Take some rows with certainty, sample the rest

Composes a design out of two parts: rows at or above a threshold are all taken, and any other design is applied to what remains. This is the standard shape of an audit or financial sample — every invoice over a hundred thousand gets examined, the long tail below is sampled — and it is the cheapest way to cut variance when a few units dominate the total.

Usage

design_certainty(above, threshold, rest, na_rm = FALSE)

Arguments

above

Column holding the size measure.

threshold

Rows with above >= threshold are taken with certainty.

rest

A design applied to the rows below the threshold. Its n is the number drawn from those rows, not the total.

na_rm

Drop rows whose size measure is NA instead of raising an error.

Value

A design object, for use with draw().

Details

Certainty rows have an inclusion probability of exactly 1, so they contribute their own value to a Horvitz-Thompson total with a weight of 1 and add nothing to its variance. That is the whole point: the uncertainty in the estimate comes only from the part you sampled.

See also

draw(), design_weighted() for probability-proportional-to-size, which handles dominant units by taking them with certainty automatically.

Other designs: design_bootstrap(), design_cluster(), design_multistage(), design_reservoir(), design_simple(), design_spatial(), design_spread(), design_stratified(), design_systematic(), design_temporal(), design_weighted()

Examples

set.seed(1)
invoices <- data.frame(
  id = 1:500,
  site = rep(c("a", "b"), times = c(300, 200)),
  value = round(stats::rlnorm(500, 7, 1.4))
)

# Everything over 20,000 examined; 40 drawn from the rest
d <- design_certainty("value", threshold = 20000,
                      rest = design_stratified("site", n = 40))
s <- draw(invoices, d, seed = 1, weights = TRUE)

table(certain = s$.prob == 1)
#> certain
#> FALSE  TRUE 
#>    40    13 
sum(invoices$value >= 20000)
#> [1] 13