MANOVA is one of the most widely used methods for testing differences in mean vectors from multi-groups. It has an excellent stable performance when the assumptions are satisfied, which are normality, independency and homogeneity. Normality assumptions requires selecting samples from normal distribution. Independency assumption requires samples to be chosen identically and independently. Finally, homogeneity requires that samples must be chosen from the same variance-covariance matrix. Type I error rate will be affected if assumptions are not satisfied. In this thesis, we consider the impact of assumption violations on Type I error rate. Four popular used test statistics including Wilk's Lambda, Pillai Trace, Hotelling-Lawley Trace and Roy's Maximum Root are evaluated. Variety of variance-covariance matrix structures such as compound symmetry and autoregressive(1) structure are considered. Also the impact of violation of normality assumption is discussed. The performance of the four usually used test statistics are evaluated and compared.