7.5. For sample mean ridit scores A\ and Aj for two groups, show that the Wilcoxon test statistic (7.6) equals _ Äi -0.50 _ _ Ä 2 - 0 . 5 0 VVar(Äi) v/Var(A2)'

where n2(n]+n2 + l) ç2Õß](Þ-ß])

Var(Ai) = 12ni(ni + n2)2 12m(ni +n2)3(m + n 2 - 1)'

and Var(A2) is the formula for Var(Ai) but with n\ and n2 interchanged.

Moreover, Var(Ä,) = ( ^ ) 2Var(Ä1-Ä2 ) , where Var(A! - A2) = (l/n2)Var(/?i - R2) for Vai(Ri - R2) in equation

(7.7). The equivalent expressions for the two mean ridits hold because

— Äi + — Ä2 = 0.50 and n2Var(Ä,) = n?Var(Ä2).