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 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, J?rg <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