About General Non-parametric Behrens-Fisher Problems Of Rank Sum Test Method

In statistical research, General non-parametric Behrens-Fisher problems is often encountered in the comparsion of multifactorial sample. Because the many factors of specimens are subjected to effect and influence multifactorial factors, that is the sample determined by Multiple indicators. For general nonparametric Behrens-Fisher, there are two matters to be solved. one is the difficulty brought by the multifactorial Sample of comparison, the other is the unknown variances which in the process of comparison difficult.so it is difficult to solve and draw a effective statistical conclusion.The methods of tresting general non-parametric Behrens-Fisher problem are widely used: O’Brien (1984) proposed the rank sum test and Huang et al (2005) of the improved rank sum test for Obrien rank sum test statistics.In this paper, we research and simulate the basic properties of four kinds of test statistics.Try to improve Obrien rank sum test statistics by two kinds of methods.The two new kinds of test statistics are compared with Obrien rank sum test statistics and Huang sum rank test statistics respectively.In the simulation test, this paper sets the population as two dimensional normal distribution, and use the Monte Carlo simulation method, through extensive simulation, generate a lot of random numbers, and extract two sets of samples from the different overall independently, and use various test methods to test samples. Estimate the statistical properties, test power, the first class mistake rate of the four test statistics, compare and analyse with their simulation results, finally evalute the test results, by this way, esplore the efficiency of various comparative method, The simulation results show that, In this paper, the improved two test statistics also approximately obey normal distribution, when sample size is small, the test statistics is significantly greater than the Obrien’s test power and Huang’s test power, also make the type I error probability as well as Obrien’s and Huang’s test statistics control at the same level. And in contrast, the improved two test statistics by this paper is simpler and easier than the test statistics of Huang.