# F.double.obs.prob: Compute double observer probability of detection (No external... In Rdistance: Distance-Sampling Analyses for Density and Abundance Estimation

## Description

Estimates the probability of detection in a two-observer system when observations are independent.

## Usage

 `1` ```F.double.obs.prob(df, observer = "both") ```

## Arguments

 `df` A data frame containing the components `\$obsby.1` and `\$obsby.2`. These components are either 0/1 (0 = missed, 1 = seen) or TRUE/FALSE (logical) vectors indicating whether observer 1 (`obsby.1`) or observer 2 (`obsby.2`) spotted the target. There is no flexibility on naming these columns of `df`. They must be named `\$obsby.1` and `\$obsby.2`. `observer` A number of text string indicating the primary observer. Primary observers can be observer 1, or observer 2, or "both". If, for example, observer 2 was a data recorder and part-time observer, or if observer 2 was the pilot, set `observer` = 1. This dictates which set of observations form the denominator of the double observer system. For example, if `observer` = 1, observations by observer 1 that were not seen by observer 2 are ignored. The estimate in this case uses targets seen by both observers and those seen by observer 2 but not observer 1. If observer = "both", the denominator is computed twice, once assuming observer 1 was the primary, once assuming observer 2 was the primary, and then computes the probability of one or more observers sighting a target.

## Details

When `observer` = "both", the observers are assumed to be independent. In this case the estimate of detection is

p = p1 + p2 - p1*p2

where p1 is the proportion of targets seen by observer 2 that were also seen by observer 1, p2 is the proportion of targets seen by observer 1 that were also seen by observer 2. This estimator is very close to unbiased when observers are actually independent.

## Value

A single scalar, the probability of detection estimate.

## Author(s)

Trent McDonald, WEST Inc., tmcdonald@west-inc.com

`dfuncEstim`, `abundEstim`
 ```1 2 3 4 5 6 7``` ```# Fake observers set.seed(538392) obsrv <- data.frame( obsby.1=rbinom(100,1,.75), obsby.2=rbinom(100,1,.5) ) F.double.obs.prob( obsrv, observer=1 ) F.double.obs.prob( obsrv, observer=2 ) F.double.obs.prob( obsrv, observer="both" ) ```