TP/FP/FN/TN matrix with sensitivity and specificity callouts.
A free, animated 2x2 diagnostic table you can read here or embed on any website, from Scrollchart.
2x2 Diagnostic Table
The 2x2 diagnostic table is the foundational structure for evaluating any binary test. The columns represent true disease status (disease present vs absent); the rows represent test result (positive vs negative). The four cells are: true positives (TP), false positives (FP), false negatives (FN), and true negatives (TN).
From these counts, four performance metrics are computed. Sensitivity (TP / (TP + FN)) measures how reliably the test detects disease when it is present. Specificity (TN / (TN + FP)) measures how reliably it rules out disease when it is absent. Positive predictive value (PPV) and negative predictive value (NPV) reflect accuracy given a positive or negative result respectively, and unlike sensitivity and specificity, they depend on disease prevalence in the tested population.
Sensitivity = TP / (TP + FN). A test with sensitivity 0.95 misses 5% of true cases.
Specificity = TN / (TN + FP). A test with specificity 0.90 falsely flags 10% of healthy individuals.
PPV = TP / (TP + FP). This depends heavily on prevalence. The same test applied to a low-prevalence screening population yields a far lower PPV than when applied to a high-prevalence clinical population, even with identical sensitivity and specificity. A positive result from a rare-disease screen can therefore still be more likely false than true.
The ROC curve (Hanley and McNeil, 1982) is the natural extension of the 2x2 table: it traces sensitivity and (1 - specificity) across all possible thresholds, making the threshold-independence of test quality explicit.
The meaning and use of the area under a receiver operating characteristic (ROC) curve , Hanley, J. A. and McNeil, B. J. (1982) - Radiology, 143(1): 29-36. Connects the 2x2 table to the full ROC framework.
Sensitivity and specificity are properties of the test applied to a specific population and gold standard. They can change when applied to a different spectrum of disease severity (spectrum bias): a test evaluated only in severe cases may appear more sensitive than when tested across mild and severe cases together.
PPV and NPV are context-dependent. Quoting PPV from a high-prevalence clinical study and applying it to a low-prevalence screening context overstates the test's utility. Likelihood ratios (LR+ = sensitivity / (1 - specificity)) are prevalence-independent and preferred for clinical reasoning across different base rates.
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Source & accuracy
This 2x2 diagnostic table is an editorial illustration built to represent the concept accurately. Where it shows figures, they are typical or representative values chosen to make the relationship clear, not a single underlying dataset. The diagram and its explainer are reviewed and maintained centrally, and updated over time as understanding improves.
True positives, false positives, and the 2x2 grid
A 2x2 diagnostic table maps test results (positive/negative) against ground truth (disease present/absent), yielding four cells: true positives (TP, correctly identified cases), false positives (FP, healthy people flagged), false negatives (FN, missed cases), and true negatives (TN, correctly identified healthy). The grid reveals trade-offs: a sensitive test (high TP, few FN) catches disease but may over-flag. A specific test (high TN, few FP) rarely false-alarms but may miss cases. Perfect tests do not exist, so clinical and research contexts demand different priorities.
Sensitivity, specificity, and the clinical choice
Sensitivity (TP divided by TP plus FN) measures catch rate; specificity (TN divided by TN plus FP) measures false-alarm avoidance. A cancer screening test might aim for 95% sensitivity to minimize missed diagnoses, accepting higher false alarms that trigger followup imaging. A drug test for employment might prioritize 99% specificity to avoid false convictions, accepting occasional missed users. Positive predictive value (TP divided by TP plus FP) flips the question: given a positive result, how likely is disease? This depends on disease prevalence, which 2x2 tables make explicit.
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Reference
What this is
A free, embeddable, animated 2x2 diagnostic table for any website.
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