When a positive test is probably wrong: a maths EPQ idea
A title to start from
Why can a positive result from an accurate medical test still be more likely wrong than right?
Why it works as an EPQ
Conditional probability gives a surprising, important answer, and you can judge how it should change screening policy.
Scope and difficulty
Accessible. Accessible. Tree diagrams, then natural frequencies, then one real screening programme.
The maths
Builds on these A Level topics: Probability.
You would learn:
- Bayes' theorem
- Sensitivity, specificity and prevalence
- Natural frequency explanations
One possible plan
- Explain sensitivity, specificity and prevalence.
- Calculate the chance a positive is a true positive in several settings.
- Test which explanation people understand best (a small, consented, anonymous survey).
- Judge the case for and against screening a whole population.
Pitfalls
- Personal medical advice.
- Figures for real tests with no source.
Where to start reading
- The Art of Statistics (David Spiegelhalter)
- NHS screening programme information on nhs.uk
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