Numbers of false positives to a test

Input values


This utility calculates the expected probability of numbers of false positive results to a test for a given sample size and test specificity, assuming the sample is from an uninfected population. It answers the question: 'For a given sample size and test specificity, and assuming that all animals are uninfected, what is the probability that there will be 1, 2, 3 etc false positives ?'. It also answers the related questions: 'What is the probability of x (1, 2, 3, etc) or more false positive results? and What is the probability of x (1, 2, 3, etc) or less false positive results?'

Inputs required

  • Test unit specificity; and
  • Sample size.


A table and plot of probabilities for each of the following:
  • the likely numbers of false positives (x);
  • less than or equal to x false positives; and
  • greater than or equal to x false positives.


There is no simple formula for these caclulations, which utilise the properties of the binomial probability distribution in R or excel. See example scripts/spreadsheet for details.


Vose, 2000, Risk analysis: A quantitative guide, 2nd ed. John wiley & Sons Ltd, Chichester, UK. pp 106-108.


Excel example
R function
Binomial probability distribution
Test specificity:
Sample size:


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