The robustness of the one-samplet-test over the pearson system

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Abstract
The present paper has as its objective an accurate quantification of the robustness of the one-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. The details parallel those of a previously published study for the two-sample t-test and indicate that the results are quite accurate. The study was conducted over the range β1=0.0(0.4)2.0(negative and positive skewness) and β2=1.4(0.4)7.8 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 one-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.

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