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pa_CV: Coefficient of Variation (CV) of the probability of detection (pa).

Source: R/callDensityEstimate.R
pa_CV.Rd

CV.pa is calculated using the standard deviation of the means and the sum of the standard deviations of the transects. This approach assumes independence between transects and homogeneity of error. The summation of SDs assumes a conservative model.

Usage

pa_CV(pa.all.transects, wt = rep(1, dim(pa.all.transects)[1] - 1))

Arguments

pa.all.transects

  • matrix containing two columns and same number of rows as number of transects. The first column contains the mean pa and the second column contains the standard deviation of pa for each transect. The final column contains the overall mean and sd.

Value

CV.pa - CV of the probability of deteciton in the area

Details

Follows from Eqn. 6.19 and 6.20 from Harris (2012) PhD Thesis Chapter 6 var_total_Pa = SE_Pa^2 + (sum(SD_Pa_t)/n_t)^2 Eqn.6.19 SE_total_Pa = sqrt(var_total_Pa) Eqn.6.20

where:

var_total_Pa = variance of the overall mean probability of detection incorporating all sources of variance SE_total_Pa = standard error of the overall mean probability of detection incorporating all sources of variance

SE_Pa = standard error of the n_t transect-specific mean probabilities of detection, i.e. sd(Pa_t)/sqrt(n_t): how much the transect means disagree with each other. NOT mean(Pa_t)/sqrt(n_t), which is what this function computed between 2025-06-27 and 2026-07-17 (see NEWS/commit 0a9cb2f). That formula divides the estimate by a constant depending only on n_t, so CV.pa collapsed to ~1/sqrt(n_t) regardless of how much the underlying detection curve actually varied. Verified: across a sweep of 32 detector configurations with true p_a bias from 0% to 68%, the old formula reported CV.pa = 0.50-0.51 throughout (test-pa_CV.R). SD_Pa_t = standard deviation of each transect-specific mean probability of detection, driven by pDetInArea's outerloop bootstrap of the detection curve's coefficients and of SL/NL. This term was correct throughout. t = transect (1 - n_t) n_t = total number of transects (8 in Harris's thesis, but adjustable here)

Note: to allow the lengths of transects to vary requires additional weighting beyond that described by Harris (2012). We account for this with the wt parameter, which should contain the area for each transect. We adapt Eqn.6.19 so that both SE_Pa and the mean of standard deviations are weighted means, using Hmisc::wtd.var for a weighted variance of the transect means that reduces exactly to var() when weights are equal.