Wilcoxon Signed-Rank Test
The logic and computational details of the Wilcoxon test
are described in Subchapter 12a of Concepts and Applications.
For n=.

Like the t-test for correlated samples, the Wilcoxon signed-ranks test applies to two-sample designs involving repeated measures, matched pairs, or "before" and "after" measures. Beginning with a set of paired values of Xa and Xb, this page will When ns/r is equal to or greater than 10, the sampling distribution of W is a reasonably close approximation of the normal distribution. In this case, the present page calculates the appropriate z-ratio along with the associated one-tail and two-tail probabilities. For smaller sample sizes (ns/r = 5 through 9), the obtained value of W can be referred to the separate table of critical values of ±W.

Data EntryQ
Data Cells S/R of
Import/Export Box S/R
 ="signed rank"
Pairs Xa Xb Xa and Xb

Clear this box

Import data
to data cells
ns/r= P(1-tail) P(2-tail)
Critical Values of ±W for Small SamplesQ
Level of Significance for a
Directional Test
.05 .025 .01 .005
Non-Directional Test
ns/r -- .05 .02 .01
  15     --     --     --  
  17     21     --     --  
  22     24     28     --  
  26     30     34     36  
  29     35     39     43  
Please note that these small-sample critical values pertain to the version of the Wilcoxon test in which the test statistic, W, is calculated as the sum of all the signed ranks, positive and negative combined. Descriptions of this version of the Wilcoxon test can be found in Subchapter 12a of Concepts and Applications of Inferential Statistics and in
Frederick Mosteller & Robert E. K. Rourke, Sturdy Statistics: Nonparametrics and Order Statistics, Addison-Wesley, 1973, 89ff.

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