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Re: st: Nominal or ordinal?

From   David Bell <>
To   <>
Subject   Re: st: Nominal or ordinal?
Date   Fri, 13 Aug 2010 11:50:41 -0400

I think Alan is referring to the method of probably the classic discussion of interval vs. ordinal regression (OLS) in sociology:

Sanford Labovitz. American Sociological Review, Vol. 35, No. 3 (Jun., 1970), pp. 515-524

“The results of the tests based on assigning interval scores to ordinal categories suggest: (1) certain interval statistics can be used interchangeably with ordinal statistics and interpreted as ordinal, (2) certain interval statistics (e.g., variance) can be computed where no ordinal equivalent exists and can be interpreted with accuracy,( 3) certain interval statistics can be given their interval interpretation with only negligible error if the variable is "nearly" interval, and (4) certain interval statistics can be given their interval interpretations with caution (even if the variables "purely" ordinal), because the "true" scoring system and the assigned scoring system, especially the equidistant system, are almost always close as measured by r and r2.”

I work hard to design and use measures that capture the interval nature of the theoretical concepts.  However, I am usually involved in testing theory, and the theoretical concepts I use are usually interval (in fact most often ratio).  Thus, when I have to make a choice, I tend to favor statistical methods that best present the theory rather than those that best present the peculiarities of measurement. 

David C. Bell
Professor of Sociology
Indiana University Purdue University Indianapolis (IUPUI)
(317) 278-1336

On Aug 13, 2010, at 12:18 AM, Richard Williams wrote:

> At 09:06 PM 8/12/2010, Alan Acock wrote:
>> I don't have a hand reference, but if you generate a series of monotonic transformations of an interval scale, the linear correlations of each transformation with the interval scale variable will almost all be over .9. Of course, a non monotonic transformation would not do this, nor would it be ordinal. Also, it is possible to have an extreme monotonic transformation for which a straight line does terribly.
>> Alan Acock
> Alan, can you clarify? Are you talking about, say, different ways of collapsing a variable into 5 categories, where you use different cutpoints each time?  Or something else?
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