Tests and Base Rates
With an imaginary disease and an imaginary test, see with dots how many people who test positive really have it.
This is an educational model of an imaginary disease and an imaginary test. It is not medical advice.
- Sick, positive: 9
- Healthy, positive: 89
- Sick, negative: 1
- Healthy, negative: 901
Of 98 positives, 9 are really sick (9.2%). By formula: 9.2%
Auto tally: 0 groups (0 people): —
The share of positives who are truly sick equals prevalence × sensitivity ÷ (prevalence × sensitivity + healthy share × false-positive rate). When the disease is rare, false alarms from the large healthy group can outnumber true positives. The base rate matters as much as the quality of the test.
How to play
Each dot is one person in a group of 1,000. Three sliders set how common the disease is (prevalence), how often sick people test positive (sensitivity), and how often healthy people test negative (specificity). "Auto" keeps making random groups of 1,000 and tallies how many positives were really sick.
Learn more
This is an educational model of an imaginary disease and an imaginary test. It is not medical advice.
The share of positives who are truly sick equals prevalence × sensitivity ÷ (prevalence × sensitivity + healthy share × false-positive rate). When the disease is rare, false alarms from the large healthy group can outnumber true positives. The base rate matters as much as the quality of the test.