# Do multiple chi square tests between a set of variables violate the assumption of independence?

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.