# Error to report with median and graphical representations?

I've used a wide array of tests for my thesis data, from parametric ANOVAs and t-tests to non-parametric Kruskal-Wallis tests and Mann-Whitneys, as well as rank-transformed 2-way ANOVAs, and GzLMs with binary, poisson and proportional data. Now I need to report everything as I write all of this up in my results.

I've already asked here how to report asymmetrical confidence intervals for proportion data. I know that standard deviation, standard error or confidence intervals are appropriate for means, which is what I'd report if all my tests were nicely parametric. However, for my non-parametric tests, should I be reporting medians and not means? If so, what error would I report with it?

Associated with this is how best to present non-parametric test results graphically. Since I largely have continuous or interval data within categories, I'm generally using bar graphs, with the top of the bar being the mean and error bars showing 95% CI. For NP tests, can I still use bar graphs, but have the top of the bar represent the median?

• Something doesn't compute. How can you have means or medians or CIs with categorical data? – rolando2 Jun 3 '11 at 0:40
• Sorry that wasn't clear @rolando2...I have categories in which I have continuous or interval data (original question was edited to clarify now). – Mog Jun 3 '11 at 0:51

You can report a confidence interval for the median. In R, you can use wilcox.test with the argument conf.int=TRUE. There's a tiny discussion of this in John Verzani's simpleR notes: see here.
The plot on the right was made with errbar() from the Hmisc package [CRAN page].