Talk:Goodman and Kruskal's gamma

Distribution of the test statistics for $$\gamma$$
Critical values for the gamma statistic are sometimes found by using an approximation, whereby a transformed value, t'' of the statistic is referred to Student t distribution, where


 * $$t \approx G \sqrt{ \frac{ N_s+N_d}{n(1-G^2)} }$$

I think the test statistics is not $$t$$ distributed, but asymptotical $$N(0;1)$$. After all $$G \sqrt{ \frac{ N_s+N_d}{n(1-G^2)} }$$ is a discrete test statistics that can be approximated by a standard normal if $$n$$ is large enough. If $$n$$ is small then an exact test would be required.

Additionally, I did not find any paper stating that $$t$$ is $$t$$-distributed. Even Goodman and Kruskal only discuss asymptotic variances. Also, all the software implementations I looked at use the z-score for the test."

But maybe I'am wrong. --Sigbert (talk) 14:53, 15 July 2024 (UTC)

Typo in formula?
Why


 * $$n \ne N_s+N_d \,$$

instead of


 * $$n = N_s+N_d \,$$

?

dfrankow (talk) 20:54, 27 April 2011 (UTC)

No it is correct as stated. It is making the point that n is the number of samples, not the number of agreements or disagreements.