An Empirical Model of Slope Ratio Comparisons.

Area of Science:

• Data Visualization
• Cognitive Psychology
• Human-Computer Interaction

Background:

• Comparing slopes is crucial for interpreting graphs.
• The "Banking to 45°" guideline suggests centering slopes around 45° minimizes visual judgment errors.
• This guideline, proposed by Cleveland et al., has influenced data visualization practices.

Purpose of the Study:

• To revisit and expand upon the empirical work of Cleveland et al. regarding slope perception.
• To develop a more general empirical model for slope ratio estimation.
• To investigate the impact of aspect ratio and visible baselines on slope judgment accuracy.

Main Methods:

• Conducted exploratory pilot studies expanding on Cleveland et al.'s experimental design.
• Developed an empirical model for slope ratio estimation, accounting for extreme judgments and common strategies.
• Executed two experiments to validate the proposed model and test hypotheses about baseline effects.

Main Results:

• The developed empirical model provides a better fit for slope ratio estimation than Cleveland et al.'s model.
• Contrary to the "Banking to 45°" guideline, slope ratio errors are generally not minimized around 45°.
• Visible baselines were found to substantially mitigate errors in slope judgments.

Conclusions:

• The "Banking to 45°" guideline may not be universally optimal for accurate slope comparisons.
• A new empirical model offers a more comprehensive understanding of slope ratio estimation.
• The findings suggest practical implications for selecting aspect ratios and incorporating baselines in graph design.