Euler box diagrams to represent independent and non-independent events

Abstract

Venn and Euler diagrams are valuable tools for representing the logical set relationships among events. Proportional Euler diagrams add the constraint that the areas of diagram regions denoting various compound and simple events must be proportional to the actual probabilities of these events. Such proportional Euler diagrams allow human users to visually estimate and reason about the probabilistic dependencies among the depicted events. The present paper focuses on the use of proportional Euler diagrams composed of rectangular regions and proposes an enhanced display format for such diagrams, dubbed “Euler boxes”, that facilitates quick visual determination of the independence or non-independence of two events and their complements. It is suggested to have useful applications in exploratory data analysis and in statistics education, where it may facilitate intuitive understanding of the notion of independence.