# 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. Apr 9, 2012 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:

• a - number of cases where characteristic is present in both variables X and Y.
• b - number of cases where characteristic present only in X.
• c - number of cases where characteristic present only in Y.
• d - number of cases where characteristic is absent in both variables.
• thanks, I have weak background on statistics so I had a hard time understanding it from the book. I can understand from your explanation, but my question still remains: is there an difference on them? By difference I mean is one more expressive than the other or it only depends on the constraints? +1 for the very quick response and descriptions on them. Apr 9, 2012 at 7:07
• To be honest, I don't catch what you mean by "expressive" and "constraints". All difference between them comes from their formulas. Try to reflect on it or test some data, to see. Apr 9, 2012 at 7:14
• if they both tell you the correlation, are they expected to tell as answer the same result? is one more reliable than the other? does this makes more sense? Apr 9, 2012 at 7:16