# R survey package: finite population correction affects point estimate in addition to the variance estimate?

Forgive me if this is an idiot question, but I believed that including a finite population correction parameter in the R survey package should only impact my variance estimates in a stratified sample (simple random sampling within stratum). Yet the addition of fpc seems to slightly modify my point estimate as well...perhaps just an unimportant artifact of calculation method?

I realize this example is very short on details, but I first wanted to confirm that my intuition that the change that I've observed is suspicious...perhaps the warning message is applicable to the difference in mean Height observed (187.751 changes to 186.83)?

dstrat=svydesign(ids=~1,strata = ~stratum, fpc=~pop, data=demo) svymean(~Height+Weight,dstrat,na.rm=T) mean SE Height 65.614 0.3091 Weight 187.751 2.4551

dstrat=svydesign(ids=~1,strata = ~stratum, data=demo) Warning message: In svydesign.default(ids = ~1, strata = ~stratum, data = demo) : No weights or probabilities supplied, assuming equal probability svymean(~Height+Weight,dstrat,na.rm=T) mean SE Height 65.62 0.3019 Weight 186.83 2.6220

Final note: I also used bootstrap estimates for SE (perhaps incorrectly), and arrived at the same point estimates as those above withOUT fpc:

demodrep=svrepdesign(data=demo, type="bootstrap", repweights=W,scale=bootresults$scale,rscale=bootresults$rscales,combined.weights=TRUE)

svymean(~Height+Weight,demodrep,na.rm=T) mean SE Height 65.62 0.4617 Weight 186.83 3.2325

R 3.2.0 Survey package version 3.29-5

Thank you in advance for any insight/pointers

yes, they will give different estimates. ?svydesign says "If population sizes are specified but not sampling probabilities or weights, the sampling probabilities will be computed from the population sizes assuming simple random sampling within strata."
looking inside survey:::svydesign.default
if (is.null(probs) && is.null(weights)) {
if (is.null(fpc$popsize)) { if (missing(probs) && missing(weights)) warning("No weights or probabilities supplied, assuming equal probability") probs <- rep(1, nrow(ids)) } else { probs <- 1/weights(fpc, final = FALSE) } }  so if weights are not specified by the user but the fpc is, then the stratified fpc gets used in the computation for the weights (which will affect point estimates as well as variance calculations) library(survey) data(api) dstrat1<-svydesign(id=~1,strata=~stype, data=apistrat, fpc=~fpc) dstrat2<-svydesign(id=~1,strata=~stype, data=apistrat) svymean( ~ api00 , dstrat1 ) svymean( ~ api00 , dstrat2 )  • It appears you're right Anthony...not sure why the stratified fpc gets used in computation for weights (if other weights not supplied), but I see it does. My motivation was to ascertain if my use of bootweights() was correct (in which I also included fpc and did some non-response adjustment to the resulting weights) by arriving at the same point estimates I expected from svydesign() with simple stratification. Because bootstrap point estimates matched the non-fpc pt estimates from svydesign(), I guess I feel comforted...if a bit uneasy by effect of fpc on svydesign() even if I'm not using it! Mar 12, 2016 at 15:25 • programmatically, you could force the weights (and therefore coefficients) to match if you add a column of ones to your data.frame.. apistrat$one <- 1 ; dstrat1 <- svydesign( id=~1,strata=~stype, data=apistrat, fpc=~fpc, weights = ~one ) but i have no clue what that means as far as what you're doing Mar 12, 2016 at 16:07