[R] significance test interquartile ranges
Prof Brian Ripley
ripley at stats.ox.ac.uk
Sat Jul 14 08:16:04 CEST 2012
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
question.
> 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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