Representing trees using Microsoft doughnut charts

Trees are widely used to represent and solve problems in Bayesian statistics, risk analysis, marketing statistics, reliability theory, and Markov chains. But they have three limitations: (1) for moderately sized problems, the tree becomes unwieldy; (2) while the tree is very good at visually representing qualitative relationships, it does not allow visual representation of quantitative information; and (3) the tree is not easily represented on a PC without special software. In the spirit of Tufte, this article presents an alternative, the circular decision tree, which visually represents all the information – problem structure, strengths of relationship, and values of nodes – using colors and arc lengths. Mathematical computations in the tree are accomplished by ‘mixing colors’ from adjacent segments. Furthermore, it is easily programmable in Excel. Hence it is especially suitable for presenting problems to students and nontechnical audiences.