The special two-sample location problem is an important problem which is useful in comparing the performance of two measuring instruments. The problem of comparing the performances of two packing machines in which one machine may underfill the packets and the other may overfill the packets on an average, fits into special two-sample location setup wherein one wishes to test for the point of symmetry versus an appropriate alternative. The only test available in the literature to the best of our knowledge is the class of tests due to Shetty and Umarani [13] which is based on U-statistics. In this paper, two classes of test statistics are proposed which are based on extremes of subsamples. The performances of the proposed classes of tests are evaluated in terms of Pitman asymptotic relative efficiency with respect to the test due to Shetty and Umarani [13]. It is observed that the members of proposed classes of tests perform better than the test due to Shetty and Umarani [13], for those distributions considered for evaluation.

asymptotic relative efficiency, subsample extremes, special two- sample location problem, U-statistics.