# [Rasch] Odds ratio as a scale

Svend Kreiner S.Kreiner at biostat.ku.dk
Wed Mar 9 01:16:11 EST 2011

```Dear A & T.

A ratio scale is a scale where the unit of measurement is arbitrary.
Comparisons of measurements by /ratios/ are therefore invariant  in  the
sense that they do not depend on  the unit of measurement.

Rasch (1960) himself asserted this. You can find discussions of this in
Chapter II, Section 3 and in Chapter V he talks about the meaning of
statements like "one person has /twice/ the ability of another" and he
says that the probability of the RM is a function of the /ratio/ (not
the difference) between the degree of ability of the person and the
difficulty of the problem. And in Chapter VII (pages 109-110) where he
says that he "undertook, along general lines, a discussion of what may
"reasonably" be read into such concepts as measuring on a ratio scale
"the ability of a person" and the "difficulty of a problem"." And later,
page 115) "/Where this law can be applied it provides a principle of
measurement on a ratio scale of both stimulus and object parameters/"
(Rasch's italics).

He never talked about interval scales, and you could argue that the
logit scale is not a proper interval scales but just a logarithmic ratio
scale because a true interval scale has both an arbitrary origin and an
arbitrary unit. On the logit scale as such, there is no unit. Or there
was no unit before Steven Humphrey defined his Rasch models for multiple
frameworks.

Best

Svend

Den 08-03-2011 12:27, Bond, Trevor skrev:
>
>     Dear Anthony
>     May I possibly have some explanations on why odds ratio is a ratio
>     scale measure?
>
>     I think you misconstrue...a ratio measurement scale and the
>     mathematical ratio between the probabilities you mention are two
>     entirely different concepts.
>     I doubt that anyone could seriously assert that RM produces ratio
>     scale measurement – some claim it produces interval level
>     measurement scales.
>     best
>     T
>
>
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--
Svend Kreiner
Professor
Department of Biostatistics
University of Copenhagen

P.O. Box 2099
DK-1014 Copenhagen K, Denmark

Email: S.Kreiner at biostat.ku.dk
Phone: (+45) 35 32 75 97

Fax: (+45) 35 32 79 07

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