# Is the Mann-Whitney U Test appropriate for assessing the busiest day of the week?

We have ten years of data where the average overall reveals that Monday is the busiest with the most visits to the hospital.

We would like to provide a p-value to support that observation.

Given that the Mann-Whitney U test is a test of the hypothesis that "a particular population tends to have larger values than the other" - then could use this test to assess that the cohort of "all Mondays" is larger than the cohort of "all other days"?

Would that be an appropriate use of the Mann Whitney U test to provide assess confidence such as p < 0.05?

(NOTE of clarification: This question is different than the answer here as we are not asking for the most appropriate statistic for assessing busiest day which that question asks, instead we are asking specifically whether Mann-Whitney U test is appropriate to use in this particular class of problem.)

• Related question here. – Richard Hardy Jan 24 '16 at 14:21
• Noted above that this question is different than the link marked as duplicate as we are not asking for the most appropriate statistic for assessing busiest day which that question asks, rather we are asking specifically whether Mann-Whitney U test is appropriate to use in this particular class of problem. – Praxiteles Jan 25 '16 at 12:16
• Duplicate or not, it remains unclear what would go into your test. If it's one group of 500 or so numbers of visits for Mondays, and another group of 3000 or so numbers of visits, then the Mann-Whitney test is applicable. I'd prefer the table of means and a graph personally. – Nick Cox Jan 25 '16 at 12:53
• Be careful. A more accurate statement of your question would be something like "after we have inspected data by groups, and discovered that one group appears to have a high average, what is our confidence that this group with the largest average in the dataset is the group with the largest average in the population?" This is not determined by the Mann-Whitney test (nor, to be clear, by any other standard test). But that leaves you hanging: maybe you should be asking for recommendations concerning how to evaluate these data correctly. – whuber Jan 25 '16 at 19:03

If you are comparing:

Popolation A: monday

Popolation B: sum from tuesday to sunday

I think yes.

If you are comparing all the days toghether you should do a multiple comparison test and apply a p value correction (such as Bonferroni) for multiple comparison.

Since you are comparing different days in a week maybe the second approach is more logic but the aim of your question is different so in this case you can compare monday with all the other days if that's what you want to study.

• This may not work so well if the populations have been changing over time, which could be the case since it is time series data. – Richard Hardy Jan 24 '16 at 14:34