Small survey example

The fpc data frame has 8 rows and 6 columns. It is artificial data to illustrate survey sampling estimators.

data(fpc)

Format

This data frame contains the following columns:

stratid

Stratum ids

psuid

Sampling unit ids

weight

Sampling weights

nh

number sampled per stratum

Nh

population size per stratum

x

data

Examples

data(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


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

withoutfpc
#> Stratified Independent Sampling design (with replacement)
#> svydesign(weights = ~weight, ids = ~psuid, strata = ~stratid, 
#>     variables = ~x, data = fpc, nest = TRUE)
svymean(~x, withoutfpc)
#>     mean     SE
#> x 5.4481 0.7413

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

withfpc
#> Stratified Independent Sampling design
#> svydesign(weights = ~weight, ids = ~psuid, strata = ~stratid, 
#>     fpc = ~Nh, variables = ~x, data = fpc, nest = TRUE)
svymean(~x, withfpc)
#>     mean    SE
#> x 5.4481 0.616

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

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

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

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

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

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

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

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

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

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