# Should I report median or mean-based data if using permutation tests?

I have used permutation tests to analyse some data (specifically, the perm.test() function in R's exactRankTests package). I understand that permutation tests are effectively repeated iterations on parametric tests. However, I have used permutation tests because my data are not normally distributed.

I believe that showing my raw data using median-based box and whisker plots (in a scientific publication) would be more informative. However, since I've used permutation t-tests, would it be more 'correct' to report mean / standard error and the corresponding plots? Or, is it entirely up to me how I display the data?

Example of box and whisker plot:

The same data, shown as means and standard error:

• What kind of variable is it you have? What's being measured? Feb 20 '15 at 14:43
• I'm measuring human response times - specifically, the time taken to notice something has happened, and respond by moving the eyes. Such data are typically positively skewed. Feb 20 '15 at 14:47
• 1. I'd be inclined model times either on the log-scale or as speeds (inverse times). Usually one of those tends to reduce both skewness and heteroskedasticity. Or I'd use a GLM, either a Gamma or inverse Gaussian model. 2. Your means-and-standard-error display has the mean not in the middle of the interval around it, which doesn't seem right to me. Feb 20 '15 at 17:10