Two-stage sample: PSUs drawn, then elements within each PSU

The within term carries the factor m/M, so it vanishes when every PSU is taken – the check that the bookkeeping is right.

Usage

Twostage(Y, Nl, M, N, level = 0.95)

Arguments

Y

List of observation vectors, one per sampled PSU.

Nl

Population size of each sampled PSU.

M

Number of PSUs in the population.

N

Number of elements in the population.

level

Confidence level.

Value

List with estimate, se, ci_lower, ci_upper, psu_mean, psu_var, between_term, within_term, m, M, N.

Details

Formula: Yhat = sum_l N_l ybar_l / sum_l N_l; V = (M/N)^2 [ ((M-m)/M)/(m(m-1)) * sum (N_l ybar_l - N_l Yhat)^2 + (1/(mM)) * sum N_l^2 ((N_l-n_l)/N_l) s_l^2 / n_l ]

References

Cochran (1977), Sampling Techniques, 3rd edition, Chapter 10 (subsampling / two-stage sampling). Chapter 10 was NOT in the scanned excerpt available to this batch, so the estimator and variance are taken from the reference implementation in the CRAN package samplingbook 1.2.4, function submean with method = "ratio".

Examples

set.seed(1)
Y <- list(rnorm(5, 10), rnorm(4, 12), rnorm(6, 11))
Twostage(Y, Nl = c(20, 15, 25), M = 10, N = 200)$estimate
#> [1] 11.0131