[SciPy-User] Questions/comments about scipy.stats.mannwhitneyu

josef.pktd@gmai... josef.pktd@gmai...
Sat Feb 16 18:51:19 CST 2013

On Fri, Feb 15, 2013 at 1:44 PM, Chris Rodgers <xrodgers@gmail.com> wrote:
> Thanks Josef. Your points make sense to me.
> While we're on the subject, maybe I should ask whether this function
> is even appropriate for my data. My data are Poisson-like integer
> counts, and I want to know if the rate is significantly higher in
> dataset1 or dataset2. I'm reluctant to use poissfit because there is a
> scientific reason to believe that my data might deviate significantly
> from Poisson, although I haven't checked this statistically.
> Mann-whitney U seemed like a safe alternative because it doesn't make
> distributional assumptions and it deals with ties, which is especially
> important for me because half the counts or more can be zero. Does
> that seem like a good choice, as long as I have >20 samples and the
> large-sample approximation is appropriate? Comments welcome.

Please bottom or inline post.

I don't have any direct experience with this.

The >20 samples is just a guideline (as usual). If you have many ties,
then I would expect be that you need more samples (no reference).

What I would do in cases like this is to run a small Monte Carlo, with
Poisson data, or data that looks somewhat similar to your data, to see
whether the test has the correct size (for example reject roughly 5%
at a 5% alpha), and to see whether the test has much power in small
I would expect that the size is ok, but power might not be large
unless the difference in the rate parameter is large.

Another possibility is to compare permutation p-values with asymptotic
p-values, to see whether they are close.

There should be alternative tests, but I don't think they are
available in python, specific tests for comparing count data (I have
no idea), general 2 sample goodness-of-fit test (like ks_2samp) but we
don't have anything for discrete data.

If you want to go parametric, then you could also use poisson (or
negative binomial) regression in statsmodels, and directly test the
equality of the distribution parameter. (there is also zeroinflated
poisson, but with less verification).


> Thanks
> Chris
> On Fri, Feb 15, 2013 at 8:58 AM,  <josef.pktd@gmail.com> wrote:
>> On Fri, Feb 15, 2013 at 11:35 AM,  <josef.pktd@gmail.com> wrote:
>>> On Fri, Feb 15, 2013 at 11:16 AM,  <josef.pktd@gmail.com> wrote:
>>>> On Thu, Feb 14, 2013 at 7:06 PM, Chris Rodgers <xrodgers@gmail.com> wrote:
>>>>> Hi all
>>>>> I use scipy.stats.mannwhitneyu extensively because my data is not at
>>>>> all normal. I have run into a few "gotchas" with this function and I
>>>>> wanted to discuss possible workarounds with the list.
>>>> Can you open a ticket ? http://projects.scipy.org/scipy/report
>>>> I partially agree, but any changes won't be backwards compatible, and
>>>> I don't have time to think about this enough.
>>>>> 1) When this function returns a significant result, it is non-trivial
>>>>> to determine the direction of the effect! The Mann-Whitney test is NOT
>>>>> a test on difference of medians or means, so you cannot determine the
>>>>> direction from these statistics. Wikipedia has a good example of why
>>>>> it is not a test for difference of median.
>>>>> http://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U#Illustration_of_object_of_test
>>>>> I've reprinted it here. The data are the finishing order of hares and
>>>>> tortoises. Obviously this is contrived but it indicates the problem.
>>>>> First the setup:
>>>>> results_l = 'H H H H H H H H H T T T T T T T T T T H H H H H H H H H H
>>>>> T T T T T T T T T'.split(' ')
>>>>> h = [i for i in range(len(results_l)) if results_l[i] == 'H']
>>>>> t = [i for i in range(len(results_l)) if results_l[i] == 'T']
>>>>> And the results:
>>>>> In [12]: scipy.stats.mannwhitneyu(h, t)
>>>>> Out[12]: (100.0, 0.0097565768849708391)
>>>>> In [13]: np.median(h), np.median(t)
>>>>> Out[13]: (19.0, 18.0)
>>>>> Hares are significantly faster than tortoises, but we cannot determine
>>>>> this from the output of mannwhitneyu. This could be fixed by either
>>>>> returning u1 and u2 from the guts of the function, or testing them in
>>>>> the function and returning the comparison. My current workaround is
>>>>> testing the means which is absolutely wrong in theory but usually
>>>>> correct in practice.
>>>> In some cases I'm reluctant to return the direction when we use a
>>>> two-sided test. In this case we don't have a one sided tests.
>>>> In analogy to ttests, I think we could return the individual u1, u2
>>> to expand a bit:
>>> For the Kolmogorov Smirnov test, we refused to return an indication of
>>> the direction. The alternative is two-sided and the distribution of
>>> the test statististic and the test statistic are different in the
>>> one-sided test.
>>> So we shouldn't draw any one-sided conclusions from the two-sided test.
>>> In the t_test and mannwhitenyu the test statistic is normally
>>> distributed (in large samples), so we can infer the one-sided test
>>> from the two-sided statistic and p-value.
>>> If there are tables for the small sample case, we would need to check
>>> if we get consistent interpretation between one- and two-sided tests.
>>> Josef
>>>>> 2) The documentation states that the sample sizes must be at least 20.
>>>>> I think this is because the normal approximation for U is not valid
>>>>> for smaller sample sizes. Is there a table of critical values for U in
>>>>> scipy.stats that is appropriate for small sample sizes or should the
>>>>> user implement his or her own?
>>>> not available in scipy. I never looked at this.
>>>> pull requests for this are welcome if it works. It would be backwards
>>>> compatible.
>> since I just looked at a table collection for some other test, they
>> also have Mann-Whitney U statistic
>> http://faculty.washington.edu/heagerty/Books/Biostatistics/TABLES/Wilcoxon/
>> but I didn't check if it matches the test statistic in scipy.stats
>> Josef
>>>>> 3) This is picky but is there a reason that it returns a one-tailed
>>>>> p-value, while other tests (eg ttest_*) default to two-tailed?
>>>> legacy wart, that I don't like,  but it wasn't offending me enough to change it.
>>>>> Thanks for any thoughts, tips, or corrections and please don't take
>>>>> these comments as criticisms ... if I didn't enjoy using scipy.stats
>>>>> so much I wouldn't bother bringing this up!
>>>> Thanks for the feedback.
>>>> In large parts review of the functions relies on comments by users
>>>> (and future contributors).
>>>> The main problem is how to make changes without breaking current
>>>> usage, since many of those functions are widely used.
>>>> Josef
>>>>> Chris
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