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Youden's J Index Calculator

Youden’s J from sensitivity and specificity (or a 2×2 test table) — with likelihood ratios, diagnostic odds ratio and predictive values at your prevalence.

True positives (test +, disease +)

False negatives (test −, disease +)

False positives (test +, disease −)

True negatives (test −, disease −)

Population prevalence for predictive values

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How it works

J = sensitivity + specificity − 1; LR+ = sens ÷ (1 − spec); LR− = (1 − sens) ÷ spec; PPV = sens·p ÷ [sens·p + (1−spec)(1−p)]

Youden's J condenses a test's sensitivity and specificity into one number from 0 (useless) to 1 (perfect), independent of disease prevalence. Its most common use is choosing the cut-off on a ROC curve: the threshold with the highest J is the point farthest above the diagonal. Likelihood ratios translate the same numbers into how much a result should shift your suspicion, and predictive values show what that means in a given population.

Worked example

Sensitivity 90%, specificity 90%: J = 0.80, LR+ = 9, LR− = 0.11. At 10% prevalence PPV is only 50% despite the excellent J.

Frequently asked questions

Why is J prevalence-independent?

Sensitivity and specificity are conditional on true status, so they do not change with how common the disease is — predictive values do.

Is the max-J cut-off always best?

It weights misses and false alarms equally. If one error is costlier, choose the threshold that minimises expected cost instead.

Related calculators

Sensitivity and Specificity Calculator

Evaluate a diagnostic test from its confusion matrix — sensitivity, specificity, PPV, NPV and accuracy from true/false positives and negatives.

F1 Score Calculator (Precision, Recall, Fβ)

From a confusion matrix get precision, recall, F1, F0.5, F2, accuracy, specificity and balanced accuracy for a classifier or a test.

Likelihood Ratio Calculator

Compute positive and negative likelihood ratios for a diagnostic test from its sensitivity and specificity.

For education — check assumptions (sample size, distribution, independence) before using a test result in a real decision.