 Goodman and Kruskal's gamma

For $C$ concordant pairs and $D$ discordant pairs, Goodman and Kruskal's gamma compares their difference with their total. It ranges from $-1$ to $1$ when $C+D>0$ and discards all pairs tied in either variable. Reversing exactly one category ordering reverses its sign; reversing both leaves it unchanged. Zero gamma does not imply independence, and ignoring numerous ties can make its magnitude larger than a tie-adjusted measure.^[ref]