Data Visualization has long been shaped by empirical evidence of the efficacies of different encodings, such as length, position, or area, in conveying quantities. Less is known, however, about what may affect comparison of multiple data series, which generally involves extraction of higher-order values, such as means, ranges, and correlations. In this work, we investigate such factors and the underlying visual processes that may account for them. We begin with a case study motivating the research, in which we modify Krona, a Bioinformatics visualization system, to support several types of comparison. Next, we empirically examine the influence of “arrangement”—that is, whether charts are shown side-by-side, stacked vertically, overlaid, etc.—on comparative tasks, in a series of psychophysical experiments. The results suggest a complex interaction of factors, with different comparative arrangements providing benefits for different combinations of tasks and encodings. For example, overlaid charts make detecting differences easier but comparing means or ranges more difficult. While these results offer some guidance to designers, the number of interactions makes it infeasible to provide broad rankings of arrangements, as has been done previously for encodings. Our subsequent efforts thus work toward understanding the visual processes that underlie the extraction of statistical summaries needed for comparison. It has recently been proposed that simpler shortcuts, called Perceptual Proxies, are used by the visual system to estimate these values. We investigate proxies for bar charts in experiments using an “adversarial” framework, in which the ranking of two charts along a task metric (e.g. mean) is opposite their ranking along a proxy metric (e.g. convex hull area). The strongest evidence we find is for use of a “centroid” proxy to estimate means in bar charts. Finally, we attempt to use using human-guided optimization to construct charts de novo, without assuming specific proxies. This work contributes both to perceptual psychology, by offering evidence for underlying visual processes that may be involved in the interpretation of comparative visualizations, and to data visualization, by providing new research methods and straightforward design guidance on how best to lay out charts to support certain tasks.