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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 (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 (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 median of X and the median of Y is zero, 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. ==Method== Let ''p'' = Pr(''X'' > ''Y''), and then test the null hypothesis H0: ''p'' = 0.50. In other words, the null hypothesis states that given a random pair of measurements (''x''''i'', ''y''''i''), then ''x''''i'' and ''y''''i'' are equally likely to be larger than the other. To test the null hypothesis, independent pairs of sample data are collected from the populations . Pairs are omitted for which there is no difference so that there is a possibility of a reduced sample of ''m'' pairs.〔 〕 Then let ''W'' be the number of pairs for which ''y''''i'' − ''x''''i'' > 0. Assuming that H0 is true, then ''W'' follows a binomial distribution ''W'' ~ b(''m'', 0.5). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Sign test」の詳細全文を読む スポンサード リンク
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