Sign Test

A Sign Test is a t-Test that ...

• See: Paired Difference Test, Statistical Power, t-Test, Wilcoxon Signed-Rank Test, Hypothesis Test, Random Variable, Non-Parametric Test.

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References

2016

• (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/Sign_test Retrieved:2016-12-17.
  • 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-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.

    The sign test is a non-parametric test which makes very few assumptions about the nature of the distributions under test – this means that it has very general applicability but may lack the statistical power of the alternative tests.

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