The quantile test for the equality of dispersions and a comparison with the other tests

THE QUANTILE TEST FOR THE EQUALITY OF DISPERSIONSAND A COMPARISON WITH THE OTHER TESTS(M.Sc.Thesis)Emrah ÖKSÜZGAZİ UNIVERSITYINSTITUTE OF SCIENCE AND TECHNOLOGYFebruary 2007ABSTRACTThe aim of this study is to present the Quantile test which is developedas an alternative to the tests like F Test, Bartlett Test and Levene Testthat are used in testing the hypothesis of the equality of variances bythe samples drawn from populations in variance analysis. In the firstchapter, the studies related to homogeneity of variances areconsidered. In the second chapter, the test for the hypothesis of theequality of two-population dispersion parameters is examined in twoparts, the tests that need the normal distribution assumption and thetests that do not need the normal distribution assumption. In the thirdchapter, some derived tests of hypothesis about the equality of thedispersion parameters of k populations are examined in two parts, thetests that need normal distribution assumption and the tests that do notneed normal distribution assumption. The Quantile test which is alsothe main purpose of this study, derived for k population has beenexplained in the fourth chapter. In addition to various explanations, asimulation study has also been conducted concerning the Quantile test.In the final chapter the Quantile test and some other tests are comparedwith a simulation study with respect to the reject rates for the nullhypothesis which is essentially true and the reject rates for the nullhypothesis which is essentially false.As a result, it has been found that the Quantile test is appropriate formost of the situations where the populations, from which samples aredrawn, do not require the assumption of normal distribution.Science Code : 205.1.066Key Words :Homogeneity Variange, Levene Test, Bartlett Test,Anomv Test, Cochran Test, Neyman-Pearson Test,Layard Test, Brown-Forsythe Test.Number of pages : 81Adviser : Prof.Dr. Hamza GAMGAM