Normal Distribution
nothing is called 95% until it has been counted
Concept

Misclassification — where it appears

Recording a unit in the wrong category — a positive as negative or the reverse — at rates set by the instrument's sensitivity and specificity. Even a small false-positive rate dominates the count when the true category is rare.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Estimating a prevalence of 0.10% from 1,000 tests. The positive rate reads 5.09%, which is 50.9 times the truth. The Rogan-Gladen correction averages 0.100% — unbiased — with a standard deviation of 0.820 points against the positive rate's 0.695, and it comes out negative on 48.6% of samples.

The prevalence the test has to estimate

Every predictive value takes a prevalence as given, and the prevalence is usually estimated from the same test's positive rate. At a true prevalence of one in a thousand that rate reads 5.09% — fifty times the truth — and the correction that inverts it is unbiased, 18% more variable, and negative on 48.6% of samples of a thousand.

screening · Baserate Thirty surveys of a thousand people, true prevalence 0.1%, test 90% sensitive and 95% specific. Each row is one survey. The thin bar is the corrected estimate ± 1.96 standard errors; the heavy bar is the exact interval for the positive rate carried through the correction; the tick is the one-sided 95% upper limit. 30 of the thirty printed intervals reach below zero and 0 lie entirely below it.

An upper limit is the finding

A survey of a thousand people with a 90%-sensitive, 95%-specific test, estimating a prevalence of one in a thousand, prints a corrected 95% interval that covers the truth 95.17% of the time — and reaches below zero in 97.95% of surveys and lies entirely below zero in 3.35%. Coverage is not the problem. The problem is what the interval can say, and the honest summary of a typical survey is one number: the prevalence is below 1.64%. Bringing that limit down to twice the truth takes 184,521 people at this specificity and 5,083 with a test that never gives a false positive.

screening · Baserate

Named alongside it

The objects these essays reach for when they reach for this one.

PrevalenceSample sizeScreeningSensitivity and specificityBase rateClopper–PearsonConfidence intervalCoverageEstimator biasPredictive value

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