# What is the relationship between two variables that Chi-Squared Test for Independence is testing for?

I am trying to understand the application of Chi-Squared test for independence between predictor and response variables as it applies to feature selection in machine learning and exploratory data analysis. I understand that there are few types of Chi-Squared test for independence.

However, I do not understand what exactly is this relationship that Chi-Squared measures. Is it simply a measure of a correlation coefficient between distributions of categorical variables?

I would prefer an intuitive explanation over mathematical proof.

Thank you!

• Just to be clear -- are you primarily interested in the 2x2 case or the general r $\times$ c case, or something else? If the r x c case, what do you mean by "correlation"? – Glen_b Dec 19 '16 at 5:54
• Correlation as a linear relationship between two variables. I am not sure what you mean by 2x2, I am interested in getting a general understanding. – verkter Dec 19 '16 at 6:26
• A chi-squared test for independence is conducted on data that falls into two (or more) categorical variables. How are you defining "linear" between things falling into categories? – Glen_b Dec 19 '16 at 11:58
• Linear is probably not a correct. I assumed that this is the relationship that Chi-Squared test is measuring. Looking at the definition of what chi-squared test for independence does: "It is used to determine whether there is a significant association between the two variables." (stattrek.com/chi-square-test/independence.aspx?Tutorial=AP) What is this "significant association" actually is? – verkter Dec 20 '16 at 0:13
• To return to the question about 2x2 vs r x c (since it impacts the possible ways of interpreting an idea of linear association)... how many categories do you have in each variable? – Glen_b Dec 20 '16 at 0:16