Survey weighted SE

SE.R

library(survey)

population<-data.frame(y=1:1000,
	strata=rep(1:3,c(100,200,700)),
	popsizes=rep(c(100,200,700),c(100,200,700))
	)
with(population, by(y,strata,var))

sampsizes<-c("1"=10,"2"=30,"3"=50)	


one.sim<-function(){	
 	in_sample<-stratsample(as.character(population$strata), sampsizes)	
	the_sample<-population[in_sample,]
	des<-svydesign(id=~1, strat=~strata, fpc=~popsizes,data=the_sample)
	m<-svymean(~y,des)

	c(mean=coef(m),SE=SE(m))
}

set.seed(2024-11-3)
 r<-replicate(10000, one.sim())
 sd(r[1,])
 median(r[2,])

PS: if you don't have R handy, the answers are 19.36173 for the simulation SD and 19.39484 for the median estimated SE