Adaptive confidence intervals of desired length and power for normal means
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Date
2009-02-02T10:45:39Z
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Abstract
In all empirical or experimental sciences, it is a standard approach to present results, additionally to point estimates,
in form of confidence intervals on the parameters of interest.
The length of a confidence interval characterizes the accuracy of the whole findings.
Consequently, confidence intervals should be constructed to hold a desired length.
Basic ideas go back to Stein (1945) and Seelbinder (1953) who proposed a two-stage procedure for hypothesis testing
about a normal mean.
Tukey (1953) additionally considered the probability or power a confidence interval should possess to hold its length
within a desired boundary.
In this paper, an adaptive multi-stage approach is presented that can be considered as an extension of Stein's concept.
Concrete rules for sample size updating are provided. Following an adaptive two-stage design of O'Brien and Fleming (1979)
type, a real data example is worked out in detail.
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Keywords
adaptive sample size planning, group sequential trial, length of a confidence interval, multi-stage confidence interval, power of a confidence interval