Wilcoxon Signed-Ranks Table

The following table provides the critical values for two-tailed tests. For a one-tailed test, double the alpha value and use the table. See Wilcoxon Signed-Ranks Test for details about the test.

Wilcoxon signed-ranks table

23 Responses to Wilcoxon Signed-Ranks Table

  1. Mike says:

    “For a 1-tail test, double the alpha value and use the table.”

    Correct me if I’m wrong, but for a one tailed test shouldn’t I cut the alpha in half and use this chart?

  2. CPE Gaebler says:

    Is there a formula or approximation for extrapolating to higher values of N?

  3. Robert Norberte says:

    Hi Sir.
    May I know if Wilcoxon Test may be applied if you only have n=5. If not what may be an alternative test?

    Thank you.

    • Charles says:

      The Wilcoxon Signed-Ranks Test can be applied with n = 5, but don’t expect much from the test since the sample size is so small. Only with a high value for alpha and extremely lopsided data will you find out anything. With so little data, there isn’t much that is meaningful that you can do. You can try the sign test.

  4. Lucia Merada says:

    I downloaded the service pack. Thank you! But how do I format Column F so it contains the adjusted rankings of the non-zero values in column E?

  5. aayushee says:

    Hi..I am trying to used Wilcoxon signed rank test on a very large dataset. The sample size is around 30000. Does the test work on large sample size like this?

    • Charles says:

      The test does work on such a large sample (using the normal approximation). I believe that the version provided by the Real Statistics Resource Pack does work on this size data set. I have tested it on large data sets, but I can’t recall what the largest size was. The easiest way to confirm that it works is to try it.

  6. Victoria Morrison says:


    If I have a sample size of 1645 can you advise if this test can be used and if so what the critical value would be for a data set of this size? If this is not the appropriate test can you please advise what would be?

    Many Thanks

  7. Armiza says:

    Can we generate z-score from Wilcoxon Signed Rank Test for small sample data? Currently I’m using SPSS as my statistical tools.

    • Charles says:

      Sorry, but I don’t know whether SPSS provides a z-score for small samples. The typical approach is to use the z-score for large samples (20 or so elements). I am sure this is provided by SPSS. It is also included in the Real Statistics Wilcoxon Signed Rank Test data analysis tool and SRank function.

  8. sinx says:

    need help solving this question “A machine which fills orange squash bottles should be set to deliver 725 ml,A sample of 50 bottles is checked and the mean quantity is found to be 721 ml and the sample standard deviation 13 ml.does this differ signficantly from 725 ml at 1% level of significance?”

  9. Pulkesh says:

    I am stuck at finding critical values for my one-sample wilcoxon signed rank test. Can you please tell me what would the two-tail critical value be for n=132. I would be really thankful

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