Approximation On P-value Function For The Mean Difference Of Two Independent Normal Samples With Fixed Variance Ratio

For investigating the mean difference of two independent random samples, a widely accepted method is the likelihood ratio test, which is also proved by Neymann-Pearson as the most powerful test. Because the likelihood ratio test has very good properties, especially for large sample size problem, the P-value function with this method is approached the true function.However, For small sample case, the P-value function of the likelihood ratio method gived has a clear deviation with the real function. To improve the likelihood ratio method, mang methods had been gived in the statistics literature, For example, Lugannani and Rice (1980) proposed a method which achieve third-order accuracy in theory.Wong (2008) proposed a likelihood based method which is proved to possess a higher order of accuracy. The simulation results compare the likelihood ratio test and the proposed higher order test, what is more, the proposed method shows outstanding performance over the first order method, likelihood ratio test.