The Sign test investigates the median difference between pairs of scores from two matched samples of size , denoted by , for . The hypothesis under test, , often called the null hypothesis, is that the medians are the same, and this is to be tested against a one- or two-sided alternative (see below).
Suppose that a significance test of a chosen size
is to be performed (i.e.,
is the probability of rejecting
when
is true; typically
is a small quantity such as
or
). The returned value of
can be used to perform a significance test on the median difference, against various alternative hypotheses
, as follows
-
(i): median of median of . is rejected if .
-
(ii): median of median of . is rejected if .
-
(iii): median of median of . is rejected if .
The tail probability,
, is computed using the relationship between the binomial and beta distributions. For
,
should be accurate to at least
significant figures, assuming that the machine has a precision of
or more digits. For
,
should be computed with an absolute error of less than
. For further details see
g01eec.
Background information to multithreading can be found in the
Multithreading documentation.
This example is taken from page 69 of
Siegel (1956). The data relates to ratings of ‘insight into paternal discipline’ for
sets of parents, recorded on a scale from
to
.