The paired sample sign test tests the median difference between pairs of scores from two matched samples.
For two match samples , . The null hypothesis iis that the medians of the paired samples are the same, while the alternative hypothesis can be one- or two-tailed (see below). We compute:
Suppose that the 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 0.05 or 0.01). The returned value of can be used to perform the significance test on the median difference, against various alternative hypothesis as follows.
For more details of the algorithm, please refer to: nag_sign_test (g08aac).