The Four Core Statistics
The four core statistics are sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV).
In the formulas below, TP = true positives, FP = false positives, TN = true negatives and FN = false negatives.
Sensitivity
Definition: The proportion of patients who have the abnormality that the examination correctly identifies.
Also called: True-positive rate.
Formula:
Sensitivity = TP / (TP + FN)
Clinical meaning: A sensitivity of 95% means that if 20 patients truly have the condition, the examination will correctly detect it in 19 and miss it in 1. High sensitivity is desirable when you want to rule out a diagnosis (a negative result is then more trustworthy).
Specificity
Definition: The proportion of patients without the abnormality that the examination correctly identifies as normal.
Also called: True-negative rate.
Formula:
Specificity = TN / (TN + FP)
Clinical meaning: A specificity of 95% means that if 20 patients do not have the condition, the examination will correctly call 19 of them normal and produce one false-positive result. High specificity is desirable when you want to rule in a diagnosis (a positive result is then more trustworthy).
Positive Predictive Value (PPV)
Definition: The probability that a patient who has a positive finding actually has the abnormality.
Formula:
PPV = TP / (TP + FP)
Clinical meaning: PPV increases as the condition’s prevalence increases. A positive finding is far more likely to be true when the condition is common in the population you are examining.
Negative Predictive Value (NPV)
Definition: The probability that a patient who has a negative finding truly does not have the abnormality.
Formula:
NPV = TN / (TN + FN)
Clinical meaning: NPV increases when the condition is rare. A negative finding is more reassuring when the condition is uncommon.
Likelihood Ratios
Sensitivity and specificity answer the question: “If the patient has (or does not have) the disease, what is the chance the test will be positive (or negative)?”
Likelihood ratios answer the more clinically relevant question: “Given this test result, how much should I change my estimate of the probability of disease?”
Likelihood ratios (LRs) are one of the most practical tools for interpreting physical examination findings (and any other diagnostic test). They convert sensitivity and specificity into a single number that directly tells you how much a positive or negative result changes the probability of disease.
Unlike sensitivity and specificity, LRs don’t depend on disease prevalence. This makes them especially useful at the bedside: you start with your clinical estimate of pre-examination probability and multiply by the LR to obtain the post-examination probability.
- Positive likelihood ratio (LR+)
How much more likely a positive finding is in a patient with the disease than in a patient without it.
LR+ = sensitivity / (1 – specificity)
- Negative likelihood ratio (LR–)
How much less likely a negative finding is in a patient with the disease compared with a patient without the disease.
LR– = (1 – sensitivity) / specificity
How to Interpret Likelihood Ratios
| Likelihood Ratio | Approximate Effect on Probability | Clinical Usefulness |
| > 10 | Large increase | Strong evidence for disease |
| 5 – 10 | Moderate increase | Useful supporting evidence |
| 2 – 5 | Small increase | Modest value |
| 1 – 2 | Minimal increase | Little practical value |
| 1 | No change | Useless |
| 0.5 – 1 | Minimal decrease | Little practical value |
| 0.2 – 0.5 | Small decrease | Modest value |
| 0.1 – 0.2 | Moderate decrease | Useful evidence against disease |
| < 0.1 | Large decrease | Strong evidence against disease |
Why Likelihood Ratios Are More Useful Than Sensitivity and Specificity Alone
A sign with 90% sensitivity and 90% specificity has:
- LR+ = 9 (moderately strong evidence for disease when positive)
- LR– = 0.11 (moderately strong evidence against disease when negative)
- A sign with 95% sensitivity but only 50% specificity has:
- LR+ = 1.9 (almost useless when positive)
- LR– = 0.1 (very useful when negative — good for ruling out)
Clinical Examples
1. HINTS examination in acute vertigo
- Sensitivity ≈ 93%, Specificity ≈ 83%
- LR+ ≈ 5.5 → moderate increase in probability of a central cause
- LR– ≈ 0.08 → strong decrease in probability of a central cause when the examination is normal (excellent for ruling out central pathology in trained hands)
2. Third heart sound (S3)
- Typically high specificity (often > 90%) but modest sensitivity
- LR+ often > 5–10 → presence of an S3 meaningfully raises the probability of significant left-ventricular dysfunction
- LR– closer to 0.5–0.8 → absence of an S3 does little to lower the probability
3. Murphy’s sign
- Sensitivity variable (50–97%), Specificity ≈ 80%
- LR+ typically 3–5 → positive sign modestly increases likelihood of acute cholecystitis
- LR– usually > 0.3 → negative sign is not strong enough to rule out the diagnosis
4. Egophony in suspected pneumonia
- LR+ ≈ 6 → presence of egophony meaningfully increases the probability of pneumonia
- Absence has limited impact
5. Palpable spleen
- Sensitivity ≈ 58%, Specificity ≈ 92%
- LR+ ≈ 7 → finding a palpable spleen usefully raises the probability of true splenomegaly
- LR– ≈ 0.46 → absence does not reliably exclude it
Practical Use at the Bedside
- Estimate the pre-examination probability (e.g., “I think there is about a 30% chance this patient has a significant abdominal aortic aneurysm”).
- Perform the examination and note whether the key finding is present or absent.
- Apply the appropriate LR:
- Positive finding → multiply pre-test odds by LR+
- Negative finding → multiply pre-test odds by LR–
- Convert the resulting post-test odds back to a probability.
