Choose the cluster size that buys the most precision per unit cost

The optimum is reported both exactly and rounded to the better of its two neighbouring integers, compared on the achieved variance rather than on the rounding.

Usage

Clusdes(rho, S2, c1, c2, budget)

Arguments

rho: Intraclass correlation, 0 < rho <= 1.
S2: Element variance in the population.
c1: Cost of adding one cluster.
c2: Cost of adding one element within a cluster.
budget: Total budget.

Value

List with k_opt, k, m, variance, deff, cost, elements.

Details

Formula: k_opt = sqrt( c1 (1 - rho) / (c2 rho) ); m = budget / (c1 + c2 k); V(ybar) = (S^2 / (m k)) [1 + (k - 1) rho]

References

Cochran (1977), Sampling Techniques, 3rd edition, Chapter 9, which develops the design effect 1 + (k - 1) rho and optimises k against the linear cost function c1 m + c2 m k. Chapter 9 was NOT in the scanned excerpt available to this batch, so the standard published form is used.

Examples

Clusdes(rho = 0.05, S2 = 1, c1 = 10, c2 = 1, budget = 1000)
#> $k_opt
#> [1] 13.78405
#> 
#> $k
#> [1] 14
#> 
#> $m
#> [1] 41.66667
#> 
#> $variance
#> [1] 0.002828571
#> 
#> $deff
#> [1] 1.65
#> 
#> $cost
#> [1] 1000
#> 
#> $elements
#> [1] 583.3333
#> 
#> $method
#> [1] "Optimal cluster size under a linear cost function"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"