Sign test

The sign test is a <a href="/facts/Statistical_test/yv9RPF6U">statistical test</a> 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 <a href="/facts/T-test/dMH8uC28">t-test</a>
or the <a href="/facts/Wilcoxon_signed-rank_test/WTG02wYE">Wilcoxon signed-rank test</a> 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 <a href="/facts/Hypothesis_test/yv9RPF6U">test the hypothesis</a> that the difference between the X and Y has zero median, assuming continuous distributions of the two <a href="/facts/Random_variable/TwTBXnLT">random variables</a> X and Y, in the situation when we can draw <a href="/facts/Paired_difference_test/lCLuSGUL">paired samples</a> 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 <a href="/facts/Non-parametric_test/svTDJHTb">non-parametric test</a> 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 <a href="/facts/Statistical_power/5KU54nW1">statistical power</a> of the alternative tests.
The two conditions for the paired-sample sign test are that a sample must be randomly selected from each population, and the samples must be dependent, or paired. 
Independent samples cannot be meaningfully paired. Since the test is nonparametric, the samples need not come from normally distributed populations. Also, the test works for left-tailed, right-tailed, and two-tailed tests.

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Sign test