Tests based on L-statistics to test the equality in dispersion of two probability distributions

The problem of testing the hypothesis that two distributions are identical except for an unknown location parameter against the alternative that one is less dispersed than the other is considered here. It is seen that various tests proposed in the literature can be unified under the present approach. General results about the power functions of these tests are given, and their consistency is shown. Of special interest is a test based on the Gini index which is shown to have better asymptotic relative efficiency properties than a test recently proposed by Marzec and Marzec (1991, Biometrika 78, 923-925).