Date:         Wed, 11 Mar 2009 14:17:21 -1000
Reply-To:     Bob Schacht <schacht@hawaii.edu>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Bob Schacht <schacht@hawaii.edu>
Subject:      Measures of dispersion for ordinal data
Content-type: text/plain; charset=us-ascii; format=flowed

For ordinal data, "dispersion" has an intuitive sense: "clustering" around
a "mode" provides a model of "central tendency"; a "uniform" distribution
implies an absence of any such clustering, and a platykurtic or bimodal
distribution forms the ideological opposite of "central tendency." These
measures are all well understood for ratio data, but are less well known
(at least to me) for ordinal data. What quantitative measures are available
for these concepts, given ordinal but not ratio data? Well, the Mode is
easily understood (i.e., most frequent category). But what about the rest?

dispersion
clustering
central tendency
Uniform distribution (Kolmogorov-Smirnoff test with equal probabilities for
every category?)
Bimodal distribution

Better yet, is there a standard set of statistics for describing the
dispersion of ordinal data?

Thanks,
Bob Schacht

Robert M. Schacht, Ph.D. <schacht@hawaii.edu>
Pacific Basin Rehabilitation Research & Training Center
1268 Young Street, Suite #204
Research Center, University of Hawaii
Honolulu, HI 96814

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