Confidence intervals for the mean of one sample and the difference in means of two independent samples based on the ordinary-t statistic suffer deficiencies when samples come from skewed distributions. In this article, we evaluate several existing techniques and propose new methods to improve coverage accuracy. The methods examined include the ordinary-t, the bootstrap-t, the biased-corrected acceleration (BCa) bootstrap, and three new intervals based on transformation of the t-statistic. Our study shows that our new transformation intervals and the bootstrap-t intervals give best coverage accuracy for a variety of skewed distributions; and that our new transformation intervals have shorter interval lengths.
Health Services Research | Statistical Methodology | Statistical Theory
Zhou, Xiao-Hua and Dinh, Phillip, "Nonparametric Confidence Intervals for the One- and Two-Sample Problems" (September 2004). UW Biostatistics Working Paper Series. Working Paper 233.