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.