# Thread: paired wilcoxon signed rank test

1. ## 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

2. Originally Posted by l0v3n
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 $n \geq 5$.