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I am using a Mann-Whitney U test to compare the willingness between subjects to once monthly injection between two groups. One group is a control while the other is the intervention. I am expanding on a question I had asked here:

What test would you use for my data. I think independent t-test?

Because I am using the Mann-Whitney U test, I am calculating the median of both groups. As such, what would you recommend as the best way to visually depict my data?

I was wondering if a simple bar chart be acceptable? Like the one shown below? It shows the median of both groups. Or would a box plot be more instructive, as pointed out by one of the users.

A portion of my data can be found below: (My data has 100 subjects, with n=50 in each group)

enter image description here

GROUP      Willingness 
           (from 1-10)
-----------------------
Group1        10.00  
Group1         1.00  
Group1         4.00  
Group2         7.00  
Group1         9.00  
Group2        10.00  
Group2        10.00  
Group2         3.00  
Group2         7.00  
Group2        10.00  
Group2        10.00  
Group2         1.00  
Group2         9.00  
Group2         4.00  
Group1         7.00  
Group2         3.00  
Group1         5.00  
Group2         5.00  
Group2        10.00  
Group1         1.00  
Group2        10.00  
Group2         9.00  
Group1         3.00  
Group1         1.00  
Group1         1.00  
Group2         8.00  
Group1         1.00
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  • $\begingroup$ This chart does not show your data: it merely depicts the two medians. $\endgroup$
    – whuber ♦
    Jan 8, 2017 at 19:31
  • $\begingroup$ It also doesn't show the results of your test. $\endgroup$
    – Michael R. Chernick
    Jan 8, 2017 at 19:32
  • $\begingroup$ I'm voting to close this question as off-topic because this question is of very poor quality $\endgroup$
    – Michael R. Chernick
    Jan 8, 2017 at 19:34
  • $\begingroup$ My apologies for the poorly worded question. I was expanding on a question I had asked here: stats.stackexchange.com/questions/246822 where I was comparing the willingness between once monthly injection between both groups. As I understand, a box plot would be more appropriate. $\endgroup$
    – TheFermat
    Jan 8, 2017 at 19:42
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    $\begingroup$ Note that the Mann-Whitney test doesn't compare medians, and indeed sample medians can differ in the opposite direction from that indicated by the test! This would suggest that displays that rely on medians to indicate location -- including boxplots -- may be less than ideal. $\endgroup$
    – Glen_b
    Jan 9, 2017 at 3:25

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Box plots would be much more informative since they provide distributional information in addition to medians. This is particularly important when you use the Mann-Whitney U since the null hypothesis tested is somewhat vague and it is important for readers to have some idea how the distributions differ. If you only want to give the medians then a graph is not a good idea since its data density is so low.

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  • $\begingroup$ I saw this submitted as a comment. It is more appropriate as a comment. $\endgroup$
    – Michael R. Chernick
    Jan 8, 2017 at 20:25
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    $\begingroup$ This is being automatically flagged as low quality, probably because it is so short. At present it is more of a comment than an answer by our standards. Can you expand on it? You can also turn it into a comment. $\endgroup$
    – gung - Reinstate Monica
    Jan 8, 2017 at 20:36
  • $\begingroup$ Thanks, David! Because my data is ordinal (Both groups rank their willingness between 1-10), the box plot looks a little funny as the whiskers for both groups span to the upper limits (1 and 10). Do you think it would be possible for me to remove the whiskers from the boxplot and only include the box in my analysis? $\endgroup$
    – TheFermat
    Jan 8, 2017 at 22:36
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    $\begingroup$ There are no right or wrong answers but keeping the whiskers would reveal that the max and min were the same for both groups which may be of interest to some readers. As an aside, a continuous variable can be ordinal and a discrete variable can be ratio. $\endgroup$
    – David Lane
    Jan 8, 2017 at 22:43
  • $\begingroup$ Alternatively, you might want to try a back-to-back stem and leaf display if you want to present more information than is contained in box plots. $\endgroup$
    – David Lane
    Jan 8, 2017 at 22:47

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