Estimate statistical power to detect a change in CPUE between seasons

Calculates the probability of detecting a fractional change in CPUE given a target sample size per season, a historical CV, and a significance level. Uses a two-sample normal approximation with equal group sizes.

Usage

creel_power(
  n,
  cv_historical,
  delta_pct,
  alpha = 0.05,
  alternative = c("two.sided", "one.sided")
)

Arguments

n

Integerish scalar (>= 1). Number of interviews per season.

cv_historical

Numeric scalar (> 0). Coefficient of variation of CPUE from historical or pilot data.

delta_pct

Numeric scalar (> 0). Fractional change to detect, expressed as a proportion — e.g., 0.20 for a 20 percent change. Note: this is a fraction, not a percentage point.

alpha

Numeric scalar in (0, 0.5]. Type I error rate. Default is 0.05.

alternative

Character. Either "two.sided" (default) or "one.sided".

Value

A numeric scalar in (0, 1): estimated statistical power.

Details

Implements the two-sample normal approximation for power under equal group sizes, parameterised in terms of the CV:

$$ncp = |\delta| \cdot \sqrt{n/2} \, / \, CV_{historical}$$

For alternative = "two.sided": $$power = \Phi(ncp - z_{\alpha/2}) + \Phi(-ncp - z_{\alpha/2})$$

For alternative = "one.sided": $$power = \Phi(ncp - z_{\alpha})$$

where delta is the fractional effect size (delta_pct), n is the number of interviews per season, and CV_historical is the pilot CV of CPUE.

A warning is issued when delta_pct > 5 because values greater than 5 are almost certainly input in percentage-point form rather than fractional form (e.g., 20 instead of 0.20).

References

Cohen, J. 1988. Statistical Power Analysis for the Behavioral Sciences, 2nd ed. Lawrence Erlbaum Associates, Hillsdale, NJ.

See also

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

Examples

# Two-sided power at n = 100, CV = 0.5, 20 percent change
creel_power(n = 100, cv_historical = 0.5, delta_pct = 0.20)
#> [1] 0.8074304

# One-sided test (higher power for same inputs)
creel_power(n = 100, cv_historical = 0.5, delta_pct = 0.20, alternative = "one.sided")
#> [1] 0.881709