A large collection of ivory inspection tokens with a few green alerts. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
Choose a concrete hypothetical population
Imagine inspecting 10,000 manufactured components. One percent are actually defective. The inspection flags 90% of defective parts and correctly passes 95% of nondefective parts. These are hypothetical rates used to explain the base-rate effect, not measured performance claims. We want the share of flagged parts that are actually defective.
Count both sources of a flag
There are 100 defective parts in expectation, of which 90 are flagged and 10 missed. There are 9,900 nondefective parts, of which 495 are falsely flagged and 9,405 correctly passed. Thus 585 parts are flagged in expectation. Only 90/585, approximately 15.3846%, are defective. The 90% sensitivity is P(flag | defective), whereas the requested precision is P(defective | flag).
| Flagged | Passed | |
|---|---|---|
| Actually defective | 90 | 10 |
| Actually nondefective | 495 | 9,405 |
Read false-positive phrases carefully
The false-positive rate is 5% among nondefective parts. The false share among all flags is 495/585, about 84.6154%. These use different denominators and can be very different numbers. The phrase “five percent false positives” is ambiguous unless its reference group is stated. Natural-frequency counts make that reference group easier to see.
Keep expected counts separate from observed counts
The False Positive Paradox Calculator scales rates into expected counts for a chosen hypothetical population. Actual finite observations can differ, and the rates must apply to the population being modeled. The tool is educational and does not turn a screening flag into an individual diagnosis or certainty. Read how prevalence changes precision to compare populations. If you already have observed integer counts, use the Confusion Matrix Calculator rather than interpreting expected fractional counts as observed data.
Check the model behind your result
Use the False Positive Paradox Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26