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What's the Difference Between Sensitivity and Specificity?

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University Course Reader · STEM

The screen was reported as 90% accurate, but its sensitivity and specificity were never given separately, so the false alarms stayed invisible.

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Overview

Sensitivity and specificity are the two scores of a yes-or-no test. Sensitivity is the share of real cases the test catches, so a test that flags 9 of 10 real cases scores 90%. Specificity is the share of non-cases the test correctly leaves alone. The scores come from different groups, and a test needs both. A test that flags everything catches all 10 real cases and is still useless, and a single accuracy number can hide exactly that.
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Overview

Sensitivity is a test's catch rate: out of the things it should spot, how many it actually spots. Specificity is its false-alarm control: out of the things it should ignore, how many it correctly ignores. You need both, and here is why. A teacher swears she can spot copied homework, and in a class of 50 essays, 5 are copied. She accuses all 50. Sensitivity: perfect, all 5 caught. Specificity: zero, 45 innocent kids in detention. Catching everything is easy. Catching only the guilty is the skill. 😎

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Detail

Sensitivity and specificity are the two scores that say how good a yes-or-no test is. Sensitivity is the share of real cases the test catches. Specificity is the share of non-cases it correctly leaves alone. Each score is measured on a different group of cases where the truth is already known. A trained dog checks 200 bags, and 10 of them carry the scent it is trained to find. The dog flags 9 of those 10, so its sensitivity is 90%. Of the 190 clean bags, it stays quiet on 171 and flags 19 by mistake, so its specificity is also 90%. The 1 scented bag it missed is a false negative; the 19 clean bags it flagged are false positives. There is also a single number called accuracy: correct calls out of all 200 bags, which is 9 plus 171, so 180 of 200, again 90%. Notice what that one number hides: of the dog's 28 flags, the 9 real plus the 19 mistaken, 19 point at nothing. Clean bags outnumber scented ones 190 to 10, so false alarms pile up even when both scores are high. That is why one number is never enough: ask what the test catches, and ask what it flags by mistake.
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Detail

Sensitivity is a test's catch rate: of the errors it was built to find, how many it flags. Specificity is its restraint: of the things that were fine, how many it correctly skips over. Take a spellchecker on a 1,000-word essay that contains 20 typos. It flags all 20: catch rate 100%. The other 980 words are spelled fine, but it flags 150 of those too, surnames and jargon mostly, and skips only 830: restraint 85%. Now the sales-page version: this checker gets 85% of words right. True, since 20 caught and 830 skipped make 850 right out of 1,000. Also useless, because that one number omits the 150 wrong flags you had to check by hand. So put two questions to a test, always the same two: how much of the real problem does it catch, and how much fine material does it flag anyway? One number answers neither. 😎

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Analogy

A porch light on a motion sensor ran all month. Of the 12 real visitors who came up the path, it lit for all 12. Of the 60 times a raccoon or a moth crossed the yard, it lit for 40. Scored as a detector, that is perfect sensitivity, every real visitor caught, and poor specificity, only 20 of 60 non-visitors left in the dark. The light never misses a visitor, and it spends most of its evenings lighting up for raccoons. Judge it on either tally alone and it is flawless or broken; both together say what it is worth.
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Analogy

You know the friend who predicted all 6 celebrity breakups this year, called in advance, a spotless record on the ones that happened. She also called 30 that did not. Sensitivity is the part she brags about, 6 for 6. Specificity is the part she skips, the 30 couples doing just fine. Anyone can go 6 for 6 by predicting doom for everybody. The skill was not the catching. It is catching without the extra 30. 😎
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AI explanations may contain errors · Not professional advice

Formal definition — The same term, explained the usual way

Sensitivity is the proportion of genuinely positive cases that a test classifies as positive, also called the true positive rate. Specificity is the proportion of genuinely negative cases that the test classifies as negative, the true negative rate. The two are computed on disjoint groups, so they can be reported for any test that returns a yes-or-no result, and neither can be inferred from the other or from a single overall accuracy figure, since overall accuracy also depends on the relative sizes of the two groups. A test may therefore combine high sensitivity with low specificity or the reverse, and evaluating a test requires both quantities.

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