Is there an alternative to test if 2 samples come from the same population given that they don't pass normality tests? (this video assumes normality: https://www.youtube.com/watch?v=mkT3SaxoBJk, so it won't work for this question)
For example, a sample may contain binomial, poisson, and normal variables, and same with the second sample. Is there some sort of bootstrap solution to know if these samples come from the same population. And if there is, would you be so kind as to provide a solution to implement it in R.
Possible Solutions I've thought of (given there's no other solution than Hotelling T2):
Thinking outside the box, could I normalize all variables and then run Hotelling T2 test?
Is there any loss of information or some serious mistake I could be running into if I tried this?
Second Solution: I thought of running K-Means clustering with both samples and then checking if the distribution of both samples is similar on regards to how they are distributed among the centroids. Eg. sample 1 is distributed 75% on Centroid 1, 20% on centroid 2, and 5% on centroid 3. Then, assume that sample 2 falls on Centroid 3 50% of the time, and centroid 2 40%, and 10% on Centroid 1 then we can assume that they don't come from the same population (thinking of running Chi-Square test on these distributions). What do you think about this idea?
Your input would be appreciated.
