Abstract:
Comparing slopes is a fundamental graph reading task and the aspect ratio
chosen for a plot influences how easy these comparisons are to make.
According to Banking to 45 degrees, a classic design guideline first proposed
and studied by Cleveland et al., aspect ratios that center slopes around 45
degrees minimize errors in visual judgments of slope ratios. This paper
revisits this earlier work. Through exploratory pilot studies that expand
Cleveland et al.'s experimental design, we develop an empirical model of
slope ratio estimation that fits more extreme slope ratio judgments and two
common slope ratio estimation strategies. We then run two experiments to
validate our model. In the first, we show that our model fits more generally
than the one proposed by Cleveland et al. and we find that, in general, slope
ratio errors are not minimized around 45 degrees. In the second experiment,
we explore a novel hypothesis raised by our model: that visible baselines can
substantially mitigate errors made in slope judgments. We conclude with an
application of our model to aspect ratio selection.