The Sign Test with Ties Included

Abstract

The sign rank test is taught in virtually all introductory Statistics classes. When teaching the sign rank test the students are told to ignore the ties. Ignoring ties that support the null hypothesis is not logical. Why should valid data that support the null hypothesis be ignored? The approach taken here demonstrates a method for testing with ties included. A typical problem presentation in a text book would indicate that if you had ten ties in a sample of size fifty the tie scores would be excluded. However, the ten tie scores are a very valuable piece of statistical information which should not be ignored. The method demonstrated here shows that a different conclusion is reached in some cases when the ties are not excluded. Further many sign tests often will have ties because in some cases the data are not a cardinal number, but an ordinal number chosen from a set often results in ties. The alternative approach uses a one-tailed distribution and considers both +’s and -'s separated. A two-tailed test for equal variances is done with a one-tail of an F distribution. This alternate approach to the sign test allows the use of important statistical information which has been ignored with the traditional sign rank test.