# [R-meta] effect size for proportion with respect to the chance expected

Wolfgang Viechtbauer wolfg@ng@viechtb@uer @ending from m@@@trichtuniver@ity@nl
Thu Aug 16 12:07:08 CEST 2018

```So, then the "effect size" would be:

50/100 - .25

and the corresponding sampling variance would be computed with:

50/100 * (100-50)/100 / 100

or in general, if p is the observed proportion and n the sample size,
then:

p * (1-p) / n

This assumes that the expected proportion is really some fixed constant
and not something that is computed based on data.

Best,
Wolfgang

> Il 16/08/2018 10:10, Viechtbauer, Wolfgang (SP) ha scritto:
>> Dear Patrizio,
>>
>> What kind of 'effect size' do you want to compute? One could compute the
>> difference between the observed proportion and the expected one (50/100 -
>> .25), or one could compute the (log transformed) ratio (log((50/100) /
>> .25)), or one could compute the (log transformed) odds ratio (log((50/100)
>> / ((100-50)/100) / (.25 / (1 - .25)))), or ... So which one ar you
>> interested in?
>>
> For the moment I need to compute the difference between the observed and
> the expected proportion.
>
> Thanks
> Patrizio

```