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

$n\neq N_{s}+N_{d}\,$

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.