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  • 1.  Mann Whitney test for proportion data

    Posted 07-14-2022 18:48

    Outcome or response data that are proportions present some challenges, of course: they are bound by 0 and 1, and they are non-Gaussian. Does anyone have any views on the use of the Mann Whitney test to compare proportion data between two groups, as was done here with student absenteeism rates, for example?

    https://journals.sagepub.com/doi/10.1177/1420326X14562257

    Thanks.

    --Chris Ryan



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    Christopher Ryan
    Clinical Associate Professor of Family Medicine
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  • 2.  RE: Mann Whitney test for proportion data

    Posted 07-15-2022 01:13
    Interesting question, Chris. There are probably many answers, including transformations of proportions. One nice thing is that if you have a large sample size, then some summary statistics, such as means, rapidly become pretty Gaussian as sample size increases. See "THE IMPORTANCE OF THE NORMALITY ASSUMPTION IN LARGE PUBLIC HEALTH DATA SETS" by Lumley, Diehr, et al, Annu. Rev. Public Health 2002. 23:151–69, 2002.  It has examples and it is very readable. We all learned about convergence toward normality as sample size increases-for particular summary statistics, such as the mean. The value of that article is learning how rapidly that convergence happens. 

    Concerning use of the  Mann -Whitney test, I see no problem in using that, because proportions are continuous numbers and can be ordered. However, it is good to look up what the assumptions are behind the M-W test and what the interpretation is if the null hypothesis is rejected. Sorry, I can't pull that out of my head right now, but I remember being surprised by what the M-W test actually tests. 

     
    I will enjoy seeing the answers of others, too. Nice community!

    Nayak





    Nayak L Polissar, PhD
    The Mountain-Whisper-Light: Statistics & Data Science
    1827 23rd Ave. East
    Seattle, WA 98112
    Tel. 206-329-9325
    Fax 206-324-5915
    nayak@mwlight.com
    Affiliate Associate Professor, Biostatistics, UW
    polissar@u.washington.edu (for university affairs only) 









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  • 3.  RE: Mann Whitney test for proportion data

    Posted 07-18-2022 16:23
    Hello, Chris

    I can see only the article's abstract. The rest of the article is behind a paywall. And all that the abstract says is that "Nonparametric statistical methods were applied". Do they say in the article that they used specifically the Mann-Whitney test?

    The reason why I ask is because the abstract indicates they have only 3 classrooms per group. With sample sizes of only 3 per group, the lowest possible 2-tailed p-value that the Mann-Whitney test will give them is p=0.0495, and to get it, they have to use the Normal approximation without a continuity correction. The Exact Mann-Whitney method yields 2-tailed p=0.100, and Mann-Whitney with the Normal approximation plus continuity correction = 0.05 yields 2-tailed p=0.0809. Um, it's not wrong to do Mann-Whitney on two groups of only 3 per group. It just seems awfully low-powered and non-robust to do so.

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    Eric Siegel, MS
    Biostatistics Project Manager
    Department of Biostatistics
    Univ. Arkansas Medical Sciences
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    Original Message


  • 4.  RE: Mann Whitney test for proportion data

    Posted 07-19-2022 12:12

    Thanks Eric and Nayak

    I had a little trouble deciphering the Methods, but it seems there were 6 classrooms; two were treated with installation of active upper room germicidal ultraviolet light (the intervention group), and 4 were not (the merged control group, containing 2 classrooms with no fixtures and 2 with placebo fixtures).

    Classroom absenteeism rates were measured monthly from September 2011 to May 2012. So the unit of analysis was the classroom, of which there were 2 intervention units and 4 control units.

    The experiment was repeated from October 2012 to January 2013.

    So besides my initial question about M-W test applied to proportion data, there is the issue of serial correlation of the monthly measurements.

    --Chris Ryan



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    Christopher Ryan
    Clinical Associate Professor of Family Medicine
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    Original Message


  • 5.  RE: Mann Whitney test for proportion data

    Posted 07-20-2022 10:53
    hi Chris,
    You may consider treating this a mixed-effect model so you can account for the correlation structure in the data. The response is 0/1 for each student in the classroom for the month, treatment and month are the fixed effects with classroom as the random effect. Do you know the individual student ids that were measured? If so, student can also be a random effect, nested within classroom. So you could fit a logistic mixed-effect model and test the treatment effect.
    Robyn

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    Robyn Ball
    Computational Scientist
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    Original Message


  • 6.  RE: Mann Whitney test for proportion data

    Posted 07-20-2022 11:39
    MW strikes me as a 20th century solution offered when we have almost completed a quarter of the 21st century. My approach would be GLMM, rather than MW.

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    Edzard van Santen
    Professor and Director
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    Original Message