2.38 For 2 x 2 tables, Yule (1900, 1912) introduced Q = 11 22 -...

2.38 For 2 x 2 tables, Yule (1900, 1912) introduced Q =

π₁₁ π₂₂ - π₁₂ π₂₁

π₁₁ π₂₂ + π₁₂ π₂₁, which he labeled Q in honor of the Belgian statistician Quetelet. It is now called Yule's Q.

a. Show that for 2 x 2 tables, Goodman and Kruskal's y = Q.

b. Show that Q relates to the odds ratio by Q = (θ - 1)/(θ + 1), a monotone trans-

formation of θ from the [0, ∞] scale onto the [-1, +1] scale.