7.2. Let m = min(r,

c) in an r x c table. Show that the maximum attainable value of n c — Ud is (m — l)/m, which occurs when the probability is uniformly distributed on m cells in a longest diagonal of the table. Hence, m(nc - Ud)

ô€ =

m — 1 can equal 1.0 in absolute value for any table size (Stuart 1953). Stuart (1963)

defined a discrete version of Spearman's rho that can equal 1.0 for any table size: namely,

in terms of the marginal ridit scores. By contrast, Kendall's |ô^| and \pb\ can equal 1.0 only when r = c.