Borhan, A: One Sample Location Test for Symmetrical

This book first studies the performance of one sample t-test,z-test and Wilcoxon test under normal and non-normal situation for location problem.The simulation results show that power functions of t-test and z-test are very much affected when the data are generated from non-normal population.Also the Wilcoxon test produces lower power than t-test and z-test for small sample sizes even in non-normal situation.To overcome the dependence on normality assumption Carolan and Rayner derived Score test and Wald test for one sample location problem under symmetric condition,where the gk(x;µ, ) family of distribution was used to produce non-normal data for simulation.For the purpose of more robust procedure this book also suggests a robust test procedure for one sample location problem under a gk(x;µ, ) distribution assumption.The procedure is based on the ratio of the restricted and unrestricted likelihood of the sample data calculated numerically,and hence named as numerical likelihood ratio test(NLRT).The powers computed suggest that the NLRT is a better alternative to all of the tests considered in this book.