Finite population correction factor for sampling without replacement

The factor multiplies the VARIANCE; the standard error carries its square root, returned separately because that is the one that gets misapplied.

Usage

Fpc(N, n)

Arguments

N

Population size (may be Inf).

n

Sample size, 1 <= n <= N.

Value

List with fpc, se_factor, fraction, N, n.

Details

Formula: f = n/N; fpc = (N - n)/N = 1 - f; V(ybar) = (1 - f) S^2 / n, se scales by sqrt(1 - f)

References

Cochran (1977), Sampling Techniques, 3rd edition, Chapter 2, where V(ybar) = (S^2/n)(N - n)/N for simple random sampling without replacement. Cross-checked against the reference implementation in the CRAN package samplingbook 1.2.4, whose Smean uses the variance (N - n)/N * (1/(n(n-1))) sum (y - ybar)^2.

Examples

Fpc(N = 5L, n = 5L)
#> $fpc
#> [1] 0
#> 
#> $se_factor
#> [1] 0
#> 
#> $fraction
#> [1] 1
#> 
#> $N
#> [1] 5
#> 
#> $n
#> [1] 5
#> 
#> $method
#> [1] "Finite population correction (1 - n/N)"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"