TITLE:
The Turtleback Diagram for Conditional Probability
AUTHORS:
Donghui Yan, Gary E. Davis
KEYWORDS:
Visualization, Graph Representation, Recursive Space Partition, Venn Diagram
JOURNAL NAME:
Open Journal of Statistics,
Vol.8 No.4,
August
16,
2018
ABSTRACT: We elaborate on an alternative representation of
conditional probability to the usual tree diagram. We term the representation “turtleback
diagram” for its resemblance to the pattern on turtle shells. Adopting the set
theoretic view of events and the sample space, the turtleback diagram uses
elements from Venn diagrams—set intersection, complement and partition—for
conditioning, with the additional notion that the area of a set indicates
probability whereas the ratio of areas for conditional probability. Once parts
of the diagram are drawn and properly labeled, the calculation of conditional
probability involves only simple arithmetic on the area of relevant sets. We
discuss turtleback diagrams in relation to other visual representations of
conditional probability, and detail several scenarios in which turtleback
diagrams prove useful. By the equivalence of recursive space partition and the tree,
the turtleback diagram is seen to be equally expressive as the tree diagram for
abstract concepts. We also provide empirical data on the use of turtleback diagrams
with undergraduate students in elementary statistics or probability courses.