This is a very open ended question. Suppose I have two sets of data samples of the same form, say [item, rating]. Rating is a value on the interval [0,100] and item is a unique identifier given to a particular item. I would like to compare these two sets of data samples and determine whether the null hypothesis holds.
One caveat though. I can't look at the rating distribution. This because I have literally thousands of groups that I would like to compare and it would be too time consuming to determine the rating distribution (normal, bimodal, etc) of each group. Therefore groups that I may be comparing may have different distributions.
The naive approach would be to assume that each distribution is normal and to use something like students t test to compare groups. This is what I have been doing but I would like something more robust. Therefore how might one determine how similar/different two groups are when the two groups may have different non-normal distributions (the number of elements in the two groups may be different as well)?
edit: The item really doesn't matter. What matters is the ratings for each group.