Design effect

How much precision the design costs against simple random sampling of the same size (Kish 1965). deff = 1 means the design is doing as well as a coin flip over the frame; above 1 it is doing worse, which is the usual price of clustering; below 1 it is doing better, which is what stratification and probability-proportional-to-size buy you.

Usage

deff(x)

Arguments

x

A result from ht_total() or ht_mean().

Value

A single number, or NA when the design has no variance estimate.

Details

Read it as an exchange rate on sample size: at deff = 2, a sample of 400 carries about as much information as 200 drawn at random.

survey has a deff() of its own, and attaching survey after this package masks this one. Both work on an estimate from ht_total() or ht_mean(), so the masking is harmless.

References

Kish, L. (1965). Survey Sampling. Wiley.

See also

ht_total(), ht_mean(), plan_size(), which takes a design effect as an input.

Examples

set.seed(1)
# Sites differ from each other, and rows within a cluster are alike --
# exactly the structure that makes stratifying pay and clustering cost.
pop <- data.frame(
  id = 1:400,
  site = rep(c("a", "b", "c", "d"), each = 100),
  cl = rep(paste0("c", 1:40), each = 10)
)
pop$y <- rep(c(20, 60, 120, 200), each = 100) + round(stats::rnorm(400, 0, 8))

# Stratifying on something that matters buys precision (deff below 1)
deff(ht_total(draw(pop, design_stratified("site", n = 40), seed = 1,
                   weights = TRUE), "y"))
#> [1] 0.01174153

# Clustering usually costs it (deff above 1)
deff(ht_total(draw(pop, design_cluster("cl", n_clusters = 4), seed = 1,
                   weights = TRUE), "y"))
#> [1] 12.91977