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Gridlines Mitigate Sine Illusion in Line Charts

Clayton Knittel, Jane Awuah, Steven Franconeri, Cindy Xiong Bearfield

TL;DR

The paper investigates the sine illusion in line charts and evaluates three visual interventions (dotted lines, gridlines aligned with comparison points, and gridlines offset) through a large online experiment. It shows aligned gridlines most effectively mitigate the illusion and builds a threshold model linking illusion strength to the ratio of vertical deltas $d1/d2$, with the illusion arising when this ratio exceeds roughly 0.5–0.7 depending on design. The authors compare perpendicular-distance and equal-triangle explanations for the illusion, finding the equal-triangle heuristic to be more predictive. The findings inform visualization design by quantifying how gridlines and alignment shift perceptual thresholds and by highlighting that viewers may rely on orthogonal cues rather than true vertical deltas, suggesting practical guidelines for reducing misperception in multi-line charts.

Abstract

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.

Gridlines Mitigate Sine Illusion in Line Charts

TL;DR

The paper investigates the sine illusion in line charts and evaluates three visual interventions (dotted lines, gridlines aligned with comparison points, and gridlines offset) through a large online experiment. It shows aligned gridlines most effectively mitigate the illusion and builds a threshold model linking illusion strength to the ratio of vertical deltas , with the illusion arising when this ratio exceeds roughly 0.5–0.7 depending on design. The authors compare perpendicular-distance and equal-triangle explanations for the illusion, finding the equal-triangle heuristic to be more predictive. The findings inform visualization design by quantifying how gridlines and alignment shift perceptual thresholds and by highlighting that viewers may rely on orthogonal cues rather than true vertical deltas, suggesting practical guidelines for reducing misperception in multi-line charts.

Abstract

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.
Paper Structure (13 sections, 3 figures)

This paper contains 13 sections, 3 figures.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Experiment
  4. Participant
  5. Experimental Design
  6. Procedure
  7. Results: Overall
  8. Mirroring
  9. Effect of Gridlines On/Offset
  10. Relationship between Time 1 and Time 2 on Accuracy
  11. When Time 1 is Actually Larger
  12. Design Guidelines and Summary of Findings
  13. Limitation and Future Directions

Figures (3)

  • Figure 1: Left: Key explaining the line aspects we manipulated in this paper. Middle: Two examples showing conditions where the delta at Time 1 and Time 2 is greater respectively. Right: The mirrored condition of the Time 1 > Time 2 example.
  • Figure 2: Overall accuracy for the three conditions and gridlines two counterbalancing conditions (aligned and offset).
  • Figure 3: Accuracy by the ratio of deltas at Time 1 and Time 2, for the original data, in comparison to the two models: perpendicular and equal triangle. The higher performance accuracy under both models suggests that participants were relying on the orthogonal distance to make their comparisons.