (say developed by PIE TUTORS) is better than the standard training method (say that is common in the industry). In order to support this claim, we might want to look at the effect of our new statistical training style on average value of many dependent variables such as satisfaction of the participants, their level of participation, and their score on a statistical test. Multivariate Analysis of Variance (MANOVA) allows us to test all our claims at once.

Multivariate Analysis of Variance (MANOVA) is a multivariate statistical analysis technique that is used to test hypotheses regarding the effect of one or more independent variables on two or more dependent variables. In simple words, it will help you understand three things:

1. Relationship among independent variable(s),
2. Relationship among dependent variable(s), and
3. Changes in independent variable(s) impact the dependent variable(s).

The multivariate F value (Wilks’ lambda) is based on the comparison of the error variance/co-variance matrix and the effect variance/co-variance matrix. The two measures might have some correlation and that is the reason it is important to have ‘covariance’ matrix included while performing the significance test. When we use correlated measures, there is some new information that we are gaining, how there will be redundant information as well which is express in terms of co-variance between the variables.