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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?

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    $\begingroup$ 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. $\endgroup$
    – Stéphane Laurent
    Apr 9, 2012 at 7:01

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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.
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  • $\begingroup$ 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. $\endgroup$
    – Oeufcoque Penteano
    Apr 9, 2012 at 7:07
  • $\begingroup$ 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. $\endgroup$
    – ttnphns
    Apr 9, 2012 at 7:14
  • $\begingroup$ 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? $\endgroup$
    – Oeufcoque Penteano
    Apr 9, 2012 at 7:16

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