I a have a series of small samples taken not randomly from a reference population with a complex distribution over a categoric variable with 21 levels and a continuous one in the x > 0 domain.
I would like to check which of these samples is more representative of the reference distribution. My approach until now has been to divide the continuous variable into 20 groups, compute the frequency of the combination of the two variables (now both categorical) and compare it with the same combinations in the samples. For the comparison, I thought of using either Cramer V or Spearman correlation or the multiplication of both.
Does it make sense? which of the three correlation methods (cramer, spearman, multiplication of both) should I use?
Another nicer possibility would be to use the posterior probability of the population distribution given the sample, using the second answer to this: Probability that a sample came from a known distribution, but I'm not sure how to build the prior (should I just set it to 1?).
Finally, these methods are based on the arbitrary subdivision of the continuous variable in 20 groups. It would be better to able to use the variable as continuous but I wouldn't know how.