# detect.prop: Probability of detecting a feature that covers a proportion... In emon: Tools for Environmental and Ecological Survey Design

## Description

The function can calculate the probability of a feature that occupies a proportion `theta` of the sampling area and where the sampling point density of the survey is specified; the sampling point density needed to achieve a specified probability of detection, where `theta` is also specified ; or the value of `theta` that will be detected with specified probability and sampling density.Unless the feature is made of a large number of random segments (see below for how to deal with this situation), these methods apply only when the pattern of points in the sampling deisgn is random.

## Usage

 `1` ```detect.prop(statistic, theta=NA, pdetect=NA, ssize=NA) ```

## Arguments

 `statistic` Describes what aspect of design you want calculated. The choices are `"P"` (probability detection); `"N"` (sample size) or `"F"` (feature proportion). `theta` Feature proportion. Not needed if `statistic="F"`. `pdetect` Probability detection. Not needed if `statistic="P"`. `ssize` Sample size. Not needed if `statistic="N"`.

## Details

The probability of detection is `p = 1 - (1 - theta)^{N}`. Formulae for `theta` and `N` are readily obtained from this formula. If the spatial pattern of the feature consists of lots of small, random uniformly distributed fragments, then we can redefine `theta = Na/A` where `a` is the area of the sampling unit and `A` is the sampling area.In this situation, the probability of patch detection applies no matter what the spatial pattern of points in the sampling design. Unlike `detect`, `detect.prop` works for vectors - so long as the input vectors are of the same length.

## Value

 `prob` Probability of detection `ssize` Sample size `prop` Feature proportion

## Author(s)

Jon Barry: [email protected]

## Examples

 ```1 2 3``` ```detect.prop(statistic='P', theta=0.02, ssize=80) detect.prop(statistic='N', theta=0.02, pdetect=0.9) detect.prop(statistic='F', pdetect=0.9, ssize=80) ```

emon documentation built on May 30, 2017, 1:42 a.m.