Date: Sun, 8 Mar 2009 11:55:21 -0400 Peter Flom "SAS(r) Discussion" Peter Flom Re: ordinal data To: Arthur Tabachneck text/plain; charset=UTF-8

Arthur Tabachneck <art297@NETSCAPE.NET> wrote > >I haven't kept current in the area, but still wouldn't be as quick as Peter >to agree. > >Take a look at: http://en.wikipedia.org/wiki/Level_of_measurement > >Can an underlying theoretical distribution be postulated that one could use >as an argument that the scale is more than just ordinal? I would think >that the critical issue will be the properties of the numbers themselves. >I.e., if 3 isn't three times greater than 1, than who can one justify using >multiplication or division on those numbers? >

This gets into tricky areas.

The levels of measurement have become enshrined, although this makes no more sense than the enshrinement of .05 as THE level of significance.

Technically, with (say) a five point ordinal scale, one could use

1 1.1 1.2 1.3 1000000

just as much as

1 2 3 4 5

that is, after all, what ordinal means.

But, in the real world, we often have a sense, even if we cannot prove it, that the scale is *roughly* interval. And fairly few things are really ratio scaled .... even something like income, which looks to be perfectly interval (\$10,000 is ten times \$1,000, right?) might better be treated differently, as the difference in (say) \$20,000 annual income and \$10,000 is not the same as between \$100,000 and \$110,000.

Further, if one looks into the details of many techniques proposed for ordinal scale really depend on more than ordinality.

Ordinal logistic regression at least allows a test of the proportional odds assumption, although the test isn't very good, and violations, unless they are extreme, seem not to make a big difference.

So, what to do?

Rather than get hung up on technical details, I sometimes do the analysis several ways, and compare results. If the predicted values from the different models are similar, then I go with the simplest model.

Peter

Peter L. Flom, PhD Statistical Consultant www DOT peterflomconsulting DOT com

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