Sensitivity, Specificity, PPV and NPV: Formulas and Examples

Sensitivity asks how often a test is positive when disease is present; specificity asks how often it is negative when disease is absent. PPV and NPV reverse the question: what does a positive or negative result mean? The quickest way to separate them is to draw a 2×2 table and choose the correct denominator.

Below, two worked examples use the same assumed sensitivity and specificity at different disease prevalences. You can check every calculation, see why predictive values change, and learn where the SnNout/SpPin shortcut needs caution.

What sensitivity, specificity, PPV and NPV measure

A diagnostic test gives evidence about a condition. These four statistics describe its results from different starting points.

Two describe performance within disease-defined groups, at a specified threshold and in the population studied:

• Sensitivity — how good the test is at picking up disease when it is truly present.
• Specificity — how good the test is at correctly clearing people who are truly disease-free.

Two of them describe what a result actually means for the patient in front of you:

• Positive predictive value (PPV) — given a positive result, how likely the patient really has the disease.
• Negative predictive value (NPV) — given a negative result, how likely the patient really is disease-free.

For the calculations below, we hold sensitivity and specificity fixed and change prevalence. PPV and NPV then change. Do not turn that modelling assumption into a claim that measured sensitivity and specificity are identical in every population: case-mix, disease severity, thresholds and study methods can change observed performance. An analysis of 6,909 diagnostic-accuracy studies documents why this distinction matters.

This sits squarely in the statistics and clinical-measurement corner of Paper A. If you want the wider map, our EDAIC statistics made simple guide covers probability, error types and study design, and the physics and clinical measurement high-yield article handles the sister topics that share the same exam questions.

Build the 2x2 table first — always

Almost every diagnostic-statistics question yields to one habit: draw the 2x2 table before you do anything else. It converts a wordy stem into four boxes, and every formula is just a ratio of those boxes.

The two columns are the reference classification (disease present or absent). In these examples we treat that classification as correct; real reference standards can also be imperfect. The two rows are the test result (positive or negative).

Four cells, four names. Learn them as a unit:

• True Positive (TP) — test says yes, disease is there. Correct.
• False Positive (FP) — test says yes, no disease. A false alarm.
• False Negative (FN) — test says no, but disease is there. A missed case. The consequences depend on the condition and the decisions that follow.
• True Negative (TN) — test says no, disease is absent. Correct.

Once those four numbers are in the boxes, every statistic falls out mechanically.

The four formulas, read off the table

Notice the pattern: sensitivity and specificity read down the columns (you condition on the truth). Predictive values read across the rows (you condition on the test result).

• Sensitivity = TP / (TP + FN) — of all the people who truly have the disease, the fraction the test catches. Down the "disease present" column.
• Specificity = TN / (TN + FP) — of all the people who are truly disease-free, the fraction the test correctly clears. Down the "disease absent" column.
• PPV = TP / (TP + FP) — of all the people who test positive, the fraction who genuinely have the disease. Across the "test positive" row.
• NPV = TN / (TN + FN) — of all the people who test negative, the fraction who are genuinely disease-free. Across the "test negative" row.

A clean way to remember the direction: Se and Sp start from the truth and look at the test; PPV and NPV start from the test and look at the truth. That distinction is the heart of positive predictive value vs sensitivity — they sound similar but answer opposite questions, and swapping those denominators changes the answer.

SnNout and SpPin: useful reminders, not guarantees

• SnNout: a highly sensitive test with a negative result can help rule disease out.
• SpPin: a highly specific test with a positive result can help rule disease in.

Neither mnemonic proves that disease is absent or present. The starting probability, both sensitivity and specificity, and the clinical decision threshold still matter. A useful result reduces uncertainty enough for the decision being considered; it does not create certainty.

Use this original numerical check. Assume sensitivity 99%, specificity 50% and a pre-test probability of 90%. The negative likelihood ratio is (1 − 0.99)/0.50 = 0.02. Pre-test odds are 9, so a negative result gives post-test odds 9 × 0.02 = 0.18, or a disease probability of 15.3%. High sensitivity alone has not made disease impossible.

For revision, learn the mnemonic and then ask what it leaves out. That habit is useful when reading each statement in an EDAIC MTF question.

A fully worked example

Numbers make this stick. Imagine a hypothetical screening test evaluated against a correct reference classification in 1,000 patients. The true prevalence of the disease in this group is 10%, so 100 patients genuinely have it and 900 do not.

Suppose the test has a sensitivity of 90% and a specificity of 80%. Let's populate the table.

• Of the 100 diseased patients, sensitivity 90% catches 90 → TP = 90, leaving FN = 10.
• Of the 900 disease-free patients, specificity 80% correctly clears 720 → TN = 720, leaving FP = 180.

Now read the statistics straight off the boxes:

• Sensitivity = 90 / (90 + 10) = 90% ✓ (matches the input, a good sanity check)
• Specificity = 720 / (720 + 180) = 80% ✓
• PPV = 90 / (90 + 180) = 90 / 270 = 33.3%
• NPV = 720 / (720 + 10) = 720 / 730 = 98.6%

Pause on the PPV. The test is 90% sensitive and 80% specific, yet a positive result corresponds to genuine disease only one time in three. Two-thirds of the positives are false alarms. That result follows from the combination of the assumed specificity and the low prevalence. The 180 false positives are drawn from the large pool of 900 healthy people, and they swamp the 90 true positives drawn from the small pool of 100 diseased ones.

The NPV is 98.6%, leaving about a 1.4% probability of disease after a negative result in this model. Whether that residual probability is acceptable depends on the decision; it is not answered by calling the NPV “high”.

How prevalence changes the predictive values

For a second hypothetical population, assume sensitivity remains 90% and specificity remains 80%, but prevalence is now 50% (500 diseased and 500 disease-free people in 1,000). This deliberately isolates the effect of prevalence; it does not establish that a real test transfers unchanged to a referral clinic.

• Diseased 500 × 0.90 → TP = 450, FN = 50
• Healthy 500 × 0.80 → TN = 400, FP = 100

• Sensitivity = 450 / 500 = 90% (unchanged)
• Specificity = 400 / 500 = 80% (unchanged)
• PPV = 450 / (450 + 100) = 81.8% (up from 33.3%)
• NPV = 400 / (400 + 50) = 88.9% (down from 98.6%)

With sensitivity and specificity held fixed, higher prevalence increases PPV and reduces NPV. The relative sizes of the disease-present and disease-absent groups change, so the mix of true and false results changes too.

Do not confuse the mathematical experiment with differences between clinical studies. Prevalence may accompany changes in case-mix and measured accuracy; that does not mean changing the group sizes alone causes sensitivity or specificity to change. Leeflang and colleagues examine this distinction.

Common true/false traps to practise

Because Part 1 is a Multiple True/False paper — a stem with five A–E statements each marked independently — the examiners can probe one misconception per statement. Use these original revision statements to check the distinction:

• "PPV is a fixed property of the test." False. PPV and NPV depend on prevalence as well as the test performance in that setting.
• Swapping the denominators. A statement might define sensitivity as TP/(TP+FP). That is PPV, not sensitivity. Sensitivity divides by all the truly diseased (TP+FN). Drawing the table prevents this every time.
• "A negative result on a highly specific test rules out disease." False. Specificity alone does not establish the meaning of a negative result; consider the negative likelihood ratio and pre-test probability.
• "A 95% sensitive test means 95% of positives are true." False — that conflates sensitivity with PPV, the positive predictive value vs sensitivity confusion again.
• "Raising the test threshold increases both sensitivity and specificity." False. For a continuous test with higher values defined as positive, raising the cut-off generally reduces sensitivity and increases specificity; ties can leave either unchanged. This is exactly what the ROC curve depicts, with the area under the curve summarising overall discrimination.
• Likelihood-ratio confusion. The positive likelihood ratio is sensitivity / (1 − specificity); the negative LR is (1 − sensitivity) / specificity. Neither formula contains prevalence, but both depend on sensitivity and specificity. Do not assume they transfer unchanged between populations; combine an applicable likelihood ratio with pre-test odds to obtain post-test odds.

