Book Description

The purpose of this study is to investigate the asymptotic behaviour of certain (conditional) rank tests for comparative experiments proposed by Hodges and Lehmann (1962), and their extensions and variations. The results obtained in this thesis are extensions of the results of Mehra and Sarangi (1965) (where the case of complete designs was discussed) to the case of balanced and partially balanced incomplete block designs. The methods employed are based on certain properties of the U-statistics derived by Hoeffding (1948). In Chapter I, a brief resume of the relevant earlier work has been given and the test proposed by Hodges and Lehmann described. In Chapter II, a simplified large sample version of this test is discussed, which reduces its application to reading the critical value from the chi-square tables. In Chapter III, the asymptotic distribution of the test statistic, under a sequence of alternatives approaching the null hypothesis has been found to follow a non-central chi-square law. This helps us to study the power properties and the Pitman efficiency of the test statistics in Chapter IV. Explicit numerical evaluations of the expressions for asymptotic efficiency, which has been limited to the normal form of the parent distribution, indicates a rather high degree of efficiency of the test. Chapters IV and V contain several remarks that follow from the results of our investigation, including a useful lower bound for the asymptotic efficiency of the investigated test relative to the classical F-test. Further investigations that will throw more light on our present findings have been suggested at suitable places.