When X and Y are ordinal with counts {nij}:a. Explain

When X and Y are ordinal with counts {nij}:

a. Explain why the (n 2) pairs of observations partition into C + D + TX + TY – TXY, where TX = ∑ni + (ni+ –1)/2 pairs are tied on X, TY pairs are tied on Y, and TXY pairs are tied on X and Y.

b. 

Explain why d is the difference between the proportions of concordant and discordant pairs out of those pairs united on X (Somers 1962). (For 2 × 2 tables, d equals the difference of proportions, and tau-b equals the correlation between X and Y.)

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