weighted.var.se<-function(x, w, na.rm=FALSE){
# Computes the variance of a weighted mean following Cochran 1977 definition
if (na.rm) { w <- w[i <- !is.na(x)]; x <- x[i] }
n = length(w)
xWbar = weighted.mean(x,w,na.rm=na.rm)
wbar = mean(w)
out = n/((n-1)*sum(w)^2)*(sum((w*x-wbar*xWbar)^2)-2*xWbar*sum((w-wbar)*(w*x-wbar*xWbar))+xWbar^2*sum((w-wbar)^2))
return(out)}
#'
#' x=rlnorm(100)
#' w=1:100
#'
#' weighted.var.se(x,w)^.5
#'
#' http://stats.stackexchange.com/questions/25895/computing-standard-error-in-weighted-mean-estimation
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