Sensitivity vs Specificity

Sensitivity is the proportion of people with the disease who test positive; specificity is the proportion of people without the disease who test negative. They describe how well a test performs against a reference standard and do not depend (in principle) on disease prevalence.

From the 2×2 table

• Sensitivity = TP / (TP + FN)
• Specificity = TN / (TN + FP)

Illustrative example with worked numbers

Invented for teaching. Of 100 patients with a condition, a test is positive in 90 (TP = 90, FN = 10): sensitivity 90%. Of 900 patients without the condition, the test is negative in 810 (TN = 810, FP = 90): specificity 90%.

Using them in practice

• A highly sensitive test, when negative, helps rule out disease ("SnNout") because it rarely misses cases.
• A highly specific test, when positive, helps rule in disease ("SpPin") because it rarely gives false alarms.
• These mnemonics are rules of thumb; always consider the pre-test probability and the cost of errors.

Trade-off and thresholds

For tests with continuous results, moving the cut-off increases sensitivity and decreases specificity, or the reverse. The ROC curve displays this trade-off (see What Is an ROC Curve?).

What they do not tell you

Sensitivity and specificity do not tell you the probability that a positive result is correct in a particular patient: that depends on prevalence (see Positive Predictive Value vs Negative Predictive Value). Their values can also vary across patient spectrums and settings.

Common pitfalls

• Reporting accuracy without confidence intervals.
• Assuming they transfer unchanged to a different population.

Key takeaways

• Sensitivity = detects disease; specificity = excludes non-disease.
• Interpret with prevalence and clinical context.

This page is general educational information about research methods. It is not medical, legal or regulatory advice; follow your institution's ethics board and your target journal's instructions.