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)**

**Alpha = .01 (two-tailed)**

**Alpha = .10 (two-tailed)**

**Alpha = .20 (two-tailed)**

Hi. I have a very small sample size of five divided into two groups, n1=3 and n2=2. I have already computed for Ua=0 and Ub=6. How will I know the P(1), P(2), critical intervals for Ua (lower and upper limit)?

Ramon,

The fact that there are no values in the table indicates that you can’t really perform a meaningful test with such small samples.

Charles

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

Abby,

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

Charles

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

Chelsea,

Generally alpha is set to .05. See Null and Alternative Hypothesis for more details.

Charles

Hello,

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

Atika,

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.

Charles

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

Alyssa,

For samples this large you can use the normal approximation as explained on the following webpage instead of using the table, which usually only goes up to n = 20.

Mann-Whitney Test

Charles

Thanks! 🙂

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

Stewart,

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

Charles

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.

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

Hello

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.

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.

Charles

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?

Cheers

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.

Charles

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?

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.

Charles

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

Sorry Anne, I don’t have a table value for n1=30 and n2=30, but the normal approximation described on the following webpage should be pretty accurate.

Mann-Whitney Test

Charles

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

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.

Hi!

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

Thanks

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.

Charles

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?

Katri,

The table is related to the Mann-Whitney exact test. See Mann-Whitney Exact Test for details.

Charles

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

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.

Charles

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

Julia,

The critical value is 65 for n1 = 8 and n2 = 30 (alpha = 5%; two-tailed test)

Charles

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.

Tom,

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.

Charles

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

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.

Charles

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

Pilou,

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?

Charles

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

Prin,

For such large samples you need to use the normal approximation instead of the table. How to do this is described on the webpage http://www.real-statistics.com/non-parametric-tests/mann-whitney-test/. 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.

Charles

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 ?

The critical value for the Mann-Whitney test when n1 = 5 and n2 = 30 (alpha = 5%; two-tailed test) is 33.

Charles