- 1. Average Estimates in Line Graphs are Biased Toward Areas of Higher Variability Dominik Moritz, Lace Padilla, Francis Nguyen, and Steven Franconeri
- 2. Bias Towards Areas of Higher Variability Experiments Results
- 3. Bias Towards Areas of Higher Variability Experiments Results
- 4. William Playfair, