False Positive Paradox Calculator

What Is the False Positive Paradox?

The false positive paradox shows that a positive test result can still mean you probably do not have the disease when the condition is rare. Even a 98% accurate test produces mostly false alarms at low prevalence. This is a classic example of base rate fallacy. Use the Bayes Theorem Calculator for general conditional probability.

Positive Predictive Value Formula

$$\text{PPV} = \frac{SE \times BR}{SE \times BR + (1 - SP) \times (1 - BR)}$$

Where $SE$ is sensitivity, $SP$ is specificity, and $BR$ is prevalence (base rate).

Example: Rare Disease Screening

A disease affects 1% of people. A test is 98% sensitive and 98% specific. After a positive result, the chance you actually have the disease is only about 33%, not 98%. Most positive results are false alarms because healthy people vastly outnumber sick ones.

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