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

Viechtbauer, Wolfgang (SP) wo||g@ng@v|echtb@uer @end|ng |rom m@@@tr|chtun|ver@|ty@n|
Thu Sep 5 18:53:08 CEST 2019

```No, you shouldn't subtract 0.5 if you want to estimate what Rosenthal and Rubin call bar(pi) (e.g., 0.78 as given at the bottom left on page 335). If you would subtract 0.5 from each yi value, then you would be estimating bar(pi) - 0.5.

However, if you want to test H0: bar(pi) = 0.5, then yes, first subtract 0.5 from each yi value (and no change to vi is needed).

Best,
Wolfgang

-----Original Message-----
From: R-sig-meta-analysis [mailto:r-sig-meta-analysis-bounces using r-project.org] On Behalf Of Patrizio Tressoldi
Sent: Thursday, 05 September, 2019 17:20
To: r-sig-meta-analysis using r-project.org
Subject: Re: [R-meta] How to define Rosenthal & Rubin's Proportion Index?

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:
>
> 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.
>
> 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
>
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