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Statistical techniques are used in all branches of science to determine thefeasibility of quantitative hypotheses. One of the most basic applications ofstatistical techniques in comparative analysis is the test of equality of twopopulation means, generally performed under the assumption of normality. Inmedical studies, for example, we often need to compare the effects of twodifferent drugs, treatments or preconditions on the resulting outcome. The mostcommonly used test in this connection is the two sample $t$-test for theequality of means, performed under the assumption of equality of variances. Itis a very useful tool, which is widely used by practitioners of all disciplinesand has many optimality properties under the model. However, the test has onemajor drawback; it is highly sensitive to deviations from the ideal conditions,and may perform miserably under model misspecification and the presence ofoutliers. In this paper we present a robust test for the two sample hypothesisbased on the density power divergence measure (Basu et al., 1998), and showthat it can be a great alternative to the ordinary two sample $t$-test. Theasymptotic properties of the proposed tests are rigorously established in thepaper, and their performances are explored through simulations and real dataanalysis.

Robust Tests for the Equality of Two Normal Means based on the Density Power Divergence