# Which statistical test for count data with small samples?

I am comparing frequency count data for observed behaviours in a 3 minute time frame, between two small groups of people. My hypothesis is that there will be significantly more of certain behaviours in one of the groups. As I understand it, frequency count data is by nature non-normal, so from what I have read I would have two options:

1. Transform the data to normality using arcsine of the square root, then doing t tests.
2. Doing a two sample Poisson distribution, which if I understand rightly should give a p value.

Which is best? I am a stats novice.

Probably the easiest thing for you to do is to use the Mann-Whitney U-test. That will test if the counts in one group tend to be higher than the counts in the other group.

If you need a test that is specific to the means of the two counts, things get a little more complicated. Count data are often overdispersed relative to the Poisson distribution, so you should take that into account (there are several strategies available). I would be less of a fan of using a transformation and a t-test here. If you have a lot of data in each group, and if the counts are far from 0, then this will be more workable. You should use Welch's t-test (for unequal variances) by default, though, whether or not the variances seem similar.

• Thanks for your answer. Will a mann whitney U be possible with very small groups (in one of my conditions I have n=2 in each group : I know I could just not test for sig with such small samples but it would be good to try if possible. Would it be worth taking it down to a lower level i.e. p=0.10 ?) – Laura Aug 7 '17 at 16:48
• @Laura, you won't be able to get a significant result form MW w/ only 4 data; you need at least 4 per group (8 total) for significance w/ MW even if the groups don't overlap at all. You could conduct a Poisson test (cf, Statistical analysis of number of flood events), but I wouldn't put too much stock in the answer. – gung Aug 7 '17 at 16:55