Optimal allocation when the cost per unit differs by stratum:
\(n_h \propto N_h S_h / \sqrt{c_h}\). With equal costs this reduces to
Neyman allocation, \(n_h \propto N_h S_h\), which is also available
directly as Neyman. The cost form matters whenever some
strata are markedly more expensive to enumerate than others, as remote
communities usually are.
Usage
morie_alloc_optimal(N_h, S_h, n, cost_h = NULL)
Arguments
- N_h
Stratum population sizes.
- S_h
Stratum standard deviations of the study variable.
- n
Total sample size to allocate.
- cost_h
Per-unit cost in each stratum. Default NULL, meaning
equal costs (Neyman allocation).
Value
A list with n_h (unrounded allocation), n_h_int
(integers summing to n), and share.
Examples
morie_alloc_optimal(N_h = c(8000, 1500, 500), S_h = c(1, 1.4, 2),
n = 900, cost_h = c(1, 3, 9))
#> $n_h
#> [1] 754.26087 114.31159 31.42754
#>
#> $n_h_int
#> [1] 754 114 32
#>
#> $share
#> [1] 0.83806764 0.12701288 0.03491948
#>
