10.11 In the context of the Jonckheere–Terpstra test of Section 10.6, show that under H0 for i < j < r, cov(Uij,UirjH0) ¼ cov(Uji,UrijH0) ¼

ninjnr 12 cov(Uij,UrijH0) ¼ cov(Uji,UirjH0) ¼ 

ninjnr 12 Hint: 2cov(Uij,Uir) ¼ var(Uij,Uir)  var(Uij)  var(Uir) ¼ var(Ui, jþr)  var(Uij)  var(Uir), where Ui, jþr is the Mann–Whitney U statistic computed between the ith sample and the combined jth and rth samples.