I am trying to compare two probability distribution functions with the chi-square test. The formula for computing the chi-square sum [(o-e)^2/e] indicates that the result is not normalized (i.e., if you change the units of o and e, you could get a different chi-square value) When you apply this test, should I be only using the 'bincounts' for o and e?
If the two distributions being compared have different x-ranges, how do I incorporate that into the test? (for e.g., distribution1 could be sampling from 0-100, and distribution2 could be sampling from 100-200).
Should I be using some other test for comparing two distributions?
(1) Yes, the chi-square test applies only to bin counts.
(2) If you know already that the two distributions are not the same, this is pointless; if you have a large enough sample, you will reject the null hypothesis that they are the same. "I have a large sample" isn't an interesting or useful conclusion. This applies to any null-hypothesis significance test, such as the chi-square test or Kolmogorov-Smirnov test. (Even if you don't know a priori that the distributions are the same, I am inclined to claim that a significance test is still useless, but that is a different question.)