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Compute the expected CV achievable with a known sample size

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

Calculates the coefficient of variation attainable given a fixed sample size, acting as the algebraic inverse of creel_n_effort() (when type = "effort") or creel_n_cpue() (when type = "cpue").

Usage

cv_from_n(type = c("effort", "cpue"), n, ...)

Arguments

type

Character. Either "effort" or "cpue". Selects the formula branch and required additional arguments.

n

Integerish scalar (>= 1). Available sample size (sampling days for "effort", interviews for "cpue").

...

Additional arguments passed to the relevant branch:

For type = "effort":

  • N_h — Named numeric vector; total available days per stratum (>= 1).

  • ybar_h — Numeric vector; pilot mean effort per day per stratum (>= 0).

  • s2_h — Numeric vector; pilot variance of effort per day per stratum (>= 0).

For type = "cpue":

  • cv_catch — Numeric scalar; pilot CV of catch per interview (> 0).

  • cv_effort — Numeric scalar; pilot CV of effort per interview (> 0).

  • rho — Numeric scalar; pilot correlation between catch and effort, in [-1, 1]. Default is 0.

Value

A numeric scalar (> 0): the expected CV achievable at sample size n.

Details

Effort branch (type = "effort"): $$CV = \frac{\sqrt{\sum_h N_h s_h^2 / n}}{\sum_h N_h \bar{y}_h}$$

This is the inverse of the Cochran (1977) stratified sample-size formula implemented in creel_n_effort().

CPUE branch (type = "cpue"): $$CV = \sqrt{(CV_{catch}^2 + CV_{effort}^2 - 2\rho \cdot CV_{catch} \cdot CV_{effort}) / n}$$

This is the inverse of the ratio-estimator formula implemented in creel_n_cpue().

Because creel_n_effort() and creel_n_cpue() apply ceiling(), the round-trip property is cv_from_n(type, n = creel_n_*(cv, ...), ...) <= cv (the recovered CV is at or below the target).

References

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

See also

creel_n_effort(), creel_n_cpue()

Other "Planning & Sample Size": compare_designs(), creel_n_cpue(), creel_n_effort(), creel_power(), power_creel()

Examples

# Effort round-trip
n_days <- creel_n_effort(0.20,
  N_h = c(weekday = 65, weekend = 28),
  ybar_h = c(50, 60), s2_h = c(400, 500)
)
cv_from_n("effort",
  n = n_days[["total"]],
  N_h = c(weekday = 65, weekend = 28),
  ybar_h = c(50, 60), s2_h = c(400, 500)
)
#> [1] 0.02028398

# CPUE round-trip
n_int <- creel_n_cpue(cv_catch = 0.8, cv_effort = 0.5, rho = 0, cv_target = 0.20)
cv_from_n("cpue", n = n_int, cv_catch = 0.8, cv_effort = 0.5, rho = 0)
#> [1] 0.1967121