# What descriptive statistics to report for non-normal data

Let's say I run an experiment with one dependent variable and three experimental groups. In the end I would like to report both the results of a statistical test to know if there are any group effects, but also some descriptive statistics (center and spread) for the individual populations. The data won't be normally distributed (the dependent variable is continuous but bounded between 0 and 1), so I plan to use a Kruskal-Wallis test and report the median and interquartile range. However, I've been reading (here, and elsewhere) that the Kruskal-Wallis test isn't necessarily appropriate to use in cases of normality violations.

So if I use the more standard ANOVA instead, would it still be appropriate to report the median and interquartile range, or would that not 'fit' with the test?

: The data look similar to (truncated) Gamma distributions.

• The Kruskal-Wallis test is a fine choice if your data aren't normal; the ANOVA would be more suspect. Can you say more about what your data actually are? How is it they are bound by 0 & 1? Aug 14, 2015 at 0:22
• In addition to what @gung requested also include the n for each group and state more specifically what you'd like to say about your data. You don't just change the descriptive statistics based on the data. It depends on what you want to say about them because they mean different things.
– John
Aug 14, 2015 at 0:37
• @John - I'm surprised that you say that you wouldn't change descriptive statistics based on the data. If I want to describe the center of a distribution, my intuition is that mean would be appropriate if the data are approximately normal (or at least continuous and not skewed), whereas the median is more appropriate otherwise. Similarly for spread and standard deviation vs. iqr/mad.
– Evan
Aug 14, 2015 at 13:46
• Evan, you and @John both have good points. Descriptive statistics ought to be motivated by what you intend to say about the data--and this can be determined before seeing the data. After obtaining the data, though, you might want to add to that description to describe important or interesting departures from your expectations or assumptions.
– whuber
Aug 14, 2015 at 13:51
• The two things have different purposes. You use resistant statistics, such as median and IQR, in order to insulate yourself from being misled by outlying data, etc. There's nothing contradictory in also planning to test additional assumptions you might want to evaluate, such as symmetry of the distribution, its normality, etc. In fact, you can do anything you like--mix and match frequentist and Bayesian approaches, make different (incompatible) assumptions at different times, etc. You have to be careful about how you compute p-values if you're going to do any formal testing, that's all.
– whuber
Aug 14, 2015 at 14:21