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I would like to compare the nutrient intake of males with that of females. One of the assumptions of the Mann Whitney test U test is that the two variables must not be normally distributed. The nutrient intake of males is normal but not of females. Would this be a problem? Also, the data is on intake of seven nutrients. To do the comparison wouldn't I have to do the Mann whitney test 7 times? Is there any other alternative? The following are the qq plots I obtained for women and men respectively.

Chi square qq plot for Women nutrient intake Chi square qq plot for men nutrient intake

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One of the assumptions of the Mann Whitney test U test is that the two variables must not be normally distributed.

This assertion is quite false. Not only is that not an assumption of the Mann-Whitney, it's actually a very good test at the normal, having an asymptotic relative efficiency of $3/\pi$ - around 95.5%. Do you have a book or other reference that makes the claim here?

The nutrient intake of males is normal

I doubt you have any basis on which to assert this as a fact. I doubt it's true. What makes you think it is?

Would this be a problem?

If the distribution shapes differ, it might be a problem, depending on how you wanted to interpret the test results.

Also, the data is on intake of seven nutrients.

This is very important. You should probably lead with it.

To do the comparison wouldn't I have to do the Mann whitney test 7 times? Is there any other alternative?

One of the issues with doing multiple univariate tests is that you can easily miss clear changes in the multivariate distribution that are not strong on any one variable. Which you do depends on which questions are important to answer.

How non-normal are the data? What's the dependence structure like?

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  • $\begingroup$ Thank you for your reply. What do you mean by 'how non-normal'? I checked the normality of intakes of men using MVN package in R software. $\endgroup$
    – user52672
    Jul 25, 2014 at 18:27
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    $\begingroup$ 1) So you did a hypothesis test of multivariate normality? Failure to reject normality doesn't mean your data are normal. It just means the sample size was too small to find the non-normality you have. Hypothesis tests of normality don't answer the question you want to answer here. 2) it's not necessarily helpful to formally test normality if you're then choosing what procedure you use on the basis of the outcome of that test. 3) "How non-normal" == What kind of non-normality is present and how severe is it? $\endgroup$
    – Glen_b
    Jul 26, 2014 at 1:05
  • $\begingroup$ Please suggest a procedure to check the equality of intakes of men and women. $\endgroup$
    – user52672
    Jul 26, 2014 at 12:01
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    $\begingroup$ I don't presently have sufficient information to offer a suggestion. I've asked several questions which cover part of what I'd need to know. If possible a Q-Q plot of each response and a scatterplot matrix of their values would help. I have some followup questions. $\endgroup$
    – Glen_b
    Jul 26, 2014 at 13:30
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    $\begingroup$ @user52672 Glen_b's first point is the most important: the Mann Whitney test most assuredly does NOT assume that data must not be normal. Where either one, both or neither of your groups have normally distributed scores is irrelevant to whether or not you can use the test, period. $\endgroup$
    – Alexis
    Jul 27, 2014 at 6:42

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