Robustness of the Two-sample Sequential t-test

Abstract

Hajnal’s pooled variance sequential two-sample and a Welch type sequential two-sample t-test proposed by Reed and Frantz are compared for different forms of violation of the underlying normal assumption. For Monte-Carlo studies eight alternative distributions of the Fleishman System with given values of skewness γ₁ and kurtosis γ₂ were used. The results show that both tests are robust for α and β when the violation of the normal assumption in the X-population and Y-population is of the same nature. The influence of unequal variances is also considered. The results show that for small deviations of σ_x/σ_y from 1 both tests can be used if we take one x- and one y-observation at each stage of the sequential test, or if we take x- and y-observations with the same probability π_x = π_y = 1/2. For π_x ≠= π_y only the Welch type test can be used because Haj rial’s test tends to have uncontrolled type I or type II error in this case.