# [R-meta] How to define Rosenthal & Rubin's Proportion Index?

Patrizio Tressoldi p@tr|z|o@tre@@o|d| @end|ng |rom un|pd@|t
Thu Sep 5 17:20:29 CEST 2019

```Il 05/09/2019 00:00, r-sig-meta-analysis-request using r-project.org ha scritto:
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> This isn't built into metafor. But the computations are easy to carry out 'by hand'. Let's say you have data like this:
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> dat <- data.frame(study = 1:4, ni = c(32, 10, 14, 7), hits = c(14, 3, 0, 6), ki = c(4, 6, 5, 4))
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> which is actually Table 5 in the paper.
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> Then we can compute this outcome measure and the corresponding sampling variances with:
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> dat\$Pi <- with(dat, ifelse(hits == 0, 0.5 / (ni + 1), hits / ni))
> dat\$yi <- with(dat, Pi*(ki-1) / (1 + Pi*(ki-2)))
> dat\$vi <- with(dat, 1/ni * yi^2*(1-yi)^2 / (Pi*(1-Pi)))
> dat
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Thank you for this implementation in metafor, however a trick of this
effect size is that values above .5 are related to a positive effect
(hits above chance) and viceversa.

Running a fixed or random model  in metafor, all values are considered
as positive. Do I have to calculate the dat\$yi subtracting .5?

And if this adjustment is correct, the calculation of dat\$vi remains the
same?

Patrizio

--
Patrizio E. Tressoldi Ph.D.
Dipartimento di Psicologia Generale
via Venezia 8