= 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.]] You can also adapt this to compare medians using this [[FAQ/bootmed| SPSS syntax.]] 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://pages.infinit.net/rlevesqu/SampleSyntax.htm#Bootstrap|in SPSS]] and more succinctly [[FAQ/bootR| in R]] with a stand-alone free program by Howell (2013, p.663) also available for download as a zipped file [[http://www.uvm.edu/~dhowell/StatPages/Resampling/ResamplingPackage.zip|from here.]] __References__ See [[attachment:boot.pdf|here.]] Efron B. & Tibshirani R.J. (1993), An introduction to the bootstrap, Chapman & Hall. Howell DC (2013) Statistical methods for psychology. 8th Edition. International edition. Wadsworth:Belmont,CA.