The Two by Two Truth Diagram

Details

External ID

47471944

Source

HN

Company

—

Product

The Two by Two Truth Diagram

Website domain

github.io

Launched

March 21, 2026

Cohort

—

Upvotes

5

Upvotes percentile

0.1070110701107011

Tags

—

Fetched at

Sept. 7, 2026, 9:26 p.m.

Updated at

Sept. 7, 2026, 9:26 p.m.

Description

I am diagnostic radiologist with over 40 years experience. In diagnostic testing, many terms are used to describe how well the test detects the disease or disorder. Examples are “sensitivity”, “specificity”, “predictive values”, “odds ratio”, “likelihood ratios” and numerous others. In the literature and medical presentations there is often not much consistency in their use; as a physician listening to or reading research, I was perpetually unclear on how these terms “fit together”. My solution was to invent the visual 2 by 2 diagram, or truth diagram, as a graphical alternative to the standard contingency table used in diagnostic testing (Johnson 1999). The concepts listed above, and many others, are represented graphically, and their inter-relationships can be clearly visualized. Instead of four numbers in a grid, a single rectangle on a coordinate system encodes all four cells of the 2×2 table through its position and shape. Each hemi-axis corresponds to one cell (see below). The vertical height corresponds to the number of subjects with the disorder, and the horizontal width corresponds to the number of subjects without the disorder. A low, wide box represents a low prevalence of the disorder; a high narrow box represents a high prevalence. The diagram makes it possible to see statistics like sensitivity, specificity, PPV, NPV, likelihood ratios, and even Bayes’ theorem as geometric relationships — lengths, areas, slopes, and proportions — rather than abstract formulas. Drag or resize the box to see how the cell values change. The other lessons in this app explain each of the terms and how they appear on the diagram. Any of these screens can be saved for presentation and publication purposes.Please take a look and feel free to give me feedback.REFERENCESJohnson KM. The two by two diagram: a graphical truth table. J Clin Epidemiol. 1999;52(11):1073-82. [PubMed] [ResearchGate] Johnson KM, Johnson BK. Visual presentation of statistical concepts in diagnostic testing: the 2×2 diagram. AJR Am J Roentgenol. 2014;203(1):W14-20. [PubMed] [ResearchGate] Johnson KM. Using Bayes’ rule in diagnostic testing: a graphical explanation. Diagnosis (Berl). 2017;4(3):159-67. [PubMed] [ResearchGate]

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