A LEARNING EXPERIMENT / UNIVABIO 2026
A test can detect most cases and still produce more false alarms than true positives. Count the people. Change one assumption. See why.
For learning only. These invented rates do not estimate anyone’s health risk or recommend a screening test.
Four possible outcomes.
Expected counts may be fractional. Squares are rounded; calculations use the exact counts.
Pin one experiment, then change the lab above. The test can stay exactly the same while the meaning of a positive result changes.
A is pinned to the rare-condition example. B follows the lab.
| Measure | A · pinned | B · current |
|---|
The same test, across different populations.
| Prevalence | True among positive |
|---|
The line uses B’s test settings. It starts at 0% prevalence; an undefined value is left blank.
THE ASSUMPTION MATTERS
Only people positive on the first test go through this second step. These rates describe that selected group, not the whole population.
Independence is an invented assumption here, not evidence about a real test.
AMONG TWO POSITIVE RESULTS
76.6%A second step can lose true positives as well as remove false positives. This is a mathematical demonstration, not a recommendation to repeat a real test.
Three short experiments. Make an estimate before revealing the arithmetic, then name the group in the denominator. This is practice, not a test of your health knowledge.
YOUR LEARNING NOTEBOOK
Your first guesses are kept for this tab only. A smaller gap on these cases is not proof of learning or a clinical result. Try explaining the change in your own words to the coach.
| Case | Guess | Actual | Gap | Denominator choices |
|---|
Answers stay in this tab. Export saves numeric guesses and selected options to a file; coach explanations are excluded.
Explain the current lab result. A small trained classifier suggests a review topic. Confirm or change the focus, check a factual answer, then revise your explanation. A topic suggestion cannot verify your reasoning.
A SECOND LOOK AT YOUR REASONING
How can a rare condition and a small false-positive rate combine to produce this result?
Model feedback is a suggestion. The arithmetic is calculated separately and does not depend on AI.
REPRESENTATION
Natural frequencies make the relevant groups visible. The square grid and frequency tree are two views of the same expected counts. The result uses Bayes’ theorem; population size changes counts, not proportions.
Hoffrage et al., 2015 · original study ↗Research informed the representation. BaseRate itself has not had a learner study.
SCREENING
False positives and missed cases matter. These three rates cannot establish the benefits, harms or suitability of a real screening program. There is no personal diagnosis, risk estimate or treatment advice here.
National Cancer Institute · overview ↗MODEL CARD
The app does not send your explanation to a generative model. Static files are downloaded from GitHub Pages.
For population N, prevalence p, sensitivity s and specificity c, expressed as proportions:
TP = N × p × s
FP = N × (1 − p) × (1 − c)
FN = N × p × (1 − s)
TN = N × (1 − p) × c
PPV = TP ÷ (TP + FP)For a second test among first-positives: both-positive true cases = TP × conditional detection; both-positive non-cases = FP × conditional false-positive rate. Reusing unconditional rates requires a conditional-independence assumption. A zero denominator has no defined proportion.
Only visual squares are rounded. Expected counts, comparisons, curves and practice answers retain the unrounded values.