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All content in this area was uploaded by Ronald A Rensink on Sep 18, 2015

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The perception of Pearson correlation in scatterplots can be described via simple laws (Rensink & Baldridge, 2010): just noticeable difference (jnd) follows a Weber-like (linear) law, and subjective estimate follows a Fechner-like (logarithmic) law. Behavior is largely invariant to the size, shape or color of the dots (Rensink, 2014), suggesting that correlation is (or is related to) a perceptually simple property carried via spatial position. To determine if features other than spatial position can carry information in the same way, a set of "augmented stripplots" was developed for visualizing two-dimensional data. As for the case of scatterplots, the first dimension was carried by spatial position along the horizontal axis. But the second dimension was carried by a visual feature such as orientation, size, or color. Precision was measured via the jnd in correlation for two above-and-below stripplots, each 2° high x 5° wide. Accuracy was determined via reference plots with fixed upper and lower values, with a test plot adjusted to have its apparent correlation be midway between them. Twenty observers were tested in each condition. Results showed the same pattern in all conditions. For all features, precision followed a Weber-like law, with jnds increasing linearly with distance from r=1. And for all features, accuracy followed a Fechner-like law, with subjective estimates a logarithmic function of the distance from r=1. The constants of these functions were similar as well; indeed, performance for color-augmented stripplots (both red-green and blue-yellow) was somewhat more accurate than that for scatterplots. These commonalities provide further evidence that correlation perception is a general process that is both sophisticated and rapid, relying on more than superficial appearance alone (e.g., the shape of the dot cloud). They also suggest that many if not all basic visual features can effectively carry information. Meeting abstract presented at VSS 2015.

Content uploaded by Ronald A Rensink

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All content in this area was uploaded by Ronald A Rensink on Sep 18, 2015

Content may be subject to copyright.

... They do not, however, affect performance (Rensink, 2012(Rensink, , 2014. Indeed, estimation and discrimination of correlation follow similar laws even when the graphical representations involved are entirely different in appearance ( Figure 11)-for example, when the second data dimension of a data element is represented by size or color rather than vertical position (Rensink, 2012(Rensink, , 2014(Rensink, , 2015, or when line graphs or bar charts are used (Harrison et al., 2014). ...

... (9)), c is inversely proportional to σ, which may explain why accuracy of correlation perception improves when dot clouds have smaller standard deviations (Cleveland et al., 1982) Note that these developments do not rely on the way that information is represented; instead of corresponding to positions in the image, dimensions x and y might correspond to values in a more abstract parameter space. This could explain the existence of similar laws when other graphical representations are used (Harrison et al., 2014;Rensink, 2014Rensink, , 2015. ...

... For example, the proposal that correlation is based on probability distributions over an abstract parameter space implies that the values of data points need not be conveyed by spatial position-they could instead be represented by other properties, such as color or orientation (cf. Figure 11). Given that the perception of correlation in such representations is similar to that found in scatterplots (Rensink, 2014(Rensink, , 2015, and given that such visualizations could take up less space (Figure 11), there may be practical advantages to their use. ...

For scatterplots with gaussian distributions of dots, the perception of Pearson correlation r can be described by two simple laws: a linear one for discrimination, and a logarithmic one for perceived magnitude (Rensink & Baldridge, 2010). The underlying perceptual mechanisms, however, remain poorly understood. To cast light on these, four different distributions of datapoints were examined. The first had 100 points with equal variance in both dimensions. Consistent with earlier results, just noticeable difference (JND) was a linear function of the distance away from r = 1, and the magnitude of perceived correlation a logarithmic function of this quantity. In addition, these laws were linked, with the intercept of the JND line being the inverse of the bias in perceived magnitude. Three other conditions were also examined: a dot cloud with 25 points, a horizontal compression of the cloud, and a cloud with a uniform distribution of dots. Performance was found to be similar in all conditions. The generality and form of these laws suggest that what underlies correlation perception is not a geometric structure such as the shape of the dot cloud, but the shape of the probability distribution of the dots, likely inferred via a form of ensemble coding. It is suggested that this reflects the ability of observers to perceive the information entropy in an image, with this quantity used as a proxy for Pearson correlation.
(Enhanced pdf at http://link.springer.com/article/10.3758/s13423-016-1174-7)

... For example, performance on detecting linear trends was better for line graphs than stripplots when the trends were decreasing (Fuchs et al., 2013). However, the performance was similar or possibly even better for stripplots than scatterplots when the trends were increasing (Rensink, 2015). These seemingly inconsistent patterns could easily be explained by bias. ...

... Extracting trends from scatterplots and stripplots both likely require a probability distribution of how one visual feature (vertical position or color) varies as a function of another visual feature (horizontal position). Correlation perception for color stripplots has shown to be somewhat more accurate than correlation perception for scatterplots, suggesting that basic visual features (e.g., color) can effectively convey correlation information (Rensink, 2015). ...

Useful data visualizations have the potential to leverage the visual system's natural abilities to process and summarize simple and complex information. Here, we tested whether the design recommendations made for pairwise comparisons generalize to the detection of trends. We created two different types of graphs: line graphs and stripplots. These graphs were created from identical datasets that simulated temperature changes across time. These datasets varied in the type of trend (linear and exponential). Human observers performed a trend detection task for which they judged whether the trend in temperature over time was increasing or decreasing. Participants were more sensitive to trend direction with line graphs compared to stripplots. Participants also demonstrated a systematic bias to respond that the trend was increasing for line graphs. However, this bias decreased with increasing sensitivity. Despite the better sensitivity to line graphs, more than half of the participants found the stripplots more appealing and liked them more than the line graphs. In conclusion, our results indicate that, for trend detection, depicting data with position (line graphs) leads to better performance compared to depicting graphs with color (stripplots). Yet, graphs with color (stripplots) were preferred over the line graphs, suggesting that there may be a tradeoff between the aesthetic design of the graphs and the precision in communicating the information.

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