Statistical tests for the comparison of two samples: The general alternative

ABSTRACT

It is common to test the null hypothesis that two samples were drawn from identical distributions; and the Smirnov (sometimes called Kolmogorov–Smirnov) test is conventionally applied. We present simulation results to compare the performance of this test with three recently introduced alternatives. We consider both continuous and discrete data. We show that the alternative methods preserve type I error at the nominal level as well as the Smirnov test but offer superior power. We argue for the routine replacement of the Smirnov test with the modified Baumgartner test according to Murakami (2006), or with the test proposed by Zhang (2006).

KEYWORDS:

• Nonparametric statistics
• Rank tests
• Smirnov test

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G10
• 62G09

Acknowledgment

We thank two anonymous reviewers for their comments that greatly improved the article, and Daniela Zöller and Kristina Weber for their help with the simulation study.