Mann-Whitney Table

The following tables provide critical values of  for various values of alpha, two-tailed. For one-tail tests double the value of alpha and use the appropriate two-tailed table. See Mann-Whitney Test for details.

Alpha = .005 (two-tailed)

Mann-Whitney alpha .005

Alpha = .01 (two-tailed)

Mann-Whitney Table, alpha = .01Alpha = .02 (two-tailed)

Mann-Whitney Table, alpha = .02Alpha = .05 (two-tailed)

Mann-Whitney alpha .05

Alpha = .10 (two-tailed)

Mann-Whitney Table, alpha = .10

Alpha = .20 (two-tailed)

Mann-Whitney alpha .20

41 Responses to Mann-Whitney Table

  1. Abby says:

    Hi, I’m struggling to understand how to calculate approximations for Ucrit when n1=21 and n2=24 ????

    • Charles says:

      You won’t be able to since these values are outside the range of the table. For values over 20, generally you wouldn’t us the table, but would use the normal approximation instead. See the following webpage (esp. Example 2)
      Mann-Whitney Test

  2. Chelsea says:

    How do you know that the alpha value for your data is?

  3. Atika says:

    is there any minimum sample size to perform the mann whitney u test? can I do the test with sample size n1=n2=2?
    Thank you

    • Charles says:

      With such a small sample, the power of the test is bound to be very low. E.g. if I estimate the power of the MW test by using the power of the t test, I see that the power for the test with effect size .5 is only 6%. Even with a huge effect size, you can’t expect much with such a very small sample. You can find out more by using the Statistical Power and Sample Size data analysis tool or G*Power.

  4. Alyssa says:

    Hi, what is the critical value if n1=11 and n2= 29? Thank you!

  5. stewart says:

    can any of my u values have a decimal point like 2.5 or did i do something wrong in my calculations

    • Charles says:

      They can be whole numbers or numbers that end in .5. A value of 2.5 doesn’t mean that you did anything wrong.

  6. Francis Mcgonigal says:

    Is the default to Reject or NOT Reject Ho if the Test Statistic and the Critical Value are equal?
    I find some textbooks are not clear in such cases.

    • Charles says:

      This is not clear to me either. I have typically considered p < alpha as reject and p = alpha as not rejection of H0, but others may disagree. In any case since even the value for alpha (typically .05) is rather arbitrary, it probably is not that important. Best is to say the test is borderline. Charles

  7. salma says:


    I am applying Man Whitney U test to identify the significance difference in ranking of some factors by two different groups

    can i show the results to be significant if Alpha less than 0.05 but there is huge difference in sample sizes. e.g. for group 1 it is 33 and group 2 it is 7 ….or group 1 = 33 or group 2 = 2.

    Please let me know ..also i cannot find U values of sample size of 33
    i will be grateful.

    • Charles says:

      You can use the Mann-Whitney test even when the group sizes are not equal.
      The critical value when n1 = 33, n2 = 7 and alpha = .05 is 60.
      In general for sample sizes larger than 20, the normal approximation is used and so you don’t need to have values from the table of critical values. You can find more information about this at the webpage
      Mann-Whitney Test.

  8. j says:

    Thanks for your page. What would be the critical value for n1=22 and n2=20? Btw, if I can ask, how do you get it?


    • Charles says:

      The critical value for n1=22 and n2=20 is 141. This comes from an extended table of critical values which I haven’t yet put on the website.

      • J says:

        Thanks for the reply.

        I got that the null theory is not valid, so the two variables do not behave equally. How can I determine the directionality of the data?

        • Charles says:

          If by directionality of the data, you mean which sample is larger, you can compare the medians of the two samples or the rank sums of the two samples.

      • Anne says:

        If n1=30 and n2=30 is there a critical value for mann whitney

  9. David Knight says:

    OK I see my mistake now……………………silly me. Please withdraw my question. Thanks again

  10. David Knight says:

    Thank you for the useful table. I have rather a basic question, apologies.

    Lets take the case where n1= 20 and n2 = 20. The critical value for two tails is 97 and 105 for alphas of 0.05 and 0.01, respectively. Lets say I come up with a t score of 100 does that mean that I cannot reject the null at a 95 % confidence interval, but can at a 99 % confidence interval? This seems a bit perverse to me and I am sure that I am going wrong somewhere. Please help.

  11. Elena says:

    How are this critical value computed? They’re empirically determined or there is an exact formula?

    • Charles says:

      Hi Elena,
      The critical values come from tables that were calculates many years ago and can be found in multiple references. I believe they were created from the exact formulas, similar to the ones I have described on the website.

  12. Katri says:

    Hey! I really do like your wed site as it is so well done. I hope you could answer my question as I can’t find a answer to it by googling. Could you tell me where does this numbers come from? Is there a formula to calculate these or it this from some kind of distribution or density function? I would like to know the density function or the function as I just can’t understand where the numbers come from. Could you help me, please?

  13. darwis rianto says:

    what about if n1 = n2 =36 (alpha = 5%, two-tailed test)

    • Charles says:

      Sorry, but I don’t have table values when both n values are so high. It is best to use the normal distribution approximation in this case.

  14. Julia says:

    What about if n1 =8 and n2=30 (alpha = 5%; two-tailed test)

  15. Tom Keane says:

    I can’t find a mann whitney u chart for an experiment in our range. We’re looking for the test statistic when n1 is 34 and n2 is 26 and I believe one tailed.

    • Charles says:

      Generally the tables end with n1 = 20 and n2 = 20. When one or both of these are larger than 20 you should use the normal approximation as explained on the webpage Mann-Whitney Test.

  16. Ahmed says:

    if test statistic for the mann whitney test is T= S – [{n1(n1+1)}/2]
    then for the following critical region
    Reject H0 if
    T w(1-∝/2) { where w(1-∝/2)= n1*n2 -w(∝/2)}
    kindly guide me for the critical values table.
    if n1= 17 and n2=10 and S = 296.5 where S is the sum of ranks of ist sample

    • Charles says:

      The critical value for a two-tailed test with n1 = 17, n2 = 10 and alpha = .05 is 45. The critical value table does not use S.

      You need to compare the critical value with U = min(U1, U2) where U1 and U2 are as defined on the webpage Mann-Whitney Test. Here S is equal to R1 in the definition of U1.


  17. Pilou says:

    At least, it looks like there are some mistakes in your tables
    My computations (and checking others tables) seem to show that for the table 0.05
    the element (20, r4) and its symmetric are 14 and not 13

    • Charles says:

      You are absolutely correct. Looks like a miscopied this value. I have corrected the value on the referenced webpage and in the software. I have also added two more Mann-Whitney tables to the referenced webpage (for alpha = .005 and alpha = .20). Thanks very much for catching this mistake. Did you find any other mistakes in the tables?

  18. Prin Munsamy says:

    What is the critical value for the Mann-Whitney test for sample sizes of n1 = 1000 and n2 = 1000?

    • Charles says:

      For such large samples you need to use the normal approximation instead of the table. How to do this is described on the webpage Property 2 shows the normal approximation. You can also use the T Tests and Non-parametric Equivalents data analysis tool (choose the independent samples and non-parametric options) to calculate the critical value.

      • luc says:

        sorry !!

        previous post failed !!

        My question is : if n1 =5 and n2=30 (alpha = 5%; two-tailed test) what is the critical value for the Mann-Whitney test ?

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