I read this from An Introduction to Biostatistics, 3rd edition by Glover, T. and Mitchell, K. (as attached in Mann Whitney right-tailed...hypotheses.jpg).
I used the Mann-Whitney test to do a two-tailed test and determined that there is a presence of an effect based on calculation of the test statistic and comparing it with the critical value.
However, when I wanted to quantify this effect (i.e. yes, there is an effect, but does A result in a decrease or an increase in B) using a right -tailed test, I could not seem to find a table of critical values for right-tailed test and left-tailed test separately.
The "An Introduction to Biostatistics" book seems to have it (as attached in the right-tailed and left-tailed Mann-Whitney critical value.jpg file), but I am unable to access that page with Table C8 of critical values for a right-tailed and left-tailed Mann-Whitney test.
But from what I read in the Right-tailed... value.jpg file, there seems to be a difference in the critical value for a right-tail versus a left-tail Mann-Whitney test, just that I am not sure and would therefore like to clarify.
Please do kindly assist.
Thank you.
Indeed, there is a difference between left- and right-tailed tests.
Imagine, you have two groups: A and B. Let's assume that EXb > EXa (the population means are different and the mean for group B is larger than the mean of group A) and Median(B) > Median(A). When you perform a right-tailed test, you ask whether Median(B) > Median(A) (and basically, this is true, that's why p-value will be low). When you perform a left-tailed test, you ask whether Median(B) < Median(A) (and, by our assumptions, this is wrong, that's why p-value will be large). When you perform two-tailed test, you ask both questions (this or this; is there any effect).
Thank you for your explanation sir, appreciate its clarity and conciseness.
I would just like to ask, now that I can confirm that there is indeed a difference between left and right-tailed test, would you know of any books or journals out there that might have a table of Mann-Whitney critical values which cover left and right-tailed tests separately for n1 = 13 and n2 = 12?
The biostatistics book I mentioned prior was very promising, but I was unable to access the page on the critical values table for left and right-tailed tests separately, so I could not make use of that book in this instance. I had tried searching though library books for it, but some only show up till 10 for both n1 and n2, or do not differentiate between left and right-tailed tests.
Thank you.
Left and right sided p-values of Mann-Whitney test you can obtain also from this web calculator http://www.socscistatistics.com/tests/mannwhitney/
By the way majority of software provides only one one-sided p-value. It is testing of difference in the direction as it is in the sample. If in samples Median(B) > Median(A) default testing is performed in this direction (and not for one sided hypothesis Median(B) < Median(A) )
Dear sir,
Apologies but I do not quite understand your 2nd paragraph. Do you mean that most software or tables generally do not divide one-tailed test into right or left tailed? And what do you mean by testing of difference in the direction as it is the sample?
Because when I compared the U test statistic I calculated (25) against the critical value for a two-tailed test at alpha = 0.05 (which is 41) and also against the critical value for a one-tailed test at alpha = 0.05 (which is 47), the test statistic is less than both critical values. Am I correct to say that should reject the null hypothesis in both cases?
Because if I set a left-tailed test (null hypothesis is that median of A is greater than median of B), and the result is to reject the null hypothesis (test statistic = 25, which is less than critical value of 47), I could have also set a right-tailed test as well (null hypothesis is that median of A is lesser than median of B), and also end up rejecting the null hypothesis as well as the test statistic and critical value does not change with regards to the tail direction.
How does left-tailed test and right-tail test work then in this case?
Please do kindly explain.
Thank you.
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Hey – hold on a minute!
The Wilcoxon Mann-Whitney test is not a test of equality of medians.
The title of the original paper spells out the hypothesis clearly: On a Test of Whether one of Two Random Variables is Stochastically Larger than the Other. (http://projecteuclid.org/euclid.aoms/1177730491). It estimates the probability that an observation from one group will be larger than an observation from the other group. And it says nothing about medians.
It is only a test for equality of medians if the two distributions are identical except for location. This assumption is unlikely to be met under the laws of physics as we know them. In particular, scales that are closed at both ends (mood, attitude, personality, attainment) will probably violate this assumption seriously.
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