Graphical methods for investigating the finite-sample properties of confidence regions
Computational Statistics & Data Analysis
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This paper compares three confidence intervals for the difference between two means when the distributions are non-normal and their variances are unknown. The confidence intervals considered are Welch-Satterthwaite confidence interval, the adaptive interval that incorporates a preliminary test (pre-test) of symmetry for the underlying distributions, and the adaptive interval that incorporates the Shapiro-Wilk test for normality as a pre-test. The adaptive confidence intervals use the Welch-Satterthwaite interval if the pre-test fails to reject symmetry (or normality) for both distributions; otherwise, apply the Welch-Satterthwaite confidence interval to the log-transformed data, then transform the interval back. Our study shows that the adaptive interval with pre-test of symmetry has best coverage among the three intervals considered. Simulation studies show that the adaptive interval with pre-test of symmetry performs as well as the Welch-Satterthwaite interval for symmetric distributions. However, for skewed distributions, the adaptive interval with pre-test of symmetry performs better than the Welch-Satterthwaite interval.