In the 2 × 2 table for matched pairs, in the notation of Section 4.9, the correlation between the responses of the two members of a pair is

ρ = p11 − π1π2 π1(1 − π1)π2(1 − π2)

.

For any given values of π1 < π2, the power of the one-sided McNemar test of H : π1 = π2 is an increasing function of ρ.

[The conditional power of the test given X + Y =

d, X = x is an increasing function p = p0l/(p01 + p10).]

Note. The correlation ρ increases with the effectiveness of the matching, and McNemar’s test under

(b) of