Robust tests for the equality of two normal means based on the density power divergence

A. Basu, A. Mandal, N. Martin, L. Pardo

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Statistical techniques are used in all branches of science to determine the feasibility of quantitative hypotheses. One of the most basic applications of statistical techniques in comparative analysis is the test of equality of two population means, generally performed under the assumption of normality. In medical studies, for example, we often need to compare the effects of two different drugs, treatments or preconditions on the resulting outcome. The most commonly used test in this connection is the two sample $$t$$t test for the equality of means, performed under the assumption of equality of variances. It is a very useful tool, which is widely used by practitioners of all disciplines and has many optimality properties under the model. However, the test has one major drawback; it is highly sensitive to deviations from the ideal conditions, and may perform miserably under model misspecification and the presence of outliers. In this paper we present a robust test for the two sample hypothesis based on the density power divergence measure (Basu et al. in Biometrika 85(3):549–559, 1998), and show that it can be a great alternative to the ordinary two sample $$t$$t test. The asymptotic properties of the proposed tests are rigorously established in the paper, and their performances are explored through simulations and real data analysis.

Original languageEnglish (US)
Pages (from-to)611-634
Number of pages24
Issue number5
StatePublished - Dec 2 2015

Bibliographical note

Funding Information:
This work was partially supported by Grants MTM-2012-33740 and ECO-2011-25706. The authors gratefully acknowledge the suggestions of two anonymous referees which led to an improved version of the paper.

Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.


  • Density power divergence
  • Hypothesis testing
  • Robustness


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