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# Confidence intervals - Bootstrap options

In bootstrapping (Efron & Tibshirani, 1993), the data of the sample are used to create a large set of new "bootstrap" samples, simply by randomly taking data from the original sample. In any given new sample, each of the same size as the original sample, some subjects will appear twice or more, and others will not.

The statistic of interest is computed in each of those bootstrap samples. The collection of these computed values is referred to as the bootstrap distribution of the statistic.

The percentile bootstrap is derived by using the 2.5 and the 97.5 percentiles of the bootstrap distribution as the 95% confidence interval of the statistics of interest. This percentile interval is used for the calculation of the confidence intervals for reference limits when estimated using the robust method.

The bias-corrected and accelerated (BCa) bootstrap (Efron, 1987; Efron & Tibshirani, 1993) adjusts for possible bias and skewness in the bootstrap distribution. The BCa bootstrap is used for Kendall's tau and in ROC curve analysis.

### Random number generation

MedCalc uses the Mersenne twister as a random number generator (implementation MT19937) (Matsumoto & Nishimura, 1998).

## Required input

• Bootstrap confidence intervals: select "None" if you do not want to calculate confidence intervals; otherwise select a 90% or 95% confidence interval.
• Bootstrap replications: enter the number of bootstrap replications. High numbers increase accuracy but also increase processing time.
• Random-number seed: this is the seed for the random number generator. Enter 0 for a random seed; this can result in different confidence intervals when the procedure is repeated. Any other value will give a repeatable "random" sequence, which will result in repeatable values for the confidence intervals.

## Literature

• Efron B (1987) Better Bootstrap Confidence Intervals. Journal of the American Statistical Association 82:171-185.
• Efron B, Tibshirani RJ (1993) An introduction to the Bootstrap. Chapman & Hall/CRC.
• Matsumoto M, Nishimura T (1998) Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactions on Modeling and Computer Simulation 8:3-30.

## An Introduction to the BootstrapBradley Efron, R.J. Tibshirani

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Statistics is a subject of many uses and surprisingly few effective practitioners. The traditional road to statistical knowledge is blocked, for most, by a formidable wall of mathematics. The approach in An Introduction to the Bootstrap avoids that wall. It arms scientists and engineers, as well as statisticians, with the computational techniques they need to analyze and understand complicated data sets.