There is a large collection of social network data available here:
https://snap.stanford.edu/data/index.html
Note that this is deliberately left at a high level: try to find interesting patterns in the data, differences between the social networks, and explanations for those differences. If you are not familiar with one or more of these networks, you may want to sign up for them and try them out.
Your task is to determine the relative power of the $t$-test, the $U$-test, and a random sampling version of the permutation test on unimodal distributions. Obvious questions to ask are:
You should probably also make sure that you are using enough random samples in the permutation test; how many is enough?
Perform numerical experiments using random sampling similar to that used in class.
Select your experiments carefully in order to come up with some general recommendations. General recommendations might look like:
Consider at least the normal distribution, the uniform distribution over an interval, and the Cauchy distribution.