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```
## Ian Kopacka
## 2010-05-05
##
## Function: computePValue
##
## Computes the probability of finding no testpositives in
## a sample of a finite population. An imperfect test is used.
##
## Input parameters:
## nPopulation...Integer. Population size.
## nSample.......Integer. Sample size.
## nDiseased.....Integer. Number of diseased in the population (according
## to the null hypothesis).
## sensitivity...Numeric between 0 and 1. Sensitivity of test (diagnostic
## test for one stage sampling, herd test for two stage
## sampling).
## specificity...Numeric between 0 and 1. Specificity of test (diagnostic
## test for one stage sampling, herd test for two stage
## sampling).
##
## Source: A.R. Cameron, F.C. Baldock, "A new probability fomula for
## surveys to substantiate freedom from disease", Prev. Vet. Med. 34
## (1998), pp. 1 - 17.
##
## Calls:
## -
##
## Is called by:
## computeOptimalSampleSize.R
## computeAlphaLimitedSampling.R
## computeAlpha.R
##
computePValue <- function(nPopulation, nSample, nDiseased,
sensitivity, specificity = 1){
## Possible number of infected in sample:
## maximum = min(nSample, nDiseased)
## Possible number of healthy in sample:
## maximum = nPopulation - nDiseased
## ==> nSample - (nPopulation - nDiseased) <= nSampleDiseased <=
## min(nSample, nDiseased)
nSampleDiseasedVector <- max(0, nSample - (nPopulation - nDiseased)) :
min(nSample, nDiseased)
probabilityHypergoemetricVector <- dhyper(x = nSampleDiseasedVector,
m = nDiseased, n = nPopulation - nDiseased, k = nSample)
out <- sum(probabilityHypergoemetricVector *
(1-sensitivity)^nSampleDiseasedVector *
specificity^(nSample-nSampleDiseasedVector))
return(out)
}
```

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