Explain the difference between sensitivity and specificity with an example.

• A. Sensitivity = true positives / (true positives + false negatives); Specificity = true negatives / (true negatives + false positives).
• B. Sensitivity = true negatives / (true negatives + false positives); Specificity = true positives / (true positives + false negatives).
• C. Sensitivity is for ruling in disease; Specificity is for ruling out disease.
• D. Sensitivity uses only positive results; Specificity uses only negative results.

Answer: (A)

Sensitivity and specificity describe how a test performs with respect to people who truly have disease and those who do not. Sensitivity is the proportion of actual positives that the test correctly identifies as positive, calculated as true positives divided by (true positives plus false negatives). Specificity is the proportion of actual negatives that the test correctly identifies as negative, calculated as true negatives divided by (true negatives plus false positives).

For example, if out of 20 people with disease, 18 test positive and 2 test negative, and out of 80 people without disease, 70 test negative and 10 test positive, then sensitivity = 18/(18+2) = 90% and specificity = 70/(70+10) = 87.5%. This matches the standard formulas.

The other statements are not accurate: one swaps the roles of positives and negatives, misstates what each metric measures, or incorrectly claims each metric uses only positive or only negative results. Sensitivity and specificity rely on all four outcome possibilities (TP, FP, FN, TN) and are best understood as the test’s ability to catch disease and to correctly exclude disease, respectively.