  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 representing abstract
concepts. We also provide empirical data on the use of turtleback diagrams with
undergraduate students in elementary statistics or probability courses.
