[Rasch] Odds ratio as a scale

Anthony James luckyantonio2003 at yahoo.com
Wed Mar 9 20:11:08 EST 2011

```Thank you Svend and others,

The odds of success is defined as:
Odds= P(X=1)/P(X=0); (Ability ) B=p/1-p
Odds=proportion correct/proportion incorrect, such as
Person A:  Odds=.8/.2=4 ( person A has got 8 items right and 2 wrong, out of 10 items)
Person B: Odds=.9/.1=9
Person C: Odds=.6/.4=1.5
etc.

Apparently these odds are ratio measures. This means that person B is more than twice as better as Person A and six times better than person C.

My understanding is that everything start from Ability=p/1-p.
Then we take the log and then exponentiate etc.

Therefore the idea of p/1-p or (proportion correct/proportion incorrect) is an axiom.
Mike's paper in RMT also implies this: http://www.rasch.org/rmt/rmt53d.htm

Cheers
Anthony

--- On Tue, 3/8/11, Mike Linacre (RMT) <rmt at rasch.org> wrote:

> From: Mike Linacre (RMT) <rmt at rasch.org>
> Subject: Re: [Rasch] Odds ratio as a scale
> To: rasch at acer.edu.au
> Date: Tuesday, March 8, 2011, 4:09 PM
>
> Anthony:
>
> You may find this helpful:
> http://www.rasch.org/rmt/rmt94b.htm
> - it describes some of the differences between Stevens'
> "ratio scale" and Georg Rasch's "scale of
> ratios".
>
>
> Mike L.
>
>
> Mike Linacre
>
> Editor, Rasch Measurement Transactions
>
> rmt at rasch.org www.rasch.org/rmt/ Latest
> RMT:  24:3 Winter 2010
>

```