Use of the Sign Test for the Median in the Presence of Ties

Abstract

The sign test was developed to examine the median difference of paired samples. Ignorance of ties—that is, zero differences—in the sign test can substantially inflate the Type I error rate. A uniformly most powerful test has been developed to test for the symmetry of the positive and negative differences but little attention has been given about inferences concerning the median difference when ties are abundant. This article examines a simple modified sign test which can be implemented in most computer packages and a likelihood ratio test.