The robustness of the two—sample t—test over the Pearson system

The present paper has as its objective an accurate quantification of the robustness of the two–sample t-test over an extensive practical range of distributions. The method is that of a major Monte Carlo study over the Pearson system of distributions and the details indicate that the results are quite accurate. The study was conducted over the range β ₁ =0.0(0.4)2.0 (negative and positive skewness) and β ₂ =1.4 (0.4)7.8 with equal sample sizes and for both the one-and two-tail t-tests. The significance level and power levels (for nominal values of 0.05, 0.50, and 0.95, respectively) were evaluated for each underlying distribution and for each sample size, with each probability evaluated from 100,000 generated values of the test-statistic. The results precisely quantify the degree of robustness inherent in the two-sample t-test and indicate to a user the degree of confidence one can have in this procedure over various regions of the Pearson system. The results indicate that the equal-sample size two-sample t-test is quite robust with respect to departures from normality, perhaps even more so than most people realize.