A positive test result: how likely is it that you really have the condition?

AA HLAA SLAI SLAI HL Solid Also in: Probability

Research question

For a screening test with published sensitivity and specificity, how does the probability that a positive result is correct depend on how common the condition is, and how much does a second independent test help?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Even an accurate test can give mostly false positives when a condition is rare — a result that surprises many doctors in surveys. Bayes' theorem makes this precise and has real consequences for screening policy.

The mathematics you'll need

Conditional probability and tree diagrams
Bayes' theorem (AA HL; explain for others)
Positive predictive value as a function of prevalence
Repeated testing and independence assumptions

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Use published sensitivity, specificity and prevalence figures for a real screening programme (cite the health authority).

WHO Global Health Observatory — 1,000+ health indicators by country (immunisation, mortality, risk factors).

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain sensitivity, specificity and prevalence.
Derive the positive predictive value.
Graph it against prevalence.
Model a second test.
Reflect on why tests are targeted at high-risk groups and on independence of repeat tests.

Pitfalls that cost marks

Confusing P(positive | ill) with P(ill | positive).
Unsourced test figures.
Assuming repeat tests are independent without comment.

Showing personal engagement

Survey adults' intuition with a scenario and compare with the truth.
Choose a test relevant to someone you know (without personal medical details).
Design a clear graphic for patients.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Add a cost for each outcome and find the prevalence at which screening everyone is worthwhile.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).