MANOVA for large hypothesis degrees of freedom under non-normality

In this paper asymptotic distributions of the three commonly used multivariate test statistics, viz.: Likelihood Ratio, Lawley-Hotelling and Bartlett-Nanda-Pillai statistics, are studied for one-way MANOVA hypothesis when the responses are non-normal and the hypothesis degrees of freedom is large. The null as well as the non-null distributions are derived for the balanced as well as unbalanced cases. The results show that these statistics have asymptotic normal distributions. A simulation study reveals the approximations are quite good for number of treatments as small as 15 in the null case. Hence, the results can be applied in real life situation where the assumption of multivariate normality is not tenable. Such situations arise, for example, in agricultural screening trials where large number of cultivars are compared with few replications per cultivar.