allocate: Optimum allocation for stratified random sampling.

In trobinj/trtools: Miscellaneous Tools for Teaching Statistics

Optimum allocation for stratified random sampling.

Description

This is a function to compute the optimum allocation for a stratified random sampling design.

Usage

allocate(Ni, si, ci = rep(1, length(Ni)), c0 = 0, ct = NA, ev = NA)

Arguments

Ni	Vector of total number of sampling units in each stratum.
si	Vector of the standard deviation for each statum
ci	Vector of the cost per unit for each stratum.
c0	Overhead survey cost.
ct	Total cost for the survey.
ev	Variance for the estimator of the population mean.

Details

The solution is based choosing the overall sample size and the sample sizes for each stratum to minimize the estimator variance for a fixed cost, or to minimize the cost for a fixed estimator variance. The solution assumes the usual estimator for the for the population mean and a variance based on a finite sample design-based approach. The total cost of the survey is assumed to be the overhead cost plus a per-unit cost for each sampled unit. See Cochran (1977) for details.

Value

A list of a vector of the proportion of units to sample from each stratum, a vector of sample sizes for each stratum, total sample size, estimator variance, and total survey cost. If neither the estimator variance (ev) or the total cost (ct) are specified then only the proportions can be computed.

Source

Cochran, W. G. (1977). Sampling techniques (3rd Edition). New York: Wiley.

Examples

# sampling fractions only
allocate(Ni = c(155,62,93), si = c(5,15,10), ci = c(9,9,16))

# allocation for estimator variance fixed at 1 
allocate(Ni = c(155,62,93), si = c(5,15,10), ci = c(9,9,16), ev = 1)

# allocation for total survey cost fixed at 500
allocate(Ni = c(155,62,93), si = c(5,15,10), ci = c(9,9,16), ct = 500)

trobinj/trtools documentation built on Jan. 3, 2025, 4:14 a.m.