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Math Help - paired wilcoxon signed rank test

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    paired wilcoxon signed rank test

    I'm figuring out a paried wilcoxon signed rank test and I'm at the step where I am trying to find critical values. How do you find the critical values? I ask this because sometimes there are 1 or 2 different pairs of them. Such as W underscore 1 or under score r. How do you find these? Thank you
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  2. #2
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    Quote Originally Posted by l0v3n View Post
    I'm figuring out a paried wilcoxon signed rank test and I'm at the step where I am trying to find critical values. How do you find the critical values? I ask this because sometimes there are 1 or 2 different pairs of them. Such as W underscore 1 or under score r. How do you find these? Thank you
    I'm not sure I understand what you're asking? You need to know the distribution of the test statistic ( W_+ or W_{-}) under the null hypothesis. This can be done in a number of ways (some obviously less practical than others depending on the size of n):

    1. Enumerate the possibilities.

    2. Use a table of critical values.

    3. Use appropriate software.

    4. A normal approximation can be used. It is found that if H_0 is true then

    W_{\pm} ~ \text{Normal}\left(\mu = \frac{n(n+1)}{4}, ~ \sigma^2 = \frac{n(n+1)(2n+1)}{24}\right)

    and that this approximation (with continuity correction) is adequat for n \geq 5.
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