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Biostatistics 2005 6(2):187-200; doi:10.1093/biostatistics/kxi002
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.

Nonparametric confidence intervals for the one- and two-sample problems

Xiao Hua Zhou*

Department of Biostatistics, University of Washington, Box 357232, Seattle, WA 98195, USA, Health Services Research & Development Center of Excellence, Veterans Affairs Puget Sound Health Care System, Metropolitan Park West, 1100 Olive Way #1400, Seattle, WA 98101, USA

Phillip Dinh

Department of Biostatistics, University of Washington, Box 357232, Seattle, WA 98195, USA

* To whom correspondence should be addressed. azhou{at}u.washington.edu

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 families. 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 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.

Keywords: BCa; Bootstrap; Confidence interval; Cost data; Edgeworth expansion; Positive skewness


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