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Sine illusion happens when the more quickly changing pairs of lines lead to bigger underestimates of the delta between them. We evaluate three visual manipulations on mitigating sine illusions: dotted lines, aligned gridlines, and offset gridlines via a user study. We asked participants to compare the deltas between two lines at two time points and found aligned gridlines to be the most effective in mitigating sine illusions. Using data from the user study, we produced a model that predicts the impact of the sine illusion in line charts by accounting for the ratio of the vertical distance between the two points of comparison. When the ratio is less than 50\%, participants begin to be influenced by the sine illusion. This effect can be significantly exacerbated when the difference between the two deltas falls under 30\%. We compared two explanations for the sine illusion based on our data: either participants were mistakenly using the perpendicular distance between the two lines to make their comparison (the perpendicular explanation), or they incorrectly relied on the length of the line segment perpendicular to the angle bisector of the bottom and top lines (the equal triangle explanation). We found the equal triangle explanation to be the more predictive model explaining participant behaviors. 

Effectively designed data visualizations allow viewers to use their powerful visual systems to understand patterns in data across science, education, health, and public policy. But ineffectively designed visualizations can cause confusion, misunderstanding, or even distrust—especially among viewers with low graphical literacy. We review research-backed guidelines for creating effective and intuitive visualizations oriented toward communicating data to students, coworkers, and the general public. We describe how the visual system can quickly extract broad statistics from a display, whereas poorly designed displays can lead to misperceptions and illusions. Extracting global statistics is fast, but comparing between subsets of values is slow. Effective graphics avoid taxing working memory, guide attention, and respect familiar conventions. Data visualizations can play a critical role in teaching and communication, provided that designers tailor those visualizations to their audience. 

The visual system evolved and develops to process the scenes, faces, and objects of the natural world, but people adapt this powerful system to process data within an artificial world of visualizations. To extract patterns in data from these artificial displays, viewers appear to use at least three perceptual tools, including a tool that extracts global statistics, one that extracts shapes within the data, and one that produces sentence-like comparisons. A better understanding of the power, limits, and deployment of these tools would lead to better guidelines for designing effective data displays.