Re: Comparing two groups, small frequencies

From: Richard Ulrich (Rich.Ulrich_at_comcast.net)
Date: 11/26/04


Date: Fri, 26 Nov 2004 16:34:27 -0500

On Fri, 26 Nov 2004 19:07:03 +0000 (UTC), atomicster@gmail.com (Marc
Johansson) wrote:

> Hi all,
>
> I'm trying to compare two groups that are not matched and observe a
> dependent variable with 3 different possible outcomes (ordinal, non
> gaussian). The total number of cases in outcome 1 and 2 are low. 2x3
> table looks like this:
> 1 1
> 0 3
> 20 27
>
> To compare both distributions, chi-square seems inappropriate because
> of the low observed frequencies in the first two rows. Mann-Whitney is
> not good because of many ties. Kolmogorov-Smirnov does not work
> because data is discrete instead of continuous. Is standard t testing
> acceptable despite strong deviation from gaussian distribution and low
> sample total (21 and 31 resp)? (expected normal distribution is all
> cases in outcome 3). What other test could I use?

N of 21 and 31 is not so much the limitation as the
fact that there are only 5 values not at the modal value.
I'd call it "lack of useful variance" rather than non-normality.
If there were 2 or three more 1+2 values, then you could
have better hopes for the simple t-test as an approximation
that might yield significance. Here, the pooled t is not
going to be a BAD test, but it can't give anything; there's
not enough there.

If those 5 were all in one group, it would be "interesting,"
but they are not. Also, if the data were like that,, the 2x2 table
would probably be considered a more acceptable way
of laying it out and showing a test.

-- 
Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html


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