Circular Designs & Designs Developable from Initial Blocks

Abstract

The thesis deals with three main problems. These are (I) obtaining designs which are fractions of balanced incomplete block designs (II) analysis of circular designs with block sizes 2,3,4 and 5 and (III) analysis of designs with two plots per block. Balanced incomplete block designs have the drawback that they require too many replications. In order to obviate this difficulty designs like partially balanced incomplete block designs, lattice designs have been evolved. An attempt has been made in the present investigation to exploit alternative ways to get over this difficulty. Given a balanced incomplete block design obtainable by developing more than one initial block, new designs can be obtained by taking only those blocks which are obtained by developing only one of the initial blocks. The method of analysis of such designs has been presented. In an attempt to got incomplete block designs for each and every number of treatments, the problem of analysis of circular designs which was introduced by das and solved completely for the design with blocks of two plot and two replications only has been solved for all designs with up to blocks of size five. Necessary tables required for obtaining the analyses readily have also been prepared and presented. Circular designs with a given block size can be obtained in alternative ways depending on the initial block taken. An investigation has been made to indicate the more efficient designs when the block sizes are 3 & 4. A special class of circular designs with blocks of two plots and having more than one initial block has been investigated in the last section of the thesis. These designs were also investigated by Kempthorne. Such designs for any given number of treatments can be obtained in several alternative ways. A method of choosing the design with maximum efficiency has been described. Theses designs fall into several classes in respect of efficiency. The method of analysis of three classes of these designs for plot size two with replications four have presented together with efficiency factors in the case of all numbers of treatments up to 30.though the tables for the analysis of such designs have been prepared up to number of treatments 50. Many of designs given by Kempthorne do not have option efficiency.