While Analysis of variance (ANOVA) only handles 1 dependent variable, multivariate analysis of variance (MANOVA) is used to perform an ANOVA style analysis on several response variables simultaneously. This means that MANOVA will test whether the mean vector of the response variables across different groups are equal or not.
The advantage of MANOVA derives from the fact that the linear combination maximizes the differences among the different groups. Hereby we are improving the chance of detecting differences across the group. Moreover it will acknowledge relationships between the different groups and therefore becomes more powerful.
Several assumptions are taken when using MANOVA:
- The random samples from different populations are independent.
- Each population is multivariate normal. However, small violations on the normality assumption are usually not fatal.
- Homogeneity of Variance-Covariance Matrices.