Negative predictive value
Section of Predictive values of a test, part of Statistical inference
Negative predictive value
| Type | Section |
| Taught in | Predictive values of a test |
| Part | Statistical inference |
| Questions using it | 1 |
The negative predictive value is the probability the condition is absent given a negative test,
\mathrm{NPV}=\mathbb{P}(D^c\mid T-)=\frac{p_0(1-\alpha)}{p_0(1-\alpha)+p_1\beta}=\frac{1-\alpha}{(1-\alpha)+R\beta}.
For the screening test with sensitivity and specificity 0.95 and prevalence 0.005,
\mathrm{NPV}=\frac{0.995\times 0.95}{0.995\times 0.95+0.005\times 0.05}=\frac{0.94525}{0.9455}=0.9997.
A negative result is very trustworthy precisely because the condition is rare and the test does not miss many cases. The asymmetry with the PPV is the point of keeping the two names. A test can be trusted when it says “absent” and not trusted when it says “present”, or the reverse if the condition is common and the sensitivity is poor. Reporting only the sensitivity describes neither of those decisions.
The same split is why a small p-value and a large p-value are not mirror images in a rare-effect setting. A rejection can still be a false rejection if most hypotheses tested are null. A non-rejection, when the power is decent and the effect would have mattered, is stronger evidence for the null than the PPV analogy suggests only if the prior odds are not already tiny. The formula, not the surprise, decides which way the asymmetry goes.
Used in
- Taught in Predictive values of a test
- Questions that use it (1) — The matching negative predictive value
- All 2 questions on Predictive values of a test
See also
Positive predictive value · Fallacy of the transposed conditional · Sensitivity and specificity