# Which statistical test to use on half-normal distribution of discrete data points

I have two datasets. Each contains integer data points, ranging from 0 to 34 and they follow an approximately half-normal distribution, as 0 occurs very frequently and 34 occurs only once.

I would like to test whether one dataset shows significantly lower values than the other. I have never worked with half-normal distributions before, so my questions are:

1. Should I first test whether I am allowed to consider this a half-normal distribution? If so, how?

2. What test do I use to assess whether means or medians are different? T-test? Mann-Whitney U test? Other? To decide this, does it matter that my data points are discrete/integer and thus not continuous?

EDIT: Here is a boxplot summarizing the data. "+" shows the mean. All individual data points are shown from left to right per set. Total number of data points on top. It looks pretty clear to me that there is a difference, but I also have some less clear cases and I am not sure which statistical test is formally correct here.

• Could you post some plots of your data? Mar 5, 2019 at 10:15
• Please see edit above, @kjetil-b-halvorsen. Thanks. Mar 5, 2019 at 12:04
• From the plots it is very clear that at least the medians are different. And variances cannot be equal! Mar 6, 2019 at 20:21
• Why do you need a statistical test for these data, which are clearly different (or are the datapoints dependent and is the sample size effectively smaller)? What do you want to show with the statistical test? You have doubts that these two sets could be samples from the same distribution? Mar 19, 2022 at 20:40

You will need to formalize what that means. Different means? Different medians? Or that $$P(X \le Y) \not= \frac12$$? Or something else. I would bystep the question about which theoretical distribution "the data follows", with your sample size bootstrapping should be adequate. Or if you instead just want to test the null hypothesis that the distributions are equal, you could use a permutation test.