Simulating by sampling with replacement (bootstrapping)

Consider trying to give a confidence interval for the mean from [attachment:before.jpg Raw positive skewed data.]

One way to achieve this is to bootstrap (Efron and Tibshirani, 1993) and repeatedly sample a large number of times. Sampling 500 times, taking the means of these samples and then repeating this 49 more times creates 50 sample [attachment:after.jpg bootstrapped means.]

This distribution is symmetric and, therefore, by taking the 5% and 95% percentiles we obtain a 95% Confidence interval for the sample mean.

Code is available [http://www.stat.tamu.edu/ftp/pub/mspeed/stat653/spss/ in SPSS] and more succinctly [:FAQ/bootR: in R.]

Have a look [http://www.stanford.edu/~kcobb/hrp261/cobb7.ppt here] for an example

Reference

See [attachment:boot.pdf here.]

Efron B. & Tibshirani R.J. (1993), An introduction to the bootstrap, Chapman & Hall.