I have a dataset of 28 nominal and ordinal categorical variables, 161 observations. If I use chi sq tests of association between variables, for example I test var1 and var2, var1 and var3 and var1 and var4, do I violate the independence assumption of the test (I know I must use Bonferoni or similar) because var 1 is common to all three tests? If so, could someone explain why this is the case and propose an alternative? I don’t think I need to give a data sample here as it’s a theory question? Also, some of the tests have expected cell values less than 5 but are in bigger than 2$\times$2 contingency tables. My understanding is that Fishers exact is only for 2$\times$2. Can someone suggest a good alternative for, say, 4$\times$9 table categorical variables? Thanks.
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Sounds to me just a multiple testing question. It does not seem specific to chi-square test. Even if you do t-test, you can test one group against multiple other groups respectively. It is fine, as long as you do the appropriate multiplicity adjustment.
Independence between the variables is the null hypothesis you are testing. It is not an assumption?
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$\begingroup$ Great thanks. Any idea of a replacement for Fisher For mxn contingency tables where both m and n are greater than two and some expected frequencies are smaller than 5; 20% of the cells in fact? $\endgroup$– steveCommented Oct 20, 2020 at 19:21
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$\begingroup$ Yes it is but I thought there was an assumption that the groups be independent? $\endgroup$– steveCommented Oct 20, 2020 at 19:22
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1$\begingroup$ You can't really have an assumption of independence with categorical data, as you have a number of variables, essentially denoting properties, more than one of which can be simultaneously true of a single tested individual. You can, for example, test whether "gender" and "smoking" are independent, but there is no sense in assuming that males/females and smokers/non-smokers are independent. For t-tests and ANOVAS things are a bit different. $\endgroup$ Commented Oct 20, 2020 at 19:27
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$\begingroup$ Ok, but can you test the association between smoking and gender, smoking and race and smoking and education without any problem? Or does the fact that smoking is common to all three cause an issue with the chi square test? I may be misunderstanding something here, sorry. $\endgroup$– steveCommented Oct 20, 2020 at 21:37
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$\begingroup$ I do not think it is a problem. It is OK if the test statistics for multiple tests are correlated. Bonferroni adjustment is a conservative adjustment anyway. $\endgroup$– heheCommented Oct 21, 2020 at 2:12