The specificity of a test is the probability that the test will be negative among patients who do not have the disease. Specificity is sometimes abbreviated Sp. The formula for specificity is
Sp = TN / (TN + FP)
where TN and FP and the number of true negative and false positive results, respectively. You can think of specificity as 1 - the false positive rate. Notice that the denominator for specificity is the number of healthy patients. Using conditional probabilities, we can also define specificity as
Sp = P [ Test is negative | Patient is healthy ]
The following table summarizes these calculations.
A large specificity means that a positive test can rule in the disease. David Sackett coined the acronym "SpPIn" to help us remember this.
Here is an example of a specificity calculation.
- In a study of the urine latex agglutination test (AJPH
1998;88(2):285-288), children were tested for H. influenzae using blood,
urine, cerebrospinal fluid, or some combination of these.
Of all the children tested, 1,352
did not have H. influenzae in any of these fluids.
Only 9 of these patients tested positive
on the urine latex agglutination test, the
remaining 1,343 tested negative. The
specificity is 1343 / 1352 = 99.3%.