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st: RE: interval ordinal


From   "Newson, Roger B" <r.newson@imperial.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: interval ordinal
Date   Tue, 27 Nov 2007 14:50:11 -0000

By definition, you cannot "transform the format of data from an interval
scale into an ordinal scale", because, interval data, by definition, are
also ordinal.

The categories "Nominal, Ordinal, Interval, Ratio" (abbreviated to NOIR)
are nested categories. That is to say, all data are at least nominal,
some nominal data are also ordinal, some ordinal data are also interval,
and some interval data are also ratio. This is because nominal data are
numbers (or vectors) X or Y for which it is meaningful to make the
statements (in Stata notation)

X==Y or X!=Y

and ordinal data are numbers (or vectors) X and Y for which it is
meaningful to make the statements

X<Y, X>Y, X<=Y, or X>=Y

and interval data are numbers for which it is meaningful to calculate

X-Y or Y-X

and ratio data are numbers for which it is meaningful to calculate

X/Y or Y/X

So, therefore ratio implies interval implies ordinal implies nominal,
because positive numbers are a subset of numbers, which are a subset of
sorted vectors, which are a subset of vectors which may or may not be
sorted.

Interval data can be analysed as interval data or as ordinal data. If we
analyse them as interval data, then we are interested in estimating
interval parameters, such as mean (or median) differences, with
confidence limits or P-values. If we analyse them as ordinal data, then
we are interested in estimating ordinal (or rank) parameters, with
confidence intervals or P-values. Well-known rank parameters are Somers'
D, Kendall's tau-a and Spearman's rho. Therefore, "analysing data as
interval data" means estimating interval parameters, and "analysing data
as ordinal data" means estimating ordinal (or rank) parameters.

To get P-values for ordinal parameters, use -ranksum-, -ktau- or
-spearman- in Stata. To get confidence intervals for ordinal parameters,
use the -somersd- package, which you can download from SSC using the
-ssc- command. More about ordinal parameters can be found on my website
(see my signature below).

I hope this helps.

Best wishes

Roger



Roger Newson
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk 
Web page: www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/pop
genetics/reph/

Opinions expressed are those of the author, not of the institution.

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
H.Riese@med.umcg.nl
Sent: 27 November 2007 13:19
To: statalist@hsphsun2.harvard.edu;
statalist-digest@hsphsun2.harvard.edu
Subject: st: interval ordinal

Dear Statalist readers,

I try to find the syntax to transform the format of data from an
interval scale into an ordinal scale. 
Can someone help me?

Thank you in advance for your reply,
Harriette Riese


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