R Under development (unstable) (2024-03-07 r86063 ucrt) -- "Unsuffered Consequences"
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> library(survey)
Loading required package: grid
Loading required package: Matrix
Loading required package: survival

Attaching package: 'survey'

The following object is masked from 'package:graphics':

    dotchart

> ## check many permutations of fpc specification
> example(fpc)

fpc> data(fpc)

fpc> fpc
  stratid psuid weight nh Nh   x
1       1     1      3  5 15 2.8
2       1     2      3  5 15 4.1
3       1     3      3  5 15 6.8
4       1     4      3  5 15 6.8
5       1     5      3  5 15 9.2
6       2     1      4  3 12 3.7
7       2     2      4  3 12 6.6
8       2     3      4  3 12 4.2

fpc> withoutfpc<-svydesign(weights=~weight, ids=~psuid, strata=~stratid, variables=~x, 
fpc+    data=fpc, nest=TRUE)

fpc> withoutfpc
Stratified Independent Sampling design (with replacement)
withoutfpc<-svydesign(weights=~weight, ids=~psuid, strata=~stratid, variables=~x, 
   data=fpc, nest=TRUE)

fpc> svymean(~x, withoutfpc)
    mean     SE
x 5.4481 0.7413

fpc> withfpc<-svydesign(weights=~weight, ids=~psuid, strata=~stratid,
fpc+ fpc=~Nh, variables=~x, data=fpc, nest=TRUE)

fpc> withfpc
Stratified Independent Sampling design
withfpc<-svydesign(weights=~weight, ids=~psuid, strata=~stratid,
fpc=~Nh, variables=~x, data=fpc, nest=TRUE)

fpc> svymean(~x, withfpc)
    mean    SE
x 5.4481 0.616

fpc> ## Other equivalent forms 
fpc> withfpc<-svydesign(prob=~I(1/weight), ids=~psuid, strata=~stratid,
fpc+ fpc=~Nh, variables=~x, data=fpc, nest=TRUE)

fpc> svymean(~x, withfpc)
    mean    SE
x 5.4481 0.616

fpc> withfpc<-svydesign(weights=~weight, ids=~psuid, strata=~stratid,
fpc+ fpc=~I(nh/Nh), variables=~x, data=fpc, nest=TRUE)

fpc> svymean(~x, withfpc)
    mean    SE
x 5.4481 0.616

fpc> withfpc<-svydesign(weights=~weight, ids=~interaction(stratid,psuid),
fpc+ strata=~stratid, fpc=~I(nh/Nh), variables=~x, data=fpc)

fpc> svymean(~x, withfpc)
    mean    SE
x 5.4481 0.616

fpc> withfpc<-svydesign(ids=~psuid, strata=~stratid, fpc=~Nh,
fpc+  variables=~x,data=fpc,nest=TRUE)

fpc> svymean(~x, withfpc)
    mean    SE
x 5.4481 0.616

fpc> withfpc<-svydesign(ids=~psuid, strata=~stratid,
fpc+ fpc=~I(nh/Nh), variables=~x, data=fpc, nest=TRUE)

fpc> svymean(~x, withfpc)
    mean    SE
x 5.4481 0.616
> 
> 
> proc.time()
   user  system elapsed 
   1.06    0.09    1.15