On the optimality of bivariate ranked set sample design for the matched pairs sign test

An optimal alternative bivariate ranked set sample designs for the matched pairs sign test are obtained. Our investigation revealed that the optimal bivariate ranked set sample designs for matched pairs sign test are those with quantifying order statistics with labels ((r+1/2, r+1/2)) when the set size r is odd and ((r/2, r/2), (r/2 + 1, r/2 + 1)) when the set size r is even. The exact null distributions, asymptotic distributions and Pitman efficiencies of those designs are derived. Numerical analysis of the power of the proposed optimal designs is included. An illustration using real data with a bootstrap algorithm for P-value estimation is used.