What sensitivity measures
Sensitivity — also called the true positive rate (TPR), recall, or the hit rate — is the proportion of people who genuinely have a condition that a test correctly identifies as positive. It answers a single question: of everyone who actually has the disease, how many does the test catch?
The formula is:
Sensitivity = TP / (TP + FN)
Here TP (true positives) is the number of diseased people who test positive, and FN (false negatives) is the number of diseased people the test wrongly clears. The denominator TP + FN is the total number of people who actually have the condition. Sensitivity is always a value between 0 and 1 (0% to 100%), and it depends only on the diseased group — it says nothing about people who are healthy.
Worked example
Suppose 100 people in a study truly have a disease. A screening test flags 90 of them as positive and misses 10. Then TP = 90, FN = 10, and sensitivity = 90 / (90 + 10) = 90 / 100 = 0.90, or 90%. The 10 missed cases are false negatives, giving a false negative rate of 1 − 0.90 = 10%.
Why sensitivity matters
A highly sensitive test is good at ruling a condition out: because it rarely misses true cases, a negative result is trustworthy. This is captured by the mnemonic SnNout — a highly Snsensitive test with a Nnegative result rules the disease out. Screening tests (for cancer, infectious disease, or newborn conditions) are deliberately built for high sensitivity, because the cost of missing a real case is severe.
Sensitivity versus specificity
Sensitivity has a mirror-image partner, specificity = TN / (TN + FP), the true negative rate. Sensitivity uses only sick people; specificity uses only healthy people. The two are usually in tension: lowering a test's positivity threshold catches more true cases (higher sensitivity) but also raises false alarms (lower specificity). A complete evaluation of a test reports both, often alongside predictive values, which — unlike sensitivity — also depend on how common the disease is (prevalence).
Typical reference values
- A rapid antigen test for a respiratory virus might have sensitivity around 70–85% (it misses some genuine infections).
- A well-run PCR or laboratory reference test often reaches 95–99% sensitivity.
- Mammography screening sensitivity is commonly cited near 85%, varying with breast density.
- Sensitivity of 100% means the test never misses a true case (FN = 0); sensitivity of 0% means it catches none.
Frequently Asked Questions
What is sensitivity in a diagnostic test?
What is the difference between sensitivity and specificity?
Is sensitivity the same as recall or the true positive rate?
Does sensitivity depend on how common the disease is?
Common Tip Percentages
| Service | Typical Tip Range | Notes |
|---|---|---|
| Restaurant (sit-down) | 15–20% | 20%+ for exceptional service |
| Food delivery | 10–20% | Consider extra for long distances |
| Taxi / rideshare | 10–20% | More for assistance with luggage |
| Hotel housekeeping | $2–5/night | Leave daily, not just at checkout |
| Barber / hair salon | 15–20% | On pre-discount total |
| Pizza delivery | 10–15% or $3–5 minimum | Higher in bad weather |
General Household Budget Ratios (50/30/20 Rule)
| Category | % of Net Income | Examples |
|---|---|---|
| Needs | 50% | Rent, groceries, utilities, insurance |
| Wants | 30% | Dining out, entertainment, hobbies |
| Savings / Debt | 20% | Emergency fund, retirement, extra payments |
Common Measurement Conversions for Everyday Use
| Quantity | US / Imperial | Metric Equivalent |
|---|---|---|
| 1 cup | 8 fl oz | 237 mL |
| 1 pint | 16 fl oz | 473 mL |
| 1 quart | 32 fl oz | 946 mL |
| 1 gallon | 128 fl oz | 3.785 L |
| 1 lb | 16 oz | 453.6 g |
| 1 ft | 12 in | 30.48 cm |