It says here that the test statistic for Goodman and Kruskal's gamma is
$z=G\sqrt{\frac{n_c+n_d}{N(1-G^2)}},$
where $n_c$ and $n_d$ are the numbers of concordant and discordant pairs, resp.
Translated to the case of Yule's Q, this should be
$z=Q\sqrt{\frac{ad+bc}{N(1-Q^2)}}.$
In either case, this is undefined whenever $Q^2=1$ regardless of $N$.
Given for example $N=2$ and $a=d=1$, I get $Q=1$. Intuitively, I should get a very low significance if $N=2$ no matter the score value. Instead, significance is undefined.
That seems wrong. What am I missing?
