Allocate n units to strata in proportion to stratum size

Largest-remainder apportionment is used rather than rounding each n_h independently, because rounding can miss the target total by several units; ties break on the lowest stratum index so the two language arms agree exactly.

Usage

Propalloc(Nh, n)

Arguments

Nh

Population size of each stratum.

n

Total sample size to allocate.

Value

List with nh, nh_exact, Wh, fraction, N, n, L.

Details

Formula: n_h = n W_h = n N_h / N, apportioned by largest remainder

References

Cochran (1977), Sampling Techniques, 3rd edition, Section 5.3, Corollary 2, "stratification with proportional allocation of the n_h", n_h/n = N_h/N. Chapter 5 read from the scanned original. Cross-checked against the reference implementation in the CRAN package samplingbook 1.2.4, whose stratasamp(type = "prop") sets wh <- Nh/N.

Examples

Propalloc(Nh = c(1, 2, 3, 4, 5, 6, 7, 8), n = 5L)
#> $nh
#> [1] 0 0 0 1 1 1 1 1
#> 
#> $nh_exact
#> [1] 0.1388889 0.2777778 0.4166667 0.5555556 0.6944444 0.8333333 0.9722222
#> [8] 1.1111111
#> 
#> $Wh
#> [1] 0.02777778 0.05555556 0.08333333 0.11111111 0.13888889 0.16666667 0.19444444
#> [8] 0.22222222
#> 
#> $fraction
#> [1] 0.1388889
#> 
#> $N
#> [1] 36
#> 
#> $n
#> [1] 5
#> 
#> $L
#> [1] 8
#> 
#> $method
#> [1] "Proportional allocation (largest remainder)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"