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
nag_prob_beta_dist (g01eec).
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
.