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) [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.