Distribution-free methods in experimental design

Abstract

The purpose of the work presented was firstly to develop distribution-free methods of analysis and multiple comparison procedures for basic experimental designs where the treatments form multi-way classification, and secondly to present these to present these methods in such a wat that a research worker with an elementary knowledge of biometry would be able to apply these methods without much difficulty This thesis is divided into two parts Part I deals with the matter of test statistics and their exact distributions (under the null for different experimental designs as well as the investigation of the applicability of the tests based on these test statistics under an alternative hypothesis by means of simply studies; Part II deals with the application of the tests derived in Part l, tended to be conservative. did not reject the null hypothesis too soon) under different alternative hypotheses and due to this and certain theoretical considerations was concluded that these tests were applicable under the null as well as under an alternative hypothesis. Distribution-free tests were also developed for a factorial design, known as the single degree of freedom approach. The underlying theory and practical investigation led to the above-mentioned results, are given in Chapter III of this thesis. The theoretical development of test statistics and their distributions under the null hypothesis for the different components of a multi-way classification of treatments when the design was a balanced incomplete block design is presented in Chapter IV. Since a balanced incomplete block design, where the treatments consisted of more than one component, is very seldom used, the formulae are of little use in practice. They are, however, of theoretical interest since the formulae for a randomized block design are obtainable from them as a special case