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Methods and Applications of Statistics in Clinical Trials, Volume 2: Planning, Analysis, and Inferential Methods by N. Balakrishnan

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Chapter 6

Bootstrap

Tim Hesterberg

6.1 Introduction

We begin with an example of the simplest type of bootstrapping in this section, then discuss the idea behind the bootstrap, implementation by random sampling, using the bootstrap to estimate standard error and bias, the central limit theorem and different types of bootstraps, the accuracy of the bootstrap, confidence intervals, hypothesis tests, planning clinical trials, and the number of bootstrap samples needed and ways to reduce this number, and we conclude with references for additional reading.

Figure 1 shows a normal quantile plot of arsenic concentrations from 271 wells in Bangladesh, from http://www.bgs.ac.uk/arsenic/bangladesh/Data/SpecialStudyData.csv referenced from statlib http://lib.stat.cmu.edu/datasets. The sample mean and standard deviation are = 124.5 and s = 298, respectively.

Figure 1: Arsenic concentrations in 271 wells in Bangladesh

The usual formula standard error is = 18.1, and the usual 95% confidence interval is (88.8, 160.2). This interval may be suspect because of the skewness of the data, despite the ...

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