[R-meta] Random-effects meta-analyses with inverse-variance weights cannot include studies with sample sizes of two?

[Viechtbauer, Wolfgang (SP)]

Maybe I am a bit dense here, but I still do not fully understand what you are computing. You wrote earlier that there are two participants that "contributed to a percentage of hits, e.g. .30 and .40". Ok, that sounds like these participants did a series of trials that could yield hits/successes. I assume N is the number of trials. So the first participant had .3*N hits and the second participant had .4*N hits. So far so good. But what is 'z = binomial z'? Where does that equation for the variance come from? It would also help if you could provide a fully reproducible example of the computations.

Best,
Wolfgang

-----Original Message-----
From: Patrizio Tressoldi [mailto:patrizio.tressoldi using unipd.it] 
Sent: Friday, 09 November, 2018 8:40
To: Viechtbauer, Wolfgang (SP); r-sig-meta-analysis using r-project.org
Subject: Re: [R-meta] Random-effects meta-analyses with inverse-variance weights cannot include studies with sample sizes of two?

Il 08/11/2018 19:59, Viechtbauer, Wolfgang (SP) ha scritto:
> What kind of effect size measure would you compute based on this? And what would be the corresponding sampling variance?
In this case we would compute z/Sqr(N) where z = binomial z; N = number
of trials.
Variance = Sqr(1/(1-q)*(1-1/(1-q))/N, where q = chance probability, e.g. .5

Best
Patrizio

--
Patrizio E. Tressoldi Ph.D.
Dipartimento di Psicologia Generale
Università di Padova
via Venezia 8
35131 Padova - ITALY
http://www.patriziotressoldi.it
https://orcid.org/0000-0002-6404-0058

Science of Consciousness Research Group
http://dpg.unipd.it/en/soc

Make war history
support http://www.emergency.it