Probably it is a trivial question, but I've have some doubts on how to calculate the effect size and corresponding standard error or variance of the difference between a proportion and its chance expectation, e.g. n. trials = 100; n. hits = 50; chance outcome = .25. Thank you Patrizio
[R-meta] effect size for proportion with respect to the chance expected
4 messages · Patrizio E Tressoldi, Wolfgang Viechtbauer
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? Best, Wolfgang -----Original Message----- From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces at r-project.org] On Behalf Of Patrizio Tressoldi Sent: Thursday, 16 August, 2018 9:47 To: r-sig-meta-analysis at r-project.org Subject: [R-meta] effect size for proportion with respect to the chance expected Probably it is a trivial question, but I've have some doubts on how to calculate the effect size and corresponding standard error or variance of the difference between a proportion and its chance expectation, e.g. n. trials = 100; n. hits = 50; chance outcome = .25. Thank you Patrizio
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
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