Hypercubic design (HCD), E-optimal RGD, Partially balanced incomplete block design (PBIBD), Extended-group divisible partially balanced incomplete block design (EGD-PBIBD), Semi-regular graph design (SRGD),

It is shown that the exact null distribution of the likelihood ratio criterion for sphericity test in the p-variate normal case and the marginal distribution of the first component of a p − 1 -variate generalized Dirichlet model with a given set of parameters are identical. The exact distribution of the likelihood ratio criterion so obtained has a general format for every p. A novel idea is introduced here through which the complicated exact null distribution of the sphericity test criterion in multivariate statistical analysis is converted into an easily tractable marginal density in a generalized Dirichlet model. It provides a direct and easiest method of computation of p-values. The computation of p-values and a table of critical points corresponding to p = 3 and 4 are also presented.

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In this article, we develop a new method of construction of E-optimal generalized group divisible designs through group testing designs. Keywords: Balanced Incomplete Block Design (BIBD); Group Divisible (GD); Generalized Group Divisible Design (GDD); E-optimality. © 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i1.1697

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.