Generalized Staircase Designs and their Applications

Abstract

Gray bill and Pruitt (1958) introduced a class of designs which they called Staircase designs. These designs provide for the analysis of one more type of non-orthogonal data having only two types of cell frequencies viz., o and l. Such designs have the drawback that they do not provide for any block of size greater than the number of treatments. Both to remove such limitations as also to provide for analysis of one more type of non-orthogonal data, a generalized definition of the staircase designs has been given . The generalized staircase designs have in each block two types of frequencies which may change from block to block and need not be zero and unity. The number of treatments having one type of frequency need not be the same from block to block. Such designs are particularly suitable for plant breeding trials as also for experiments with animals as the experimental units. A complete method of analysis of such designs has been presented in the thesis in a simplified and systematic way. A much more simplified method of analysis of the staircase designs of graybill and Pruitt has also been presented in the thesis. In many investigations it becomes necessary to get subdivisions of the adjusted treatment sum of squares. No general and simplified method for obtaining the components of adjusted sum of squares having more than one degree of freedom seems to be available in literature. In the present thesis a general method of obtaining such subdivisions has been presented. It has been shown that in the case of staircase designs such subdivisions to suit some particular hypothesis can be obtained in a very simple way. These investigations have been illustrated by means of two examples.