The two by two diagram: a graphical truth table.

Abstract

The two by two table is widely used in statistics, and in particular in the medical literature, to present the results of experimental and clinical studies in which two different operators (such as a reference standard and a new diagnostic test) sort a sample into two groups. The four cells of the table reflect the four possible categories of results. Despite the simplicity of the table, the interplay of its contents is surprisingly complex, and description of this interplay can be confusing if rendered with the conventional descriptive terms alone, such as sensitivity and predictive value. We present a graphical transformation of the table, comprised of a rectangular box in a special coordinate system. This diagram is offered as a flexible and subtle conceptual tool to help physicians, authors, and students to understand, plan, and present clinical research studies.