Ranking Visualizations of Correlation Using Weber's Law

Abstract

Despite years of research yielding systems and guidelines to aid visualization design, practitioners still face the challenge of identifying the best visualization for a given dataset and task. One promising approach to circumvent this problem is to leverage perceptual laws to quantitatively evaluate the effectiveness of a visualization design. Following previously established methodologies, we conduct a large scale (n=1687) crowdsourced experiment to investigate whether the perception of correlation in nine commonly used visualizations can be modeled using Weber's law. The results of this experiment contribute to our understanding of information visualization by establishing that: (1) for all tested visualizations, the precision of correlation judgment could be modeled by Weber's law, (2) correlation judgment precision showed striking variation between negatively and positively correlated data, and (3) Weber models provide a concise means to quantify, compare, and rank the perceptual precision afforded by a visualization.

Map LineUps: Effects of spatial structure on graphical inference

“…These results allow us, for the first time, to construct a visual equivalent of statistical power for geospatial data. Our JND results add to those provided in recent years by Klippel et al (2011), Harrison et al (2014 and Kay & Heer (2015) for correlation visualization. Importantly, they provide an empirical basis for an improved construction of visual line-ups for maps and the development of theory to inform geospatial tests of graphical inference.…”

“…We re-implement the staircase procedure employed by Rensink & Baldridge [16] and Harrison et al [7] as closely as possible, using Moran's I as our measure of spatial autocorrelation. For a given spatial autocorrelation target, we show participants two choropleth maps side-by-side with different values of Moran's I and ask them to select the one they perceive to have the greater spatial autocorrelation structure.…”

“…Three notable studies [16,7,9] attempt to model how humans perceive data properties, in these cases bivariate correlation structure, when such data are presented at different baseline levels of correlation and in different visualization types. Crucial to this work is the concept of Just Noticeable Difference (JND) -how much a given stimulus must increase or decrease before humans can reliably detect changes in that stimulus [7].…”

“…Crucial to this work is the concept of Just Noticeable Difference (JND) -how much a given stimulus must increase or decrease before humans can reliably detect changes in that stimulus [7]. We believe the concept of JND, and Rensink & Baldridge's and later Harrison et al's procedure for estimating it, might provide useful information for constructing map line-up tests with varying intensities of spatial autocorrelation structure -potentially giving an estimate of the size of effect required to discriminate that structure.…”

“…[16,7,9]) have contributed empirically-validated models for describing how individuals perceive non-spatial correlation in different visualization types. These models quantify how ability to perceive differences in statistical correlation varies at different baseline intensities of that structure, as measured by Pearson product-moment correlation coefficient (r) [16], and between visualization types [7,9]. We apply and adapt the techniques used in these studies in order to model how individuals perceive spatial autocorrelation in differing choropleth maps.…”