11.3 Two independent random samples of sizes m and n contain no ties.

A set of m þ n paired observations can be derived from these data by arranging the combined samples in ascending order of magnitude and

(a) assigning ranks,

(b) assigning sample indicators. Show that Kendall’s tau, calculated for these pairs without a correction for ties, is linearly related to the Mann–Whitney U statistic for these data, and find the relation if the sample indicators are (i) sample numbers 1 and 2, (ii) 1 for the first sample and 0 for the second sample as in the Z vector of Chapter 7.