  Understanding a visualization is a multi-level process. A reader must extract
and extrapolate from numeric facts, understand how those facts apply to both
the context of the data and other potential contexts, and draw or evaluate
conclusions from the data. A well-designed visualization should support each of
these levels of understanding. We diagnose levels of understanding of
visualized data by adapting Bloom's taxonomy, a common framework from the
education literature. We describe each level of the framework and provide
examples for how it can be applied to evaluate the efficacy of data
visualizations along six levels of knowledge acquisition - knowledge,
comprehension, application, analysis, synthesis, and evaluation. We present
three case studies showing that this framework expands on existing methods to
comprehensively measure how a visualization design facilitates a viewer's
understanding of visualizations. Although Bloom's original taxonomy suggests a
strong hierarchical structure for some domains, we found few examples of
dependent relationships between performance at different levels for our three
case studies. If this level-independence holds across new tested
visualizations, the taxonomy could serve to inspire more targeted evaluations
of levels of understanding that are relevant to a communication goal.
