Two factory inspection trays with different mixes of green and ivory components. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
Hold conditional performance fixed and vary the population
Suppose a hypothetical classifier has sensitivity 90% and specificity 95%. Those rates describe performance within actual positive and actual negative classes. Precision instead asks what fraction of predicted positives are actually positive. Even when the two class-specific rates stay fixed, changing the actual positive prevalence changes the mixture of cases arriving in the predicted-positive group.
Compare two prevalence settings
At 1% prevalence, the positive predictive value is (0.9×0.01)/[(0.9×0.01)+(0.05×0.99)], approximately 15.3846%. At 10% prevalence, it is (0.9×0.1)/[(0.9×0.1)+(0.05×0.9)] = 66.6667%. The classifier's entered sensitivity and specificity did not improve; the population mixture changed.
| Prevalence | Sensitivity | Specificity | Precision |
|---|---|---|---|
| 1% | 90% | 95% | 15.3846% |
| 10% | 90% | 95% | 66.6667% |
Do not assume transportability without evidence
This comparison is conditional on holding the class-specific rates fixed. In practice, a changed population may contain different case difficulty, measurement conditions or label quality, so sensitivity and specificity can change too. A controlled thought experiment is useful for isolating prevalence; it is not proof that performance transfers unchanged between settings.
Report the population behind a precision figure
Use the False Positive Paradox Calculator to explore prevalence while keeping the assumptions visible. Increasing the illustrative population size scales expected counts but leaves precision unchanged. The natural-frequency guide explains the count table. For a general binary-evidence update without the population-count emphasis, use the Bayes' Theorem Calculator. A model's precision should be reported with its evaluation population and threshold rather than treated as a permanent property detached from how and where the model is used.
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