Need help with Mann-Whitney-U Test

Question

[thefirstrealace]

Hello,

i have the following problem: In a practical course, I have obtained a quite big data set X of measurements and slightly smaller data sets Y1 and Y2. I need to use the Mann-Whitney-U test in order to find out, if the measurements Y1 and Y2 are either significantly smaller or significantly bigger the ones in X. We were only given the significance level alpha = 0.05. Unfortunately I only have a poor understanding of statistical testing. As far as I understand, I have to do the following things:

• One tailed test H0: a bigger than or equal to 0 VS H1: a < 0
• Determine p-value (i have a python script for that)

The problem is, that I don't quite understand how to interpret this. Lets say I compare:

1. X and Y1 and I receive a p-value of 0.6, which is bigger than alpha = 0.05 and
2. compare X and Y2 and I receive a p-value of 0.4 (smaller than alpha)

In case 1 I would reject H0 and in case 2 I would accept H0. But what does that (in a normal language)? Which one is significantly bigger than X and which one is significantly smaller than X)

I hope someone can clear things up for me.

Best regards

[Jean-Karim Heriche]

When the result of the test is deemed significant (p<=alpha), we reject the null hypothesis, meaning that we consider H0 to be wrong which we use as support for the alternative hypothesis. However, when the test is deemed not significant (p>alpha), we can't reject H0 but that doesn't mean accepting H0. When the test is not significant, it means we don't know, there's not enough data to decide.This is because the test is designed only for testing if there's evidence to reject H0. Basically, a non-significant test indicates absence of evidence and absence of evidence is not evidence of absence.

Answer 1

[Devon Ryan]

1. "H0" is always the null, which is that there's no difference (so you swapped H0 and H1).
2. I assume you meant p-values of 0.06 and 0.04, rather than 0.6 and 0.4.
3. A p-value of 0.04 is significant, 0.06 is not. You want values < alpha.
4. You've not tested for significantly smaller. If you're doing a one-sided test and don't reject the null then your conclusion is "not significantly larger". You would need to do a different test to determine whether the group is smaller.

Answer 2

[reilly.brian.m]

I was recently in a class where we needed to perform various tests similar to Mann-Whitney, and found the GraphPad Prism tutorials to be very helpful.

In an attempt to answer your question: If you are not sure which direction the change will be in (testing if significantly smaller or larger) then it is advisable to use a two-tailed test.It is not good practice to use a one tailed test unless you have a strong indication of the direction the change will be in.

From the link I provided:

If you chose a one-tail P value, you should have predicted which group would have the larger median before collecting any data.

Check out the Graphpad site, it will help you understand the kinds of questions you need to ask/answer about your data and the test you want to perform.

EDIT: Regarding your "which one is bigger" question: The p-value only tells you if the differences are significant, you should look at the mean/median/whatever you were testing to determine which group was bigger/smaller.