Test for P ( X < Y ) in Two Stage Data Dependent Allocation Design

The present article is related to test for P(X < Y) , where X and Y are two independent random variables having some continuous distribution functions (d.f.s). We consider a data dependent ethical allocation design where the observations on X and Y are drawn sequentially in two stages. For such design, we provide an asymptotically distribution free test procedure along with various asymptotic results. This design is compared with the usual single stage equal allocation design through the performances of the respective test procedures. The proposed design is also illustrated by using a real life data set.