Hypothesis Test For Comparison Of Several Populations

Testing problem for comparing several populations is applied widely inapplications. Since the comparison of other distributions problem can be convertedinto normal distributions, so we study the normal distribution case in this paper.This problem applied to the areas of medical statistics, management, economicsand industrial production and other areas of science. The problem for comparingof multivariate populations under heteroscedasticity populations is difficult to getan exact frequency method, then some approximate solutions are given generally.So it is needed to get reasonable solution for the problem of comparing severalpopulations under heteroscedasticity.This article proposed a Parameter Bootstrap method and a Fiducial inferenceapproach to study the confidence interval of the comparison of variationcoefficients for two normal distributions, while Fiducial inference is used to solvethe problem for comparing of mean vectors for multivariate normal populationsunder heteroscedasticity.In the second chapter, a Parameter Bootstrap method and a Fiducial inferenceare proposed for intervals of the coefficient of variations of two normaldistributions. And we construct the generalized pivot quantity of the two normaldistribution variation coefficients. Finally, the simulation study for comparing twointerval estimation is given, the simulation results indicate that the Fiducialinference method is a better interval estimation method.In the third chapter, a Fiducial inference is proposed for the comparison ofmultivariate normal population mean vectors. We prove that the asymptotic size ofthe Fiducial test is equal to the nominal level, then provide some of the numericalresults from our comprehensive simulation study to compare the size of the fivetests. Simulation results show that the estimates of Type I error rates for Fiducialtest are less than the nominal level. And when the number of samples andpopulations are different, the results are well. Then the Fiducial test is very stablein the complex situation.