8.42. For 2X2 tables, gamma simplifies to a measure first proposed about 1900 by the 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,h) in row I and {c,d) in row 2, the number of concordant pairs equals ad, the number of discordant pairs equals be, and 0 = {ad — be)/{ad + be).

(b) Show thatthe absolute value ofgamma equals 1 for any 2x2 table in which one of the cell frequencies is 0.