# FUNCTION to compute the probability of finding no testpositives in a sample of a certain size.

### Description

For a population of size `nPopulation`

with a given design prevalence
the function computes the probability of finding no testpositives
in a sample of size `nSample`

if an imperfect test is used (given sensitivity
and specificity). This probability corresponds to the alpha-error
(=error of the first kind) of the overall test with null hypothesis:
prevalence = design prevalence. A modified hypergeometric formula
is used; see Cameron, Baldock, 1998.

### Usage

1 2 | ```
computePValue(nPopulation, nSample, nDiseased,
sensitivity, specificity = 1)
``` |

### Arguments

`nPopulation` |
Integer. Population size. |

`nSample` |
Integer. Size of sample. |

`nDiseased` |
Integer. Number of diseased elements in the population according to the design prevalence. |

`sensitivity` |
Numeric between 0 and 1. Sensitivity (= probability of a testpositive result, given the tested individual is diseased) of the test (e.g., diagnostic test or herd test). |

`specificity` |
Numeric between 0 and 1. Specificity (= probability of a testnegative result, given the tested individual is not diseased) of the test (e.g., diagnostic test or herd test). The default value is 1. |

### Value

The return value is a numeric between 0 and 1. It is the probability of finding no testpositives (not diseased!) in the sample.

### Author(s)

Ian Kopacka <ian.kopacka@ages.at>

### References

A.R. Cameron and F.C. Baldock, "A new probablility formula to substantiate freedom from disease", Prev. Vet. Med. 34 (1998), pp. 1-17.

### See Also

`computeOptimalSampleSize`

, `computeAlphaLimitedSampling`

### Examples

1 2 | ```
alphaError <- computePValue(nPopulation = 3000,
nSample = 1387, nDiseased = 6, sensitivity = 0.85, specificity = 1)
``` |

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