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I have four variables (attributes) describing student. They are categorical data. I need to prove that these variables are independent.

The easiest way (even not sufficient) is to see the correlation between pairs of these variables.

Could you please kindly help me with this problem? Thanks in advance.

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    $\begingroup$ You can't prove independence (at least not without the whole population). You can sometimes identify dependence (e.g. by a chi-square test), but failure to identify dependence is not at all the same as proving independence. If small amounts of dependence can be tolerated, you might consider some form of equivalence test (provided you're only concerned with the particular kinds of dependence in your equivalence test). $\endgroup$ – Glen_b Sep 29 '14 at 0:51
  • $\begingroup$ It seems unlikely that any student attributes would truly be independent. Could you elaborate on why you want to demonstrate independence? $\endgroup$ – whuber Sep 29 '14 at 20:35
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In case of categorical variables, you can either perform a $G$-test or a $X^2$-test of independence. If you do not have a lot of samples, you may consider performing Fisher's exact test instead.

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    $\begingroup$ That's not really correct. Failure to reject the null does not imply accepting it! $\endgroup$ – abaumann Sep 29 '14 at 20:27
  • $\begingroup$ You are of course correct. I did not intend to imply this in my answer. As Glen_b already mentioned, you can't prove independence. In practice however, such tests are often used to "decide" whether dependence or independence holds. $\endgroup$ – George Sep 29 '14 at 22:54

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