#####################################################################################
# Code for the simple meta analysis in "The Insignificance of Null Hypothesis       #
# Significance Testing. Political Research Quarterly, 52:3, 647-674                 #
# (September 1999).                                       Copyright 2008, Jeff Gill #
#####################################################################################

meta <- matrix(c(450,500,370,400,630,.03,.09,.01,.24,.26),5,2)
meta.nbar <- mean(meta[,1])
meta.dbar <- (sum(meta[,1]*meta[,2]))/sum(meta[,1])
meta.vard <- (sum(meta[,1]*(meta[,2]-meta.dbar)^2))/sum(meta[,1])
meta.vars <- ((meta.nbar-1)/(meta.nbar-3))*((4/meta.nbar)*(1+(meta.dbar^2)/8))
meta.vardbar <- meta.vard - meta.vars
CI95 <- c(meta.dbar-1.96*sqrt(meta.vardbar),meta.dbar+1.96*sqrt(meta.vardbar))
CI99 <- c(meta.dbar-2.575*sqrt(meta.vardbar),meta.dbar+2.575*sqrt(meta.vardbar))

round(meta.dbar,4)
round(meta.vard,4)
round(meta.vars,4)
round(meta.vardbar ,4)
round(sqrt(meta.vardbar),4)
round(CI95,4)
round(CI99,4)

> [1] 0.137
> [1] 0.0111
> [1] 0.0086
> [1] 0.0025
> [1] 0.05
> [1] 0.0391 0.2349
> [1] 0.0084 0.2657