# computePValue: FUNCTION to compute the probability of finding no... In FFD: Freedom from Disease

## 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 <[email protected]>

## 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.

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