See the math behind testing & treatment

Watch a population flow through a test and a treatment into outcomes. Change any input and every view updates live — from false positives and predictive value to who is actually helped or harmed. No verdicts, just the numbers.

Worth the Test is a free, interactive calculator and visualizer for medical-screening statistics: positive and negative predictive value (PPV / NPV), sensitivity, specificity, likelihood ratios (LR+ / LR−), Bayes’ theorem, the Fagan nomogram, false-positive rates, serial (repeat) testing, and number-needed-to-treat, -harm, and -screen (NNT / NNH / NNS). Set the prevalence, the test’s accuracy, and a treatment’s benefit and harm, then watch a single cohort flow from population → test → treatment → outcome.

What this tool shows

• A live Population → Test → Treatment → Outcome cohort cascade
• A 2×2 confusion matrix (true / false positives and negatives)
• A Bayes probability tree with a PPV read-out
• PPV & NPV plotted against prevalence — the base-rate fallacy, made visible
• A Fagan nomogram: pre-test probability → likelihood ratio → post-test probability
• Serial / repeat-testing cumulative false-positive risk (1 − specificityⁿ)
• Bayesian updating with a Beta-Binomial posterior and 95% credible interval
• Who is helped, harmed, or unchanged — with NNT / NNH / NNS

Key terms

Prevalence (pre-test probability)

How common the condition is in the group being tested. The starting point for everything downstream.

Sensitivity

Of people who have the condition, the share the test correctly flags positive.

Specificity

Of people who do not have it, the share the test correctly clears.

PPV / NPV

Given a positive (or negative) result, the chance it is right. Unlike sensitivity/specificity, these depend heavily on prevalence.

Likelihood ratio (LR)

How much a result shifts the odds. LR+ for a positive, LR− for a negative — and they do not depend on prevalence.

NNT / NNH

Number needed to treat for one person to benefit; number needed to harm for one to be harmed.

NNS

Number needed to screen for one person to be helped — screening, testing, treatment, and outcomes all folded together.

The formulas

• PPV and NPV are computed with Bayes’ theorem from prevalence, sensitivity, and specificity.
• LR+ = sensitivity / (1 − specificity)
• LR− = (1 − sensitivity) / specificity
• NNT = 1 / absolute risk reduction (ARR)
• NNS = people screened ÷ people helped

Educational model — not medical advice. It illustrates the statistics of testing and treatment; it does not describe any specific real-world test. Privacy & cookies