Population screening test

Results of a fictional community screening programme for a silent condition, using a rapid test, in 5 000 adults. Each row is one person: age group, sex, whether they truly have the condition (established later by a definitive reference test) and the rapid test result. With prevalence around 2%, sensitivity ≈0.92 and specificity ≈0.95, most positive results are false positives — the classic setting for Bayes' theorem, positive predictive value and the base-rate fallacy.

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Rows: 5,000
Columns: 5
One row is: one screened person
Version: v1

Data dictionary

Column	Type	Summary	Description
`person_id` Person	id		Anonymous participant code.
`age_group` Age group	ordinal	3 levels: 18-39, 40-59, 60+	Age band in years.
`sex` Sex	category	2 levels: Female, Male	Sex.
`has_condition` Has condition	boolean	2 levels	True condition status from the definitive reference test.
`test_positive` Test positive	boolean	2 levels	Result of the rapid screening test.

What it is good for

Build a 2×2 table of test result vs true condition.
Compute sensitivity, specificity, PPV and NPV, and explain why PPV is low when prevalence is low.
Apply Bayes' theorem and check it against the observed table.
Show how PPV changes across age groups with different prevalence.

Methods: contingency table, conditional probability, Bayes' theorem, sensitivity and specificity, predictive values, confidence interval for a proportion.

Data quality notes

Only about 2% have the condition, so the observed sensitivity rests on roughly 100 people and is imprecise.
PPV is below 30% overall even though the test is 'accurate'.
Fictional programme and condition; no missing values.

Provenance and licence

Age group: 18–39 (45%), 40–59 (35%), 60+ (20%). True condition ~ Bernoulli with age-specific prevalence 0.8%, 2.0%, 4.5% (≈2% overall). Test positive ~ Bernoulli(0.92) if the condition is present, Bernoulli(0.05) if absent.

Synthetic data · CC0-1.0 (synthetic data generated by Statistics Quest) · generated deterministically (seed 20241015). It does not describe real people or organisations; any resemblance is coincidental.

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Dataset

Population screening test

5,000 rows · one row = one screened person · synthetic data

About this dataset Open in the lab

Person	Age group	Sex	Has condition	Test positive
S0001	18-39	Male	false	false
S0002	18-39	Female	false	false
S0003	60+	Female	false	false
S0004	18-39	Male	false	false
S0005	18-39	Male	false	false
S0006	18-39	Male	false	false
S0007	18-39	Female	false	false
S0008	40-59	Male	false	false
S0009	18-39	Female	false	false
S0010	40-59	Male	false	false
S0011	60+	Female	true	true
S0012	60+	Female	false	false

Used in

Conditional probability · Probability
Bayes' theorem · Probability
Theory versus simulation · Probability
Interval for a proportion · Estimation and Confidence Intervals
Rates and proportions in public health · Applied Statistics for Professionals
Bayesian thinking: prior, likelihood, posterior · Advanced Foundations
Evaluating classifiers · Advanced Foundations
Evaluating a screening programme · Case