# What is the difference between verifying how strong is the relationship of variables on $\chi^2$ and correlation?

While studying about probability distributions I found that distributions such as $\chi^2$ only would be able to tell if there is or there is not relation between a variable, but not how strong it is.

Later, it is pointed out that it is possible to observe how strong this relation holds using a method particular to this distribution. One of the methods suggested is Yule's Q.

I am well aware from my basic statistics course of correlation.

Is there a real difference between them?

-
There are several "$\chi^2$ tests", which one are you talking about ? I have in mind the $\chi^2$ test for $2\times 2$ table; this test assumes two independent binomial samples and the null hypothesis is the equality of the probabilities of success. Please precise your context. –  Stéphane Laurent Apr 9 '12 at 7:01

You could find the formulas easily. Yule's Q is for binary data only and is $$\frac{ad-bc}{ad+bc}$$ Yule's Q is a binary form of Goodman-Kruskal Gamma (and is thus related to Kendall's tau correlation). The binary form of Pearson correlation is called Phi: $$\frac{ad-bc}{\sqrt{(a+b)(a+c)(b+d)(c+d)}}$$ You can see that these two are the same quantities, differently normalized by their respective denominators. The notation above: