Allocate a stratified sample and report the variance it achieves

Formula: proportional n_h prop. N_h; Neyman n_h prop. N_h S_h; cost-optimal n_h prop. N_h S_h / sqrt(C_h); V(ybar_st) = sum_h W_h^2 (1 - f_h) S_h^2 / n_h

Usage

Stratdes(Nh, Sh, n, Ch = NULL, kind = "neyman")

Arguments

Nh

Population size of each stratum.

Sh

Stratum standard deviations (advance estimates).

n

Total sample size, at least 1 per stratum.

Ch

Cost per unit in each stratum; required for kind = "cost".

kind

One of "prop", "neyman", "cost".

Value

List with nh, nh_exact, weights, variance, se, Wh, N, n, L, kind.

References

Cochran (1977), Sampling Techniques, 3rd edition, Sections 5.3-5.5: Theorem 5.3 for the variance, Corollary 2 for proportional allocation, and the Neyman/cost-optimal rules n_h prop. N_h S_h and n_h prop. N_h S_h/sqrt(c_h) under the linear cost function (5.17). Chapter 5 read from the scanned original. Cross-checked against the CRAN package samplingbook 1.2.4, whose stratasamp uses exactly these three weight rules.

Examples

Stratdes(Nh = 5L, Sh = 5L, n = 5L)
#> $nh
#> [1] 5
#> 
#> $nh_exact
#> [1] 5
#> 
#> $weights
#> [1] 1
#> 
#> $variance
#> [1] 0
#> 
#> $se
#> [1] 0
#> 
#> $Wh
#> [1] 1
#> 
#> $N
#> [1] 5
#> 
#> $n
#> [1] 5
#> 
#> $L
#> [1] 1
#> 
#> $kind
#> [1] 2
#> 
#> $method
#> [1] "Stratified allocation and achieved variance"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"