Question: For 2 Ã 2 tables, Yule (1900, 1912) introduced which he labeled Q in honor of the Belgian statistician Quetelet. It is now called Yules

For 2 × 2 tables, Yule (1900, 1912) introduced

TT11 T2 - T12 T 21 TT11 T2 + T12 TT 21


which he labeled Q in honor of the Belgian statistician Quetelet. It is now called Yule€™s Q.

a. Show that for 2 × 2 tables, Goodman and Kruskal€™s γ = Q.

b. Show that Q falls between €“ 1 and 1.

c. State conditions under which Q = €“ 1 or Q = 1.

d. Show that Q relates to the odds ratio by Q = (θ €“ 1)/(θ + 1), a monotone transformation of θ from the [θ, ˆž] scale onto the [€“1,+ 1] scale.

TT11 T2 - T12 T 21 TT11 T2 + T12 TT 21

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