  Data can be visually represented using visual channels like position, length
or luminance. An existing ranking of these visual channels is based on how
accurately participants could report the ratio between two depicted values.
There is an assumption that this ranking should hold for different tasks and
for different numbers of marks. However, there is little existing work testing
assumption, especially given that visually computing ratios is relatively
unimportant in real-world visualizations, compared to seeing, remembering, and
comparing trends and motifs, across displays that almost universally depict
more than two values.
  We asked participants to immediately reproduce a set of values from memory.
With a Bayesian multilevel modeling approach, we observed how the relevant rank
positions of visual channels shift across different numbers of marks (2, 4 or
8) and for bias, precision, and error measures. The ranking did not hold, even
for reproductions of only 2 marks, and the new ranking was highly inconsistent
for reproductions of different numbers of marks. Other factors besides channel
choice far more influence on performance, such as the number of values in the
series (e.g. more marks led to larger errors), or the value of each mark (e.g.
small values are systematically overestimated).
  Recall was worse for displays with 8 marks than 4, consistent with
established limits on visual memory. These results show that we must move
beyond two-value ratio judgments as a baseline for ranking the quality of a
visual channel, including testing new tasks (detection of trends or motifs),
timescales (immediate computation, or later comparison), and the number of
values (from a handful, to thousands).
