[R] significance test interquartile ranges

Schaber, Jörg joerg.schaber at med.ovgu.de
Sat Jul 14 13:35:03 CEST 2012

Thanks for your suggestions! 
The Siegel Tukey test and the permutation test sound promising, indeed.

I applied the wilcoxon test already, but understood that it mainly tests differences in the medians (location), even though being sensitive to all kinds of differences between distributions, similar to the K-S test.
I once heard that the K-S test is more sensitive to differences in the tails between distributions, whereas the U-test is more sensitive to differences in location in general. Can some knowledgeable statistician comment on that?

I do not understand the concern of Brian, saying that the permutation test suggested by Greg tests equality in distribution. When the test statistic is the ratio of IQRs, the permutation test calucates the p-value of this ratio under the null hypothesis that group label does not matter, i.e. that they are equal, right? But I am probable not knowledgeable statistician enough to judge that.



Von: Prof Brian Ripley [ripley at stats.ox.ac.uk]
Gesendet: Samstag, 14. Juli 2012 08:16
Bis: Greg Snow
Cc: Schaber, Jörg; R-help
Betreff: Re: [R] significance test interquartile ranges

On 13/07/2012 21:37, Greg Snow wrote:
> A permutation test may be appropriate:

Yes, it may, but precisely which one is unclear.  You are testing
whether the two samples have an identical distribution, whereas I took
the question to be a test of differences in dispersion, with differences
in location allowed.

I do not think this can be solved without further assumptions.  E.g
people often replace the two-sample t-test by the two-sample Wilcoxon
test as a test of differences in location, not realizing that the latter
is also sensitive to other aspects of the difference (e.g. both
dispersion and shape).

I nearly suggested (yesterday) doing the permutation test on differences
from medians in the two groups.  But really this is off-topic for R-help
and needs interaction with a knowledgeable statistician to refine the

> 1. compute the ratio of the 2 IQR values (or other comparison of interest)
> 2. combine the data from the 2 samples into 1 pool, then randomly
> split into 2 groups (matching sample sizes of original) and compute
> the ratio of the IQR values for the 2 new samples.
> 3. repeat #2 a bunch of times (like for a total of 999 random splits)
> and combine with the original value.
> 4. (optional, but strongly suggested) plot a histogram of all the
> ratios and place a reference line of the original ratio on the plot.
> 5. calculate the proportion of ratios that are as extreme or more
> extreme than the original, this is the (approximate) p-value.

I think it is an 'exact' (but random) p-value.

> On Fri, Jul 13, 2012 at 5:32 AM, Schaber, Jörg
> <joerg.schaber at med.ovgu.de> wrote:
>> Hi,
>> I have two non-normal distributions and use interquartile ranges as a dispersion measure.
>> Now I am looking for a test, which tests whether the interquartile ranges from the two distributions are significantly different.
>> Any idea?
>> Thanks,
>> joerg

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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