# wilcoxon mann whitney or t-test?

I would like to compare the number of a particular type of disease that is prevalent in men vs women. The number of diseases is interval data (0,1,2,3,etc). Should I use the wilcoxon mann whitney or t-test?

This is a sample of what the data looks like.

patientID   gender  num_dz
1   F   0
2   F   2
3   F   4
4   F   2
5   F   1
6   F   3
7   F   2
8   M   1
9   M   2
10  M   0
11  M   0
12  M   0
13  M   1
14  M   0

• Can you clarify the structure of your data? I.e., does your dataset boil down to just a 2 x 2 table of numbers (a count for men and women, with and without the disease)? Or if not, can you give a few sample rows to explain what your data looks like? Treating counts as interval or ordinal data might not be ideal; depending on the situation, a procedure specifically designed for count data should be considered, if count data is what you are dealing with. – Brent Kerby Jul 30 '17 at 17:10
• @BrentKerby I have edited the post with a sample of what the data looks like. – ybao Jul 30 '17 at 17:18
• Thanks, so then what does num_dz mean? I understand it as some kind of count of number of diseases, but you indicated that you are interested in a particular type of disease, so what does it mean for a patient to have a number of a certain type of disease? Does this represent a count of how many times they had the disease over a certain period of time? Or is it something like how many instances/varieties of the disease they are simultaneously infected with? Or is this not a count but rather a code indicating which disease they have? – Brent Kerby Jul 30 '17 at 17:29
• @BrentKerby The dataset is cross sectional, so it is the number of particular diseases that the patient has been diagnosed with at a single time point. The dataset is a study of a few chronic diseases, so the patients have them for life. – ybao Jul 30 '17 at 17:33
• Thanks, one more question: how large are the samples? – Brent Kerby Jul 30 '17 at 20:53

The two tests also address somewhat different hypotheses. For the t-test, the null hypothesis is that the two populations have equal means ($H_0: \mu_1 = \mu_2$), whereas for the Wilcoxon-Mann-Whitney test, the null hypothesis is that given random representatives $X$ and $Y$ from the first and second populations respectively, there is an equal probability that $X$ is greater than $Y$ compared to the other way around ($H_0: P(X>Y) = P(Y>X)$).