Stratified sampling

Draws a sample from each stratum. Allocation uses the largest-remainder method, so the returned row count matches n exactly rather than drifting with per-stratum rounding.

Usage

design_stratified(
  strata,
  n,
  allocation = c("proportional", "equal", "neyman"),
  allocation_by = NULL,
  min_per_stratum = 0L,
  replace = FALSE,
  na_rm = FALSE
)

Arguments

strata

One or more column names defining the strata. Several columns are cross-classified.

n

Total rows to draw across all strata, under either allocation.

allocation

How n is split across strata. "proportional" gives each stratum a share of n in proportion to its size; "equal" splits n evenly; "neyman" gives shares proportional to size * sd, using the column named by allocation_by (Neyman 1934). Neyman minimises the variance of a total for a fixed n by putting more rows where the values vary most, and is the right choice when you have a frame variable correlated with what you are measuring. Under any rule, a stratum that would be allocated more rows than it holds is taken whole and the rest of n re-split over the others by the same rule (Cochran 1977, section 5.9).

allocation_by

Column whose within-stratum standard deviation drives allocation = "neyman". Ignored otherwise.

min_per_stratum

Minimum rows from each stratum. With the default of 0, a stratum smaller than about N / n can be allocated no rows at all; its rows then have inclusion probability 0 and a total estimated from the sample silently leaves them out, so draw() warns when that happens. 1 makes every stratum reachable, which is what an unbiased Horvitz-Thompson total needs, and 2 also lets every stratum contribute to the variance estimate. Over-sampling a small stratum this way does not bias an estimate made with the design weights, which correct for it; it only moves precision around.

replace

Sample with replacement within each stratum?

na_rm

Drop rows whose stratum key is NA instead of raising an error.

Value

A design object, for use with draw().

References

Neyman, J. (1934). On the two different aspects of the representative method. Journal of the Royal Statistical Society, 97, 558–625.

Cochran, W. G. (1977). Sampling Techniques, 3rd ed. Wiley.

See also

draw()

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

Examples

df <- data.frame(id = 1:100, site = rep(letters[1:4], each = 25))
table(draw(df, design_stratified("site", n = 20), seed = 1)$site)
#> 
#> a b c d 
#> 5 5 5 5 

# Rare strata are covered only if you ask -- without the floor, the one
# "rare" row gets no allocation, and draw() warns that it is unreachable
skewed <- data.frame(id = 1:1000, g = c(rep("common", 999), "rare"))
draw(skewed, design_stratified("g", n = 10, min_per_stratum = 1), seed = 1)$g
#>  [1] "common" "common" "common" "common" "common" "common" "common" "common"
#>  [9] "common" "rare"