Draw one systematic sample with a random start, and estimate from it

The start comes from a pinned Lehmer generator so the two language arms produce the SAME sample; vary seed for a different start. Indices are one-based.

Usage

Sysrs(y, k, seed = 1)

Arguments

y

The whole population, in sampling order.

k

Sampling interval.

seed

Seed for the pinned generator that picks the start.

Value

List with start, index, sample, estimate, design_se, population_mean, N, n, k.

Details

Formula: r ~ Uniform{1..k}; sample = {r, r+k, r+2k, ...}; ybar_sy = mean of the sample

References

Cochran (1977), Sampling Techniques, 3rd edition, Chapter 8: a unit is chosen at random from the first k, and every k-th unit thereafter. Chapter 8 was NOT in the scanned excerpt available to this batch, so the standard published form is used. The design standard error is the exact one computed by the sibling module systmp.

Examples

Sysrs(y = matrix(c(1, 2, 3, 4, 5, 6), nrow = 2), k = 3L)
#> $start
#> [1] 1
#> 
#> $index
#> [1] 1 4
#> 
#> $sample
#> [1] 1 4
#> 
#> $estimate
#> [1] 2.5
#> 
#> $design_se
#> [1] 0.8164966
#> 
#> $population_mean
#> [1] 3.5
#> 
#> $N
#> [1] 6
#> 
#> $n
#> [1] 2
#> 
#> $k
#> [1] 3
#> 
#> $method
#> [1] "Systematic sample with a pinned random start"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"