[Durgical](https://durgical.com/en/) › [DurgiPedia](https://durgical.com/en/durgipedia/) › [Epidemiology](https://durgical.com/en/epidemiology/) › [Diagnostic tests](https://durgical.com/en/epidemiology/areas/diagnostic/) › Positive and negative predictive values

# Positive and negative predictive values

- Measure

If the test is positive (or negative), how likely the person is to have (or not have) the disease.

Updated Nov 5, 2026

## Key points

- PPV = TP / (TP + FP) = a / (a + b); NPV = TN / (TN + FN) = d / (c + d).
- They are calculated across rows: they start from the test result.
- They answer the patient's question: I tested positive, how likely is it that I am ill?
- They depend on prevalence: at low prevalence PPV falls and NPV rises.
- They cannot be carried over from a referral hospital to the general population.

On this page

- The basics Key points
- What it is
- Formula and reading
- Worked example
- The example table, read across rows
- Markers
- How to read it
- Common pitfalls
- Memory aid

- Study Test yourself

- Connections Connections

## What it is

Predictive values answer the question a patient asks while holding the result. The positive predictive value (PPV) is the proportion of diseased people among those who tested positive; the negative predictive value (NPV) is the proportion of healthy people among those who tested negative. They are read across the rows of the 2×2 table and, unlike sensitivity and specificity, they change a lot with the prevalence of the group tested.

## Formula and reading

- PPV = TP / all positives; NPV = TN / all negatives.
- Reading: a PPV of 33% means 2 of every 3 positives are false positives.
- PPV equals the post-test probability after a positive result; NPV equals 1 − the post-test probability after a negative one.
- They hold only for a prevalence similar to that of the study that measured them.

## Worked example

- Data: a clinic tests 1,000 people; 100 have the disease. The test has 90% sensitivity and 80% specificity.
- Diseased: 90% of 100 = 90 true positives and 10 false negatives.
- Healthy: 80% of 900 = 720 true negatives and 180 false positives.
- PPV = 90 / (90 + 180) = 90 / 270 ≈ 0.333, that is 33%.
- NPV = 720 / (720 + 10) = 720 / 730 ≈ 0.986, that is 98.6%.
- Reading: a positive is right 1 time in 3; a negative is right almost 99 times in 100.

## The example table, read across rows

| Result | Diseased | Healthy | Total | Predictive value |
| --- | --- | --- | --- | --- |
| Positive | 90 | 180 | 270 | PPV = 90/270 ≈ 33% |
| Negative | 10 | 720 | 730 | NPV = 720/730 ≈ 98.6% |
| Total | 100 | 900 | 1,000 | Prevalence = 10% |

## Markers

- PPV
- NPV

## How to read it

- When explaining a positive screening result, it helps to say that it may be false and needs confirmation.
- A high NPV allows reassurance for someone who tests negative on a screening test with good sensitivity.

## Common pitfalls

- Calculating predictive values down columns.
- Using the PPV published by a referral centre in a population with much less disease.
- Confusing PPV with sensitivity.

## Memory aid

The patient reads the row: they start from their own result, positive or negative, and ask what lies behind it.

## Test yourself

Think of the answer, then tap the question to see it.

## There are 40 true positives and 60 false positives. What is the PPV?

40 / (40 + 60) = 0.40, that is 40%.

## Which question does the negative predictive value answer?

If the test is negative, how likely it is that the person truly does not have the disease.

## Why is a test's PPV different in a referral hospital and in the community?

Because it depends on prevalence: the community has fewer diseased people, so a larger share of positives are false.

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## Connections

## Related 5

- [How prevalence changes predictive values](https://durgical.com/en/epidemiology/how-prevalence-changes-predictive-values/)
- [Sensitivity](https://durgical.com/en/epidemiology/sensitivity/)
- [Specificity](https://durgical.com/en/epidemiology/specificity/)
- [Pre-test and post-test probability](https://durgical.com/en/epidemiology/pre-test-and-post-test-probability/)
- [The 2×2 table](https://durgical.com/en/epidemiology/the-2-2-table/)

[← All of epidemiology](https://durgical.com/en/epidemiology/)

Educational content on epidemiological and statistical methods; the examples use made-up numbers to teach the calculation. Not a clinical or legal guide: current Colombian rules are in the official sources.

Sources: [Sensitivity, Specificity, and Predictive Values: Foundations, Pliabilities, and Pitfalls in Research and Practice](https://www.frontiersin.org/articles/10.3389/fpubh.2017.00307/full) (Frontiers in Public Health, 2017); [Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests - Guidance for Industry and FDA Staff](https://www.fda.gov/regulatory-information/search-fda-guidance-documents/statistical-guidance-reporting-results-studies-evaluating-diagnostic-tests-guidance-industry-and-fda) (U.S. Food and Drug Administration, 2007).

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Representative model, for educational purposes only.

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License: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Cite as: DurgiPedia (durgical.com), https://durgical.com/en/epidemiology/positive-and-negative-predictive-values/