  Data visualizations present a massive number of potential messages to an
observer. One might notice that one group's average is larger than another's,
or that a difference in values is smaller than a difference between two others,
or any of a combinatorial explosion of other possibilities. The message that a
viewer tends to notice--the message that a visualization 'affords'--is strongly
affected by how values are arranged in a chart, e.g., how the values are
colored or positioned. Although understanding the mapping between a chart's
arrangement and what viewers tend to notice is critical for creating guidelines
and recommendation systems, current empirical work is insufficient to lay out
clear rules. We present a set of empirical evaluations of how different
messages--including ranking, grouping, and part-to-whole relationships--are
afforded by variations in ordering, partitioning, spacing, and coloring of
values, within the ubiquitous case study of bar graphs. In doing so, we
introduce a quantitative method that is easily scalable, reviewable, and
replicable, laying groundwork for further investigation of the effects of
arrangement on message affordances across other visualizations and tasks.
Pre-registration and all supplemental materials are available at
https://osf.io/np3q7 and https://osf.io/bvy95 .
