Calculate camera-days required to achieve a target CV
Source:R/power-sample-size.R
creel_n_camera.RdUses the stratified sample size formula from Cochran (1977) to determine how many camera-days are needed to achieve a target coefficient of variation on the camera-effort estimate, given pilot mean and variance estimates per day-type stratum.
Arguments
- cv_target
Numeric scalar. Target coefficient of variation for the camera-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 camera count per day per stratum. Values must be >= 0.- s2_h
Numeric vector of same length as
N_h. Pilot variance of camera counts per day per stratum. Values must be >= 0.
Value
A named integer vector. Elements named after strata in N_h give the
camera-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. Budget against
"allocated"; see creel_n_effort() for why the two differ.
Details
Implements Cochran (1977) equation 5.25 under proportional allocation. 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 deploy cameras, 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.
Feltz-Middaugh (2025) empirical benchmark. That study reports the camera-day schedules at which a low-frequency time-lapse deployment performed acceptably. Its two headline scenarios are, per month:
well-performing (under 20 percent error in at least 80 percent of simulations): 12 weekdays and 7 weekend days, both at 1 count/day;
best-performing (under 10 percent error in at least 80 percent of simulations): 18 weekdays at 2 counts/day and 8 weekend days at 4 counts/day.
These are reported here as design context, not applied as a check. The
function cannot judge a computed n_h against them: N_h is the whole
survey period rather than a month, nothing here knows the counts per day
the schedule assumes, the error bands are fixed by the study rather than
taken from cv_target, and the simulations measured boat-trailer counts on
six Arkansas reservoirs, whereas ybar_h and s2_h are whatever the caller
piloted. Compare against them by hand, after converting to the same units.
Earlier versions warned when n_h fell below 12 or 7, choosing which
benchmark to apply by matching the substring "weekday" or "weekend" in
the stratum name. That comparison was between a period-scale allocation and
a per-month recommendation, so it under-fired by roughly the number of
months in the survey (#234). No sample size ever changed: the check only
ever emitted a warning.
References
Cochran, W.G. 1977. Sampling Techniques, 3rd ed. Wiley, New York.
Feltz, C.J. and Middaugh, C.R. 2025. Improving efficiency of estimating angler effort using low-frequency time-lapse camera data. North American Journal of Fisheries Management 45:322-332.
See also
creel_n_effort() for the equivalent function for angler-contact
sampling days.
Other "Planning & Sample Size":
audit_strata(),
compare_designs(),
creel_n_cpue(),
creel_n_effort(),
creel_power(),
cv_from_n(),
optimal_n(),
power_creel(),
reallocate_strata(),
simulate_strata_collapse()