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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 for each subject, the sign test determines if one member of the pair tends to be greater than the other member of the pair.
The paired observations may be designated x and y. For comparisons of paired observations , 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 , or as ranks , then the paired t-test or 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.
The sign test can also test if the median of a collection of numbers is significantly greater than or less than a specified value. For example, given a list of student grades in a class, the sign test can determine if the median grade is significantly different from, say, 75 out of 100.