Medical Tests and Base Rates
Why positive results can still be probably false.
Key idea
Why positive results can still be probably false.
In depth
A positive test for a rare condition is often a false alarm, since healthy people vastly outnumber sick ones. The base rate (prevalence) must be combined with sensitivity and specificity through Bayes’ theorem.
Worked example
A disease affects 1%, test sensitivity 99%, false positive 5%: P(sick | positive) = 0.0099/(0.0099 + 0.0495) ≈ 17%.
Real-world uses
- Explaining why a rare disease test with 95% accuracy still gives many false alarms
Common mistake
Ignoring the base rate and assuming 99% accuracy means 99% certainty.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Medical Tests and Base Rates?
Why positive results can still be probably false. It is a topic at the expert level in Probability & Statistics.
Where is Medical Tests and Base Rates used in real life?
Real-world examples: Explaining why a rare disease test with 95% accuracy still gives many false alarms.
What should I learn before Medical Tests and Base Rates?
Make sure you are comfortable with Bayes’ Theorem, the previous topic in Probability & Statistics.
What is a common mistake with Medical Tests and Base Rates?
Ignoring the base rate and assuming 99% accuracy means 99% certainty.
How can I practise Medical Tests and Base Rates?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Medical Tests and Base Rates?
Move on to Random Variables next.
Related expert topics in Probability & Statistics
- Skewness and Kurtosis – Measures of asymmetry and tail heaviness.
- Residuals and R² – Error of a fit and proportion of variance explained.
- Simpson’s Paradox – A trend reverses when groups are combined.
- Law of Total Probability – Split an event over a partition.
- Bayes’ Theorem – Update beliefs with evidence.
- Linearity of Expectation – Expectation of sums is sum of expectations.