Free explainer2 min read
Sensitivity formula
Understand the model, recognise it in a stem, separate the look-alikes, then apply it.
Start with the mental model
SensitivityThe proportion of people who truly have a condition that a test correctly identifies as positive.Read more → answers one specific question: of everyone who genuinely HAS the condition, what proportion does the test correctly catch? To find it, you never look at anyone who is disease-free, you look only down the 'diseased' column of a 2×2 table. For example, imagine testing 100 people who are confirmed, by a gold-standard assessment, to have the condition: if the test correctly flags 80 of them as positive and misses 20 (false negatives), its sensitivity is 80/100 = 80%. In practice, this means sensitivity is a property of the TEST, fixed by how good it is at catching true cases, and it does not change depending on how common the condition is in whatever population you happen to test it on.
01Core model
• SensitivityThe proportion of people who truly have a condition that a test correctly identifies as positive.Read more → = TP / (TP + FN): of those WITH disease, how many test positive.
• Only the DISEASED column of the 2×2 table is used, true positives and false negatives; the non-diseased column plays no part in this calculation.
• Worked example: in a 1,000-person table with 80 diseased-and-test-positive and 20 diseased-and-test-negative, sensitivity = 80 / (80 + 20) = 80%. The other 900 people (90 wrongly flagged, 810 correctly cleared) belong to specificityThe proportion of people who truly do not have a condition that a test correctly identifies as negative.Read more → and play no part in this sum.
• A sensitivity of 100% means zero false negatives, every true case tested positive, not that the test is perfect overall (it says nothing about how many disease-free people were wrongly flagged).
• In practice, this means before calculating, first isolate the diseased column, then divide the true positives in it by the column's own total.
02Memory anchor
SensitivityThe proportion of people who truly have a condition that a test correctly identifies as positive.Read more → looks only at people who ARE diseased: TP over (TP + FN).