Should the Median Test be Retired from General Use?

Abstract

Although several authors have indicated that the median test has low power in small samples, it continues to be presented in many statistical textbooks, included in a number of popular statistical software packages, and used in a variety of application areas. We present results of a power simulation study that shows that the median test has noticeably lower power, even for the double exponential distribution for which it is asymptotically most powerful, than other readily available rank tests. We suggest that the median test be “retired” from routine use and recommend alternative rank tests that have superior power over a relatively large family of symmetric distributions.

Key Words:

• Kolmogorov-Smirnov test
• Median test
• Nonparametric inference
• Power
• Two-sample rank tests
• Wilcoxon test