The nonrandomized sign test for the population median is valid under
very general conditions. However, the significance levels for this test
are limited and may not contain a value sufficiently near the desired
significance level except when the number of observations is quite large.
This difficulty can be partially overcome without destroying the application
generality and without introducing randomization by applying various
interpolation methods to the sign test, yielding tests whose significance
levels are approximately equal to arbitrarily specified values. This paper
considers the case of continuous populations and presents two interpolation
methods that are of a nonparametric character. Both methods are
based on the additional assumption of population symmetry but, irrespective
of population shapes, protect against gross errors in significance
level value.