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I have 5 variables - $v_{1}$, $v_{2}$, $v_{3}$, $v_{4}$, and $v_{5}$. All are categorical variables.

I conducted a $\chi^{2}$ (chi-square) test to understand the relationship between these variables. I could see that $v_{3}$ and $v_{4}$ have p-values of 0. I understand that these two variables are dependent on each other. Should I remove one of the variable from further analysis?

What if the same $v_{3}$ and $v_{4}$ are independent of other variables, like $v_{1}$, $v_{2}$, and $v_{5}$?

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I suggest you to read about multicollinearity.

– Aleksandr Blekh – 2015-08-10T04:50:12.297What type of analysis do you intend to apply to the variables, this will affect the answer, as will the size of your data set. In some circumstance highly correlated variables may contain useful discriminative information. Ultimately run your analysis with the variable removed and with it left in and see how the results differ. – image_doctor – 2015-08-10T08:24:15.340

@image_doctor - Thank you very for your advice. My intention of doing chisquare test is to check for the collinearity between the variables. I got confused between the purposes of collinearity and chisquare test. Hence i raised the question. Thanks again. – Arun – 2015-08-10T10:36:31.123