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Calculate sampling days required to achieve a target CV on effort

Source: R/power-sample-size.R
creel_n_effort.Rd

Uses the stratified sample size formula from McCormick & Quist (2017) to determine how many sampling days are needed to achieve a target coefficient of variation on the effort estimate, given pilot variance estimates per day-type stratum.

Usage

creel_n_effort(cv_target, N_h, ybar_h, s2_h)

Arguments

cv_target

Numeric scalar. Target coefficient of variation for the effort estimate (e.g., 0.20 for 20 percent). Must be in (0, 1].

N_h

Named numeric vector. Total available days per stratum (e.g., c(weekday = 65, weekend = 28)). Values must be >= 1.

ybar_h

Numeric vector of same length as N_h. Pilot mean effort per day per stratum (e.g., angler-hours per day). Values must be >= 0.

s2_h

Numeric vector of same length as N_h. Pilot variance of effort per day per stratum. Values must be >= 0.

Value

A named integer vector. Elements named after strata in N_h give the sampling days required per stratum; element "total" gives Cochran's overall sample size before proportional allocation, and "allocated" the sum of the per-stratum values actually returned.

"allocated" is the number of sampling days the returned allocation commits to, and is the one to budget against. It is greater than or equal to "total": each stratum is rounded up independently, so the parts can sum to as much as k - 1 more than the unallocated optimum for k strata. Rounding up is deliberate – it keeps every stratum at or better than its share of cv_target.

Details

Implements Cochran (1977) equation 5.25 under proportional allocation, as applied to creel surveys by McCormick & Quist (2017). The finite-population correction (FPC) factor is intentionally omitted (standard practice for pre-season planning where the goal is to determine how many days to sample, not to assess precision of a completed survey).

The per-stratum sample sizes n_h are computed from the total n_total under proportional allocation: n_h = ceiling(n_total * N_h / sum(N_h)). Because each stratum is ceiling-ed independently, sum(n_h) may exceed n_total.

References

McCormick, J.L. and Quist, M.C. 2017. Sample size estimation for on-site creel surveys. North American Journal of Fisheries Management 37:970-983. doi:10.1080/02755947.2017.1342723

Cochran, W.G. 1977. Sampling Techniques, 3rd ed. Wiley, New York.

See also

Other "Planning & Sample Size": audit_strata(), compare_designs(), creel_n_camera(), creel_n_cpue(), creel_power(), cv_from_n(), optimal_n(), power_creel(), reallocate_strata(), simulate_strata_collapse()

Examples

# Two-stratum weekday/weekend example
creel_n_effort(
  cv_target = 0.20,
  N_h = c(weekday = 65, weekend = 28),
  ybar_h = c(50, 60),
  s2_h = c(400, 500)
)
#>   weekday   weekend     total allocated 
#>         3         2         4         5