Important Limitations
- LRs are only as good as the quality of the studies that generated them. Many studies examined physical signs in selected populations, and they may perform differently in primary care than in specialist settings.
- Examiner skill, patient body habitus, and intermittent signs all influence real-world performance.
- LRs assume each finding is independent of the others used to estimate pre-test probability. When multiple signs correlate, multiplying successive LRs can overestimate the final probability.
- Very high or very low LRs are uncommon for individual physical signs. Combinations of findings (or with history) usually yield more powerful LRs than any single sign.
Converting between probability and odds
Odds = probability / (1 – probability)
Probability = odds / (1 + odds)
Worked example
Take a pre-examination probability of 30% and a sign with LR+ = 9 and LR– = 0.11 (the 90% sensitivity / 90% specificity sign above).
• Pre-test odds: 0.30 / 0.70 = 0.43
• Finding present: 0.43 × 9 = 3.86 post-test odds, which is 3.86 / 4.86 = 79% probability
• Finding absent: 0.43 × 0.11 = 0.047 post-test odds, which is 0.047 / 1.047 =
4.5% probability
Likelihood ratios turn abstract sensitivity and specificity numbers into a practical
bedside tool. They help you avoid two common errors:
- Over-valuing a positive finding that has only a modest LR+
- Under-valuing (or over-valuing) a negative finding whose LR– is not extreme enough to rule a diagnosis in or out
Used thoughtfully, they support more accurate, transparent clinical reasoning
and reduce both missed diagnoses and unnecessary over-investigation.
Key Practical Points for Physical Examination
Choosing the Right Statistic
The statistic to look at depends on what you want the examination to do.
| Goal of the examination | Preferred statistic | Why it matters |
| Confirm a diagnosis (rule in) | High specificity | Minimises false positives |
| Exclude a diagnosis (rule out) | High sensitivity | Minimises false negatives |
| Judge how much to trust a positive finding | High PPV (and prevalence) | Positive result more likely to be true |
| Judge how much to trust a negative finding | High NPV (and low prevalence) | Negative result more likely to be true |
Performance of Common Examination Signs
Physical examination findings vary widely in diagnostic performance. Most individual signs have only modest accuracy; their value increases when interpreted in clinical context and combined with history.
The tables below summarise evidence-based performance data for frequently used methods, drawn from systematic reviews and meta-analyses.
Abdominal Examination
| Sign / Method | Condition | Sensitivity | Specificity | Notes |
| Shifting dullness | Ascites | ~85% | ~50% | Moderately sensitive but not specific |
| Palpable spleen | Splenomegaly | ~58% | ~92% | Useful when present; absence does not exclude |
| Palpable liver | Hepatomegaly | Variable | Variable | Performance depends on examiner experience and body habitus |
| Murphy’s sign | Acute cholecystitis | 50–97% | ~80% | Specificity is more reliable than sensitivity |
| Right-upper-quadrant tenderness | Cholecystitis / biliary disease | Moderate | Moderate | Concordance with evidence is relatively good |
| Bulging flanks | Ascites | Lower than often estimated | Higher than often estimated | Clinicians tend to overestimate specificity |
Cardiovascular Examination
| Sign / Method | Condition | Sensitivity | Specificity | Notes |
| Third heart sound (S3) | Reduced ejection fraction | 13–78% | 88–99% | High specificity; low sensitivity especially in milder cases |
| Jugular venous distension | Elevated filling pressures | ~39% | ~92% | Specific when present |
| Systolic murmur radiating to neck | Severe aortic stenosis | 90–98% | 22–36% | Sensitive but not specific |
| Crackles / basal rales | Heart failure | ~60% | ~78% | Modest overall accuracy |
| Lower-extremity oedema | Heart failure | ~50% | ~78% | Non-specific |
Respiratory Examination
Findings in this table are reported as likelihood ratios (LR+ or LR–) rather than as sensitivity and specificity.
| Sign / Method | Condition | Performance | Notes |
| Overall clinical impression of pneumonia | Community-acquired pneumonia | LR+ ≈ 6.3 | Strongest single element |
| Egophony | Pneumonia | LR+ ≈ 6.2 | High specificity when present |
| Dullness to percussion | Pneumonia / consolidation | LR+ ≈ 2.6 | Moderately useful |
| Abnormal vital signs (fever, tachypnoea) | Pneumonia | Modest | Absence of abnormal vital signs lowers probability (LR– ≈ 0.25) |
| Auscultatory findings alone | Childhood pneumonia | Limited | Hypoxia and increased work of breathing outperform auscultation |
Neurological Examination (Acute Vertigo / Dizziness)
| Method | Condition | Sensitivity | Specificity | Notes |
| HINTS examination (Head Impulse, Nystagmus, Test of Skew) | Central cause | ~93% | ~83% | High sensitivity when performed by trained clinicians |
| HINTS+ (adds hearing) | Central cause | ~99% | ~85% | Excellent rule-out value in acute vestibular syndrome |
| General neurological examination | Central cause | ~47% | ~93% | Low sensitivity, high specificity |
| Limb weakness / hemiparesis | Central cause | ~11% | ~98.5% | Very specific but insensitive |
| Test of skew | Central cause | ~24% | ~98% | Specific when present |
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