Re: st: Recovering cell values from odds ratios

[Maarten Buis <maartenlbuis@gmail.com>]

On Tue, May 31, 2011 at 2:42 PM, King, Carina <c.king09@imperial.ac.uk> wrote:
> The 'p' is the calculation from p=o/(1+o), and all the numbers were calculated, apart from the OR and the number of cases (218) and controls (14748).
>
> Taking 'unconsciousness' as the example:
>
> P= 3.54/(1+3.54)
> P= 0.77973

The o in the formula refers to odds not the odds ratio. These are not
the same thing. As the name suggests the odds ratio is a ratio of
odds. To turn an odds ratio into odds you first need to know the
baseline odds.

An odds is the number of successes per failure

An odds ratio is the ratio by which the odds in one group differs from
the odds in another group.

Say we have two groups, A and B. We know that there are a 100 persons
in each group, the odds ratio comparing A with B is 2, and the
baseline odds (the odds in group A) is .5.

In that case we know the odds in group B is twice the odds in group A.
The odds in group A is .5, so the odds in group B is 2*.5=1. So within
group A we expect .5 successes per failure, and in group B we expect 1
success per failure. These are the odds.

We now know that in group A the probability of success is
.5/(1+.5)=1/3 and in group B the probability of success is
1/(1+1)=1/2.

Now we know that there were (approximately) 33 successes and 67
failures in group A and 50 successes and 50 failures in group B.

Notice that if we did not know the baseline odds (and unfortunately
this is often not reported) we could not compute these numbers.

-- Maarten

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany


http://www.maartenbuis.nl
--------------------------
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