Analysis of covariance in two way classification with disproportionate cell frequencies- estimation of true class effects

Abstract

The problem of estimation of true class effects and their variances has been investigated in the case of two way classification with disproportionate cell frequencies. Expressions for the true class effects and their variances are obtained in the case of analysis of variance as well as covariance with a single concomitant variate under the restrictions. In the case of analysis of variance under the first restriction it is only possible to obtain estimates of the true class effects of B factor by solving the normal equations in alone and for getting the estimates of the true class effects of a factor it is necessary to solve the normal equations in alone. It is observed that while estimating the true class effects of any factor there is on restriction imposed on the effects of that factors in fact the constraint is on the effects of the second factor. However, under the second set of restrictions. The estimates of the true class effects of any factor can be obtained by solving the normal equations involving the effects of that factor alone. The procedure has been illustrated by deriving the expressions for the estimates of true block effects and treatment effects in the case of ‘Balanced Incomplete Block Design’. The methods of estimation have been demonstrated with the help of a numerical example. In the case of analysis of covariance it is observed that, under both the sets of constraints of class effects, it is only possible to obtain estimates of the true class effects of one factor by solving the normal equations involving the effects of the second factor alone. In this case as well there is no restriction imposed on the effects of that factor for which the true class effects are estimated.