False Positive Paradox Calculator: Unraveling Test Accuracy

Calculate True Positive Probability

The percentage of the population that actually has the condition.
The probability of a positive test given the condition is present (True Positive Rate).
The probability of a negative test given the condition is absent (True Negative Rate).
Our False Positive Paradox Calculator helps you understand why a positive test result for a rare condition might still be a false positive. Input prevalence, sensitivity, and specificity to calculate the actual probability of having the condition after a positive test. Demystify Bayesian probability and improve your statistical literacy.

Formula:

Formula Behind the False Positive Paradox

The calculation for the probability of actually having the condition given a positive test result (P(D|T+)) is derived from Bayes' Theorem:

P(D|T+) = (Sensitivity × Prevalence) / ((Sensitivity × Prevalence) + ((1 - Specificity) × (1 - Prevalence)))

Where:

  • P(D|T+): The probability of having the condition given a positive test result (also known as the Positive Predictive Value).
  • Sensitivity: The true positive rate; the probability that the test correctly identifies someone who has the condition.
  • Specificity: The true negative rate; the probability that the test correctly identifies someone who does NOT have the condition.
  • Prevalence: The base rate; the proportion of the population that actually has the condition.

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