Some Bounded Significance Level Properties of the Equal-Tail Sign Test

Abstract

In addition to being easily applied and reasonably efficient for small samples, the equal-tail sign procedure for testing hypotheses about, or setting confidence intervals for, the population median is valid under very general conditions. (For brevity, the equal-tail sign procedure will be referred to as Procedure E.) Rarely, if ever, however, are these conditions exactly satisfied in practice. Thus the actual significance level or confidence coefficient for Procedure E is only an approximation to the standard value (which holds when the conditions are satisfied). Undoubtedly the equal-tail sign procedure is used in many cases when these conditions are only roughly approximated. The purpose of this paper is to investigate under what conditions Procedure E has significance levels and confidence coefficients which are satisfactory approximations to the standard values. It is found that the approximation is reasonably good for a wide variety of situations if the number of observations is not large. Thus, as far as errors of Type I are concerned, Procedure E is a sufficiently close approximation for many practical cases. This significance level stability, combined with its other favorable properties, suggests that the equal-tail sign procedure be seriously considered for application when an inference is to be made from a small number of observations to the population median.