# sensitivity and specificity

These are statistical terms that are often confused. These terms can be illustrated by way of an example:

At a particular hospital a MIBG scanner is used to detect phaeochromocytomas. A positive scan was reported in 38 cases. An audit showed:

• true positive (TP) 10, true negative (TN) 25,
• false positive (FP) 0, false negative (FN) 3

where:

• patients with phaeochromocytoma TP (person with a phaeochromocytoma and positive test)
• patients with phaeochromocytoma FN (person with a phaeochromocytoma and negative test)
• patients without phaeochromocytoma FP (person without a phaeochromocytoma with a positive test)
• patients without a phaeochromocytoma TN (person without a phaeochromoytoma with a negative test)

 phaeochromocytoma present phaeochromyctoma absent test result positive TP = 10 test result positive FP = 0 test result negativeFN = 3 test result negativeTN = 25
• sensitivity = 100xTP /(TP+FN) = 100 x 10(10 + 3) = 77%
• i.e. proportion of people with a phaeochromocytoma who are corectly identified by the screening test = 77%

• specificity = 100xTN /(TN+FP) = 100 x 25 /(25+0) = 100%
• i.e. proportion of people without phaeochromocytoma who have had a negative test result = 100%

• positive predictive value = 100xTP/(TP+FP) = 100 x 10/(10+0) = 100%

i.e. the proportion of screening tests that are correct.

Last reviewed 10/2021