A practical approach for comparing means of two groups without equal variance assumption

In this paper we consider two-groups of i.i.d. normally distributed random variables (N(mu(x),sigma(x) (2)) and N(mu(y),sigma(y) (2))) without assuming equal variance (sigma(x) (2) = sigma(y) (2)). We propose a simple method for constructing confidence bounds based on Howe's approximation I. Its applications in parallel clinical trial (testing H(0) : mu(x)-mu(y)=0 versus H(1) : mu(x)-mu(y)<0) and parallel bioequivalence (BE) trial (testing H(0):mid R:mu(x)-mu(y)mid R:delta versus H(1):mid R:mu(x)-mu(y)mid R:<delta) are studied. Sample size calculation formulae for both cases are derived. Their performances are evaluated by simulation. Our study shows that the proposed procedure can control type I error satisfactorily compared with Cochran-Cox's and Satterthwaite's approximations while maintaining a relatively high power. The proposed approach is not only simple for constructing the confidence limit, but also provides a simple and accurate formula for sample size calculation.