Using differential variability to increase the power of the homogeneity test in a two-sample problem

We consider a two-sample homogeneity testing problem often encountered in case-control studies with contaminated controls, or in detecting a treatment effect when some subjects are not affected by the treatment in biological experiments. We propose an EM-test designed to simultaneously detect mean difference and differential variability in the two samples. We show that the EM-test statistic has a chi-squared null limiting distribution. The asymptotic properties of the EM-test under local alternatives are also investigated, and sample-size calculation is given. The main results are established for general location-scale family of distributions. Simulation results show that the EM-test outperforms existing methods, and two data examples are used to illustrate the application of the proposed method.