Under two biologically different conditions, we are often interested in identifying differentially expressed genes. It is usually the case that the assumption of equal variances on the two groups is violated for many genes where a large number of them are required to be filtered or ranked. In these cases, exact tests are unavailable and the Welchs approximate test is most reliable one. The Welchs test involves two layers of approximations: approximating the distribution of the statistic by a t-distribution, which in turn depends on an approximate degrees of freedom. This study attempts to improve upon Welchs approximate test by avoiding one layer of approximation.