8.42.* For2×2 tables, gamma simplifies to a measure first proposed about 1900 by the British statistician G. Udny Yule, who also introduced the odds ratio. In that special case, gamma is called Yule’s Q.

(a) Show that for a generic table with counts

(a,

b) in row 1 and

(c,

d) in row 2, the number of concordant pairs equals ad, the number of discordant pairs equals bc, and Q = (ad − bc)/(ad + bc).

(b) Show that the absolute value of gamma equals 1 for any 2 × 2 table in which one of the cell frequencies is 0.