I have a categorical variable with binary outcomes 0,1 (say Y), I want to study the association with other variables X1,X2,X3,X4,X5….. most of Xi's are categorical and few of them are continuous. I used Chisquare test to study the same, which tell wheather I can consider two variables independent or not.

Further to rank the Xi's in order of association with Y . Now my question is can I use the pvalue from the ChiSquare test or standardized residual of the chi Square Test to measure the degree of association between the variables ?

As far as I could understand chi sqaure test can be used just to tell whether the variable are independent or not but not the degree of association. Is there any other test to do so or chi square can do that?

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#### Best Answer

There are several statistics related to the chi-square that measure association in contingency tables.

For example, there's Cramer's $phi$ (also $phi_C$ or Cramer's $V$), which in 2×2 tables is also called the *phi coefficient*.

For a $rtimes c$ table,

$V = sqrt{ frac{chi^2/n}{min(c – 1,r-1)}}$

In your case, if one of your variables is Y, which you state to be 0-1, then that will reduce to:

$V = sqrt{ chi^2/n}$

where $n$ is the total number of observations.

Wikipedia:

There are a number of other ways of measuring association in contingency tables.

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