TITLE:
The Sign Test with Ties Included
AUTHORS:
Jennings B. Marshall
KEYWORDS:
Sign Test, Ties
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.10,
June
6,
2014
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.