Sign test

The sign test is a statistical method to test for consistent differences between pairs of observations, such as the weight of subjects before and after treatment. Given pairs of observations (such as weight pre- and post-treatment) for each subject, the sign test determines if one member of the pair (such as pre-treatment) tends to be greater than (or less than) the other member of the pair (such as post-treatment). The sign test is a statistical method to test for consistent differences between pairs of observations, such as the weight of subjects before and after treatment. Given pairs of observations (such as weight pre- and post-treatment) for each subject, the sign test determines if one member of the pair (such as pre-treatment) tends to be greater than (or less than) the other member of the pair (such as post-treatment). The paired observations may be designated x and y. For comparisons of paired observations (x,y), the sign test is most useful if comparisons can only be expressed as x > y, x = y, or x < y. If, instead, the observations can be expressed as numeric quantities (x = 7, y = 18), or as ranks (rank of x = 1st, rank of y = 8th), then the paired t-testor the Wilcoxon signed-rank test will usually have greater power than the sign test to detect consistent differences. If X and Y are quantitative variables, the sign test can be used to test the hypothesis that the difference between the X and Y has zero median, assuming continuous distributions of the two random variables X and Y, in the situation when we can draw paired samples from X and Y.