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

Dear Patrizio,

Interesting -- I hadn't come across this paper / measure before.

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))

which is actually Table 5 in the paper. 

Then we can compute this outcome measure and the corresponding sampling variances with:

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

Note that there seems to be a typo for the third study (the value of yi is given as .09, while it should be .12).

Then we can meta-analyze the outcomes with: (using a fixed-effects model here, as is done in the paper)

rma(yi, vi, data=dat, method="FE")

We can also do moderator analyses (what the authors call 'focused tests'):

rma(yi, vi, mods = ~ ki, data=dat, method="FE")

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: Saturday, 10 August, 2019 12:22
To: r-sig-meta-analysis at r-project.org
Subject: [R-meta] How to define Rosenthal & Rubin's Proportion Index?

I'm using the Rosenthal & Rubin's Proportion Index as a measure of
effect size (Rosenthal, R., & Rubin, D. B. (1989). Effect size
estimation for one-sample multiple-choice-type data: Design, analysis,
and meta-analysis. Psychological Bulletin, 106(2), 332-337).

The range is 0-1, with the null effect = .50.

How can I define this particular ES with a rma analysis?

Thank you

Patrizio