nEdge: Compute the total sample size for a stratified, simple random...

In PracTools: Designing and Weighting Survey Samples

Compute the total sample size for a stratified, simple random sample based on an Edgeworth approximation

Description

Compute the total stratified, simple random sample size for various allocations that is large enough to insure adequate coverage of a normal approximation confidence interval (CI) for a population mean.

Usage

nEdge(ci.lev, side, epsilon = 0.005, dat, pop.sw = TRUE, wts = NULL, hcol=NULL, ycol,
      alloc = NULL, Ch = NULL)

Arguments

ci.lev	desired confidence level for a 1- or 2-sided normal approximation confidence interval based on an estimated mean; must be in the interval (0,1)
side	either "two.sided" or "one.sided" for type of confidence interval
epsilon	tolerance on coverage probability; the sample should be large enough that CI coverage is within \pm epsilon of ci.lev; must be in the interval (0,1)
dat	either a population or sample data frame
pop.sw	TRUE if dat is for a full population; FALSE if dat is for a sample
wts	vector of weights if dat is a sample; if dat is for a population, wts = NULL
hcol	column of dat that contains the stratum ID; strata can be character or numeric
ycol	column of dat that contains the analysis variable; must be numeric
alloc	allocation to the strata; must be one of prop, equal, neyman, totcost, totvar, or NULL
Ch	vector of costs per unit in each stratum; these exclude fixed costs that do not vary with the sample size

Details

nEdge computes the total sample size needed in either a stratified or unstratified simple random sample so that the coverage probability of a confidence interval is within a specified tolerance (epsilon) of a nominal confidence level (ci.lev). The calculation assumes that there is a single estimated mean or total of the variable ycol that is of key importance in a sample. Confidence intervals for the finite population mean are usually computed using the normal approximation whose accuracy depends on the underlying structure of the analytic variable and the total sample size. In some applications, assuring that CIs have near nominal coverage is critical. For example, for some items on business tax returns the US Internal Revenue Service allows sample estimates to be used but sets precision standards based on the lower (or upper) limit of a 1-sided CI.

Using an Edgeworth approximation to the distribution of the estimated overall mean in Qing & Valliant (2024), nEdge computes the total sample size needed so that a CI will have coverage equal to the nominal value in ci.lev plus or minus the tolerance epsilon. The calculation assumes that the sampling fraction in each stratum is negligible. The total sample size returned by nEdge is based on the overall Edgeworth criterion; the resulting stratum sample sizes may not be large enough so that the normal approximation is adequate for each stratum estimator. When dat is a sample, the weights (wts) used in the estimator of the mean (or total) are assumed to be scaled for estimating population totals. They can be inverse selection probabilities, i.e. ones used in the \pi-estimator, or weights that have been adjusted to account for nonresponse or coverage errors.

The remainder term in the approximation used in nEdge is O(n^{-1/2}). In contrast, the function nEdgeSRS uses a O(n^{-1}) approximation but applies only to simple random sampling.

Value

List with values:

CI type	one-sided or two-sided
epsilon	tolerance on CI coverage
Total sample size	numeric sample size
allocation	type of allocation to strata or NULL if no strata are used
Stratum values	Data frame with columns for stratum, number of sample units allocated to each stratum (nh), proportion of sample allocated to each stratum (ph), and skewness in each stratum (g1h); if no strata are used, only g1, the overall skewness is returned

Author(s)

Richard Valliant, Siyu Qing

References

Qing, S. and Valliant, R. (2024). Extending Cochran's Sample Size Rule to Stratified Simple Random Sampling with Applications to Audit Sampling. Journal of Official Statistics, accepted.

U.S. Internal Revenue Service (2011). 26 CFR 601.105: Examination of returns and claims for refund, credit or abatement: determination of correct tax liability. Washington DC. https://www.irs.gov/pub/irs-drop/rp-11-42.pdf

See Also

nCont, nEdgeSRS, nLogOdds, nProp, nPropMoe, nWilson

Examples

require(PracTools)
set.seed(1289129963)
pop <- HMT(N=10000, H=5)
    # run for full population
nEdge(ci.lev=0.95, side="one.sided", dat=pop, pop.sw=TRUE, wts=NULL, hcol="strat", ycol="y",
       alloc="neyman")
    # run for a stratified sample
require(sampling)
sam <- strata(data=pop, stratanames="strat", size=c(30, 40, 50, 60, 70), method=c("srswor"),
              description=TRUE)
samdat <- pop[sam$ID_unit,]
w = 1/sam$Prob
nEdge(ci.lev=0.95, side="two.sided", epsilon=0.02, dat=samdat, pop.sw=FALSE, wts=w,
       hcol="strat", ycol="y", alloc="equal")

PracTools documentation built on June 25, 2024, 1:12 a.m.