Classical tests > Sign test

The basic sign test is amongst the simplest form of comparison test possible on two samples. A set of paired observations are made and for each pair the observation which is judged better or given a higher score is assigned a plus (+), the poorer observation is assigned a minus (-); if there is no difference a 0 is assigned. If numerical observations are made then the differences between each pair are calculated and the sign of this difference recorded.

The sum of the negatives (or positives) is then used as an indicating of the difference between the two paired datasets. If the total number of positives is 13, say, and the total number of negatives is 3 (and there are some 0's, which will be ignored), we can ask "what is the probability of obtaining 13 from 16 assuming the null hypothesis of a 50:50 split?" This can be determined directly from the Binomial distribution with p=1/2, or for large samples using the Normal approximation to the Binomial. This test is clearly not very efficient, and fails to be of use for small n (<6). In preference the Wilcoxon paired sample test should be used if possible and a non-parametric procedure is required.