I want to validate that two samples of data with ties do not come from the same underlying distribution. The data itself describes the repair cost of cars and has a continuous value range. My solution would be to use a 2-sample test to show this. If the H0 hypothesis is rejected I can infer that the two samples are generated by different distributions. My question refers to the choice of appropriate tests.
In the following post, it was argued that chi-squared is probably a bad choice and that even KS-test with ties would give better results: Test for difference between 2 empirical discrete distributions
Question 1: Could someone explain to me in more detail, why the chi-squared test is not a good choice and what problems it suffers from?
Question 2: If the data itself is continuous but the number of observations of the 2 samples is fixed (e.g., ranging between 60 and a couple of hundred), can I use the KS-test? In other words: Is the KS test applicable if I compare two samples with a fixed number of observations? Or would this test require two continuous probability density functions give proper results?
Question 3: Is there any other alternative test for this data apart from assessing the similarity visually or by comparing its moments?
Characteristics of the data:
In total I have 6 samples with sample sizes between 60 and a couple of hundred observations. The data describes repair costs of different types of cars, so there are almost as many levels as there are data points. Ties differ between 5 and 30 depending on the samples compared.