# strAlloc: Allocate a sample to strata In PracTools: Tools for Designing and Weighting Survey Samples

## Description

Compute the proportional, Neyman, cost-constrained, and variance-constrained allocations in a stratified simple random sample.

## Usage

 1 2 strAlloc(n.tot = NULL, Nh = NULL, Sh = NULL, cost = NULL, ch = NULL, V0 = NULL, CV0 = NULL, ybarU = NULL, alloc) 

## Arguments

 n.tot fixed total sample size Nh vector of population stratum sizes (N_h) or pop stratum proportions (W_h) Sh stratum unit standard deviations (S_h), required unless alloc = "prop" cost total variable cost ch vector of costs per unit in stratum h (c_h) V0 fixed variance target for estimated mean CV0 fixed CV target for estimated mean ybarU population mean of y (\bar{y}_U) alloc type of allocation; must be one of "prop", "neyman", "totcost", "totvar"

## Details

alloc="prop" computes the proportional allocation of a fixed total sample size, n.tot, to the strata. alloc="neyman" computes the allocation of a fixed total sample size, n.tot, to the strata that minimizes the variance of an estimated mean. alloc="totcost" computes the allocation of a fixed total sample size, n.tot, to the strata that minimizes the variance of an estimated mean subject to the fixed total cost. alloc="totvar" computes the allocation that minimizes total cost subject to the target coefficient of variation, CV0, or the target variance, V0, of the estimated mean.

## Value

For proportional allocation, a list with values:

 alloc type of allocation: "prop", "neyman", "totcost", "totvar" Nh vector of population sizes (N_h) or pop stratum proportions (W_h) nh vector of stratum sample sizes "nh/n" proportion of sample allocated to each stratum

For other allocations, the three components above plus:

 Sh stratum unit standard deviations (S_h) "anticipated SE of estimated mean" Anticipated SE of the estimated mean for the computed allocation

## Author(s)

Richard Valliant, Jill A. Dever, Frauke Kreuter

## References

Cochran, W.G. (1977). Sampling Techniques. John Wiley & Sons.

Valliant, R., Dever, J., Kreuter, F. (2013, chap. 3). Practical Tools for Designing and Weighting Survey Samples. Springer.

nCont, nLogOdds, nProp, nPropMoe, nWilson

## Examples

  1 2 3 4 5 6 7 8 9 10 11 # Neyman allocation Nh <- c(215, 65, 252, 50, 149, 144) Sh <- c(26787207, 10645109, 6909676, 11085034, 9817762, 44553355) strAlloc(n.tot = 100, Nh = Nh, Sh = Sh, alloc = "neyman") # cost constrained allocation ch <- c(1400, 200, 300, 600, 450, 1000) strAlloc(Nh = Nh, Sh = Sh, cost = 100000, ch = ch, alloc = "totcost") # allocation with CV target of 0.05 strAlloc(Nh = Nh, Sh = Sh, CV0 = 0.05, ch = ch, ybarU = 11664181, alloc = "totvar") 

### Example output



allocation = neyman
Nh = 215, 65, 252, 50, 149, 144
Sh = 26787207, 10645109, 6909676, 11085034, 9817762, 44553355
nh = 34.641683, 4.161947, 10.473487, 3.333804, 8.798970, 38.590108
nh/n = 0.34641683, 0.04161947, 0.10473487, 0.03333804, 0.08798970, 0.38590108
anticipated SE of estimated mean = 1727173

allocation = totcost
Nh = 215, 65, 252, 50, 149, 144
Sh = 26787207, 10645109, 6909676, 11085034, 9817762, 44553355
nh = 30.605403, 9.728474, 19.989127, 4.499121, 13.711619, 40.340301
nh/n = 0.2574608, 0.0818385, 0.1681538, 0.0378478, 0.1153458, 0.3393533
anticipated SE of estimated mean = 1636053

allocation = totvar
Nh = 215, 65, 252, 50, 149, 144
Sh = 26787207, 10645109, 6909676, 11085034, 9817762, 44553355
nh = 104.54922, 33.23283, 68.28362, 15.36917, 46.83941, 137.80400
nh/n = 0.2574608, 0.0818385, 0.1681538, 0.0378478, 0.1153458, 0.3393533
anticipated SE of estimated mean = 583209.1


PracTools documentation built on Aug. 4, 2020, 1:06 a.m.