Talk:Goodman and Kruskal's gamma

Statistics Mid‑importance

	This article is within the scope of WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.StatisticsWikipedia:WikiProject StatisticsTemplate:WikiProject StatisticsStatistics articles
Mid	This article has been rated as Mid-importance on the importance scale.

Mathematics Mid‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Mid	This article has been rated as Mid-priority on the project's priority scale.

Distribution of the test statistics for $\gamma$

Latest comment: 4 months ago1 comment1 person in discussion

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^{[citation needed]}

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."