One-stage and two-stage statistical inference under heteroscedasticity

This paper presents general one-stage and two-stage sampling procedures for testing the hypotheses of the equality of means when the variances are unknown and unequal. The methods use a new range test and an ANOVA test based on independent t variables for an one-way layout. The one-stage procedure is an exact statistical procedure which provides a feasible solution to the two-stage procedure when the required two-stage sample sizes are not met due to time limitation, budget shortage, or other factors that result in early termination of the experiment. An extension to the two-way layout is also considered and the percentage points of the range test for testing the associated hypotheses are tabulated.