Nonparametric statistical significance test for largely skewed count data

My research design looks as follows: an experimental game with 4 participants (human subjects), repeated for 20 rounds. During each round, participants are allowed to form bilateral coalitions which cannot be dissolved until the end of a round. Hence, six different possible coalitions exist, but maximum two coalitions can emerge during a single round.

For the experiment, I have the data on the number of times each particular coalition was formed. It can be visually represented on a bar chart (see the attached image), on which each colored bar corresponds to each of the possible coalitions, and the vertical axis shows the number of times it occurred (count variables).

My general idea is to understand whether stable coalition relationships emerge between participants in the experiment as they play repeatedly: for example, whether participant 1 tends to form coalitions with participant 2 more often than with other players.

To that end, I would like to test:

1. Whether there are statistical differences between the frequency of occurrences of different coalitions;
2. Whether the experimentally observed frequency distribution statistically differs from a theoretical benchmark (each coalition occurs with the equal 1/6=0.15 probability).

What would be the appropriate test in this case given that we are working with count data which is (a) coutn data and not normally distributed, (b) is largely skewed (a numeric outcome is frequently zero)? My guess would be to use Wilcoxon MW test for (1) and Kolmogorov Smirnov test for (2) but I am not sure I can because of the problems (a) and (b) described above and therefore would appreciate any thoughts on this problem...

Thank you very much in advance!


TS Contributor
Looks like one-sample Chi². The expected frequencies will be
too low in all cells and the observations are not independent,

With kind regards



TS Contributor
I think your two questions are equivalent, i.e. the answer to point 2 answers point 1 as well. I would simply do a chi-squared goodness of fit test, assuming uniform distributions. this will give you a p-value to judge the null hypothesis of your data coming froma uniform distribution and if not the pairs having a large chi-squared value would be the candidates to look at as having formed stable coalitions ( or a stable aversion against each other :) .