[R] Non-parametric test for location with two unpaired sets of data measured on ordinal scale.

[Greg Snow]

What do you mean by location?  I can think of examples where 2 distributions have the same median but different means, or the same means but different medians.

Are you willing to assume that the distributions are exactly the same under the null hypothesis? (not just the same 'center/location')

I would probably do a permutation test on the difference between the means or medians (which ever you think is more meaningful), this assumes the exact same distribution under the null.

You can also do a Mann-Whitney/Wilcoxin test (but I don't like explaining, or sometimes even thinking about, what it is actually testing), you could do a bootstrap confidence interval on the difference between means/medians (does not assume distributions are the same, just have same mean/median), or you could just replace all values by their ranks and do a t-test (essentially transforms the data to a uniform distribution, the CLT for the uniform kicks in around n=5, but I would simulate just to check).

This is not the nice simple answer that you were probably looking for, but hopefully it gives you some things to think about that will help, 

-- 
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
greg.snow at imail.org
801.408.8111


> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of John Sorkin
> Sent: Thursday, September 24, 2009 1:08 PM
> To: r-help at r-project.org
> Subject: [R] Non-parametric test for location with two unpaired sets of
> data measured on ordinal scale.
> 
> Please forgive a stats question.
> 
> I have to sets of data (unpaired) measured on an ordinal scale. I want
> to test to see if the two sets are different (i.e. do they have the
> same location):
> 
> set1: 1,3,2,2,4,3,3,2,2
> set:   4,4,4,3,3,5,4,4
> 
> What is the most appropriate non-parametric test to test location?
> 
> Thanks,
> John
> 
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