When two statements in a stem sound plausible but contradict each other, build the table and let the arithmetic adjudicate. And because there is no negative marking in Part 1 — a wrong or blank answer simply scores zero — you should commit a True/False to every statement rather than leave gaps. We unpack that scoring logic in the MTF technique and no-negative-marking article.

A 60-second exam-day method

Under time pressure, run this drill whenever a diagnostic-statistics stem appears:

1. Draw the empty 2x2 grid. Truth across the top, test result down the side.
2. Anchor the totals. If you are given a prevalence and a sample size, fill the column totals first (diseased vs healthy).
3. Apply sensitivity and specificity to those column totals to get TP/FN and TN/FP.
4. Read the asked-for statistic off the boxes using the formula — column-wise for Se/Sp, row-wise for PPV/NPV.
5. Sanity-check the direction. With sensitivity and specificity held fixed, reducing prevalence lowers PPV and raises NPV. Check the actual numbers before judging whether either value is high enough.

Practising this on real questions until it becomes automatic is the whole game, and it is exactly what a structured bank is for — try a themed set in the AnesCORE question bank and review every explanation, not just the ones you got wrong. For how to fold that into a wider revision rhythm, see how to use an EDAIC question bank effectively and our notes on spaced repetition for durable recall.

Where this fits in your wider preparation

Use the two tables as a reusable practice exercise: cover the calculated values, rebuild the four cells, and explain why each denominator belongs to its statistic. The EDAIC statistics guide connects this to probability, study design and hypothesis testing.

For the broader timetable, use our EDAIC Part 1 preparation guide and check current examination information with ESAIC.

Frequently Asked Questions

What is the simplest way to remember sensitivity vs specificity?

Sensitivity is about catching disease (it divides by everyone who is truly diseased); specificity is about correctly clearing the healthy (it divides by everyone truly disease-free). Use SnNout and SpPin as reminders, then check pre-test probability and test performance before making a rule-out or rule-in claim. Read sensitivity and specificity down the columns of the 2x2 table.

Does prevalence affect sensitivity and specificity?

Changing only the relative sizes of otherwise comparable disease-present and disease-absent groups leaves sensitivity and specificity fixed in a mathematical example. Across real populations, case-mix and other factors can change measured accuracy. PPV and NPV also change directly with prevalence, even when sensitivity and specificity are held constant.

What's the difference between positive predictive value and sensitivity?

They answer opposite questions. Sensitivity asks: given that the patient has the disease, how likely is a positive test? PPV asks: given a positive test, how likely is the patient to have the disease? Sensitivity starts from the truth, PPV starts from the result. In the worked comparison, prevalence changes PPV while sensitivity is held fixed. Treating them as interchangeable is a classic MTF trap.

Do I lose marks for guessing on a statistics statement?

No. EDAIC Part 1 has had no negative marking since 2014, so a wrong or blank statement scores zero while a correct one scores. Always commit a True or False to every A–E statement rather than leaving it blank.

How much statistics is in the EDAIC Part 1?

Statistics and clinical measurement belong to Paper A preparation. Use the current official ESAIC syllabus to plan coverage; this article does not predict how many statistics questions will appear.

Continue your revision

Practise the 2×2 table until you can explain each denominator without looking at the formulas. Create a free AnesCORE account to start drilling sensitivity, specificity and predictive-value questions with worked explanations, and head to the EDAIC question bank to turn this method into automatic, exam-day recall.

Sources and calculation notes

• Murad et al. The association of sensitivity and specificity with disease prevalence: analysis of 6909 studies of diagnostic test accuracy. CMAJ, 2023.
• Leeflang et al. Variation of a test’s sensitivity and specificity with disease prevalence. CMAJ, 2013.

The worked populations and likelihood-ratio example are original, hypothetical teaching calculations, not diagnostic-performance estimates for a named clinical test. Percentages are rounded to one decimal place where needed.

Updated with AI assistance on 6 November 2026. Sources support the accuracy qualifications above; this is examination revision, not a diagnostic pathway for an individual patient.