Two-stage sampling procedures for comparing two population means when variances are heterogeneous have been developed by D. G. Chapman (1950) and B. K. Ghosh (1975). Both procedures assume sampling from populations that are normally distributed. The present study reports on the effect that sampling from non-normal distributions has on Type I error rates, statistical power, and sample size requirements. Four factors were manipulated in the simulation study: (1) distribution shape; (2) degree of variance heterogeneity; (3) initial sample size; and (4) difference in population means. For each condition, 1,000 replications were performed, and the frequency of rejecting the null hypothesis was recorded. The results indicate that Ghosh's procedure is less sensitive to non-normal distributions, but can be liberal when sampling from distributions that are skewed and have a small initial sample size. Average sample sizes needed remained constant across distribution shapes, but greater variability was found with heavy-tailed distributions. Moderate to large sample sizes at the first stage of sampling can reduce the overall total sample size needed and can minimize the inflated Type I error rate in situations where the sampled distributions are extremely non-normal. (Author/TJH)