Determination of Optimal Block Designs With Pre-assigned Variance For Elementary Contrasts

A method for obtaining optimal designs from the class of variance balanced and connected designs was developed for comparing treatment effects with a pre-assigned variance. The properties of the C-matrix of a block design are employed in developing this method. Some new results concerning the design parameters and the non-zero characteristic root of the C-matrix are also presented

Distribution of the LR criterion Up,m,n as a marginal distribution of a generalized Dirichlet model

The density of the likelihood ratio criterion Up,m,n is expressed in terms of a marginal density of a generalized Dirichlet model having a specific set of parameters. The exact distribution of the likelihood ratio criterion so obtained has a very simple and general format for every p . It provides an easy and direct method of computation of the exact p -value of Up,m,n . Various types of properties and relations involving hypergeometric series are also established

Distribution of the LR criterion Up,m,n as a marginal distribution of a generalized Dirichlet model

The density of the likelihood ratio criterion Up,m,n is expressed in terms of a marginal density of a generalized Dirichlet model having a specific set of parameters. The exact distribution of the likelihood ratio criterion so obtained has a very simple and general format for every p . It provides an easy and direct method of computation of the exact p -value of Up,m,n . Various types of properties and relations involving hypergeometric series are also established