transf.pft: Freeman-Tukey (double arcsine) transformation for proportions. See Freeman & Tukey (1950). The xi argument is used to specify the proportions and the ni argument the corresponding sample sizes. transf.ipft: inverse of the Freeman-Tukey (double arcsine) transformation for proportions. See Miller (1978). transf.ipft.hm: inverse of the Freeman-Tukey (double arcsine) transformation for proportions using the harmonic mean of the sample sizes for the back-transformation. See Miller (1978). The sample sizes are specified via the targs argument (the list element should be called ni). transf.irft: Freeman-Tukey transformation for incidence rates. See Freeman & Tukey (1950). The xi argument is used to specify the incidence rates and the ti argument the corresponding person-times at risk. transf.iahw: Inverse of the transformation of coefficient alpha as suggested by Hakstian & Whalen (1976). The integral transformation method for a transformation function h(z) integrates h(z) f(z) over z using the limits targs$lower and targs$upper, where f(z) is the density of a normal distribution with mean equal to xi and variance equal to targs$tau2. An example is provided below. Wolfgang Viechtbauer firstname.lastname@example.org package website: http://www.metafor-project.org/ author homepage: http://www.wvbauer.com/ Bonett, D. G. (2002). Sample size requirements for testing and estimating coefficient alpha. Journal of Educational and Behavioral Statistics, 27, 335–340. Fisher, R. A. (1921). On the “probable error” of a coefficient of correlation deduced from a small sample. Metron, 1, 1–32. Freeman, M. F., & Tukey, J. W. (1950). Transformations related to the angular and the square root. Annals of Mathematical Statistics, 21, 607–611. Hakstian, A. R., & Whalen, T. E. (1976). A k-sample significance test for independent alpha coefficients. Psychometrika, 41, 219–231. Miller, J. J. (1978). The inverse of the Freeman-Tukey double arcsine transformation. American Statistician, 32, 138. Viechtbauer, W. (2010). Conducting meta-analyses in R with the metafor package. Journal of Statistical Software, 36(3), 1–48. http://www.jstatsoft.org/v36/i03/. This site was developed by Ian Howson. I’m available to help with your software and statistics projects. All documentation is copyright its authors, I didn’t write any of that. Email me or if you have questions or problems. Source.