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

Patrizio Tressoldi p@trizio@tre@@oldi @ending from unipd@it
Fri Nov 9 13:01:20 CET 2018

```Il 09/11/2018 12:05, Viechtbauer, Wolfgang (SP) ha scritto:
> 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.
>
>
This is the z score obtained from a normal approximation of the binomial
test binomial test: z= (X - µ)/σ ; where X = observed percentage;  µ =
chance percentage; σ = Sqr(µ(1-µ)/N

ex. X= 31; N= 49; p = .5 = (31/46 - .5)/Sqr(.5*.5/49) = 2.4

Patrizio

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

Science of Consciousness Research Group
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