Calculate interviews required to achieve a target CV on CPUE

Determines the number of interviews needed to achieve a target coefficient of variation on a CPUE (catch-per-unit-effort) ratio estimate, using the ratio-estimator variance approximation from Cochran (1977).

Usage

creel_n_cpue(cv_catch, cv_effort, rho = 0, cv_target)

Arguments

cv_catch

Numeric scalar. Pilot coefficient of variation of catch per interview (the numerator of the CPUE ratio). Must be > 0.

cv_effort

Numeric scalar. Pilot coefficient of variation of effort per interview (the denominator of the CPUE ratio). Must be > 0.

rho

Numeric scalar. Pilot correlation between catch and effort per interview. Must be in [-1, 1]. Default is 0 (conservative; over-estimates required n when catch and effort are positively correlated).

cv_target

Numeric scalar. Target coefficient of variation for the CPUE estimate. Must be in (0, 1].

Value

An integer scalar (>= 1): number of interviews required.

Details

Implements the ratio-estimator variance approximation from Cochran (1977, Chapter 6) parameterised in terms of coefficients of variation rather than raw variances, which is more natural for pre-season planning:

$$n = \left\lceil \frac{CV_{catch}^2 + CV_{effort}^2 - 2 \rho \cdot CV_{catch} \cdot CV_{effort}}{CV_{target}^2} \right\rceil$$

Setting rho = 0 (the default) is conservative: it over-estimates the required sample size when catch and effort are positively correlated. Users with pilot data should supply the observed correlation to obtain a less conservative estimate.

The result is floored at 1L to ensure at least one interview is recommended.

References

Cochran, W.G. 1977. Sampling Techniques, 3rd ed. Wiley, New York. Chapter 6 (ratio estimator variance approximation).

See also

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

Examples

# rho = 0 (conservative, no pilot correlation data)
creel_n_cpue(cv_catch = 0.8, cv_effort = 0.5, rho = 0, cv_target = 0.20)
#> [1] 23

# With known positive correlation (smaller n)
creel_n_cpue(cv_catch = 0.8, cv_effort = 0.5, rho = 0.5, cv_target = 0.20)
#> [1] 13