Simulating by sampling with replacement (bootstrapping)
Consider trying to give a confidence interval for the mean from 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 bootstrapped means. You can also adapt this to compare medians using this 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 in SPSS and more succinctly in R with a stand-alone free program by Howell (2013, p.663) also available for download as a zipped file from here.
References
See 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.