4

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?

kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
Oeufcoque Penteano
  • 756
  • 1
  • 12
  • 23
  • 1
    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 09 '12 at 07:01

1 Answers1

4

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.
ttnphns
  • 51,648
  • 40
  • 253
  • 462
  • 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. – Oeufcoque Penteano Apr 09 '12 at 07:07
  • 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. – ttnphns Apr 09 '12 at 07:14
  • 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? – Oeufcoque Penteano Apr 09 '12 at 07:16