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Say I have a sample with m observations, each observation has two features X and Y which are continuous random variables. I'm interested in knowing if you can bin X and Y each into N quantiles, create a contingency table and do chi-suqare test using # of observations to test their independence? What are the caveats of doing that? [Edit] removed some unrelated part

user3582076
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  • You can bin continuous variables into discrete variables and perform a standard chi-squared test of independence if the bins are not dependent on the data (using quantiles to define bins would be data-dependent; that would affect the distribution). However, it's not advisable to discretize your data; you can lose a lot of information; chi-squared tests are very low-powered against typical alternatives and may exhibit bias against some alternatives. – Glen_b Dec 24 '18 at 04:47
  • The caveats I provided for the one-way chi-squared test (at https://stats.stackexchange.com/a/17148/919) apply, *mutatis mutandis,* to this two-way test. – whuber Dec 24 '18 at 15:35

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