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Sensitivity, specificity and predictive values

14 min

  • Calculate diagnostic sensitivity against the reference classification
  • Calculate diagnostic specificity against the reference classification
  • Calculate positive and negative predictive values

Read the full reference

Try first

Try first

A new rapid test is compared with a reference standard in 200 people. The counts are TP = 45, FN = 5, FP = 30 and TN = 120. What is the test's diagnostic sensitivity?

The next section explains it.

The next section explains it.

The next section explains it.

Right. The next section explains why.

The next section explains it.

Get the idea

A diagnostic accuracy study sorts every participant twice: once by the test being studied and once by a reference standard that decides who has the target condition. The four possible pairings form a two-by-two table.1,2

Reference: condition presentReference: condition absent
Test positiveTrue positive (TP)False positive (FP)
Test negativeFalse negative (FN)True negative (TN)

Each measure is a fraction of one row or one column, and the skill is choosing which.

Down the columns: sensitivity and specificity

These start from what the reference standard says.

  • Sensitivity works down the first column. It is the share of the people the reference standard calls positive that the test also calls positive.
  • Specificity works down the second column, among the people the reference standard calls negative.

sensitivity = TP ÷ (TP + FN) × 100%

specificity = TN ÷ (TN + FP) × 100%

Across the rows: predictive values

Predictive values start from the test result a clinician receives.1,3

  • The positive predictive value (PPV) is the share of positive results that are true.
  • The negative predictive value (NPV) is the share of negative results that are true.

PPV = TP ÷ (TP + FP) × 100%

NPV = TN ÷ (TN + FN) × 100%

When the population changes

The two pairs behave differently when the tested population changes.1,3

  • Sensitivity and specificity describe the test at a stated cutoff, in the kind of population studied, and they can still differ from one study setting to another.
  • Predictive values also depend on prevalence, the share of tested people who have the condition. As a condition becomes rarer, false positives make up a larger part of the positive row, so PPV falls and NPV rises, even with the same test and cutoff.

Check the denominator

A quick check catches most errors: name the denominator before dividing.

  • A column total gives sensitivity or specificity.
  • A row total gives a predictive value.
References
  1. US Food and Drug Administration. Statistical Guidance on Reporting Results from Studies Evaluating Diagnostic Tests: Guidance for Industry and FDA Staff. Final guidance. Issued March 13, 2007. Accessed September 23, 2026.
  2. Clinical and Laboratory Standards Institute. Evaluation of Qualitative, Binary Output Examination Performance. 3rd ed. CLSI guideline EP12. Clinical and Laboratory Standards Institute; 2023. Accessed August 31, 2026.
  3. Bishop ML, Fody EP, Van Siclen C, Mistler JM, Moy M. Clinical Chemistry: Principles, Techniques, and Correlations. 9th ed. Jones & Bartlett Learning; 2023.

Watch one

A screening test has a sensitivity of 95% and a specificity of 90%. It is used in 1,000 people, 10% of whom have the condition. What are the PPV and NPV in this group?

  1. Split the group by the reference standard: 10% of 1,000 = 100 with the condition and 900 without.

    Predictive values need counts in every cell, and prevalence says how the people divide between the two columns.

  2. Fill that column: TP = 0.95 × 100 = 95, so FN = 100 − 95 = 5.

    Sensitivity is a fraction of the condition-present column.

  3. Fill the other column: TN = 0.90 × 900 = 810, so FP = 900 − 810 = 90.

    Specificity is a fraction of the condition-absent column.

  4. PPV = 95 ÷ (95 + 90) = 95 ÷ 185 = 51.4%.

    PPV starts from everyone with a positive result, so it uses the test-positive row.

  5. NPV = 810 ÷ (810 + 5) = 810 ÷ 815 = 99.4%.

    NPV starts from everyone with a negative result, so it uses the test-negative row.

PPV is 51.4% and NPV is 99.4%. At 10% prevalence, about half the positive results come from people without the condition.

Your turn

Problem 1 of 3

A binary test is compared with a designated reference standard in 200 participants: TP = 90, FN = 10, FP = 20, and TN = 80. What is the estimated diagnostic sensitivity?

Incorrect. 80 ÷ (80 + 20) is specificity, using participants without the target condition.

Incorrect. 90 ÷ (90 + 20) is positive predictive value, using all test-positive participants.

Correct. Sensitivity uses participants with the target condition: 90 ÷ (90 + 10) × 100 = 90%.

Hint
  1. Sensitivity is calculated among the participants the reference standard calls positive.
  2. Those participants are the true positives and the false negatives.

Review Diagnostic performance

Problem 2 of 3

A test is compared with a reference standard in 200 participants: TP = 72, FN = 8, FP = 12 and TN = 108. What is the diagnostic specificity?

Hint
  1. Specificity looks only at the people without the condition.
  2. Those people are the true negatives and the false positives.
  3. Divide the true negatives by that column's total.
Show the answer

90 %

The reference standard calls 108 + 12 = 120 participants negative, and the test called 108 of them negative: 108 ÷ 120 × 100 = 90%.

Review Diagnostic performance

Problem 3 of 3

In a study of 200 participants, TP = 38, FP = 12, FN = 2 and TN = 148. What is the positive predictive value?

Show the answer

76 %

Fifty participants tested positive (38 + 12), and 38 of those results were true: 38 ÷ 50 × 100 = 76%.

Review Diagnostic performance

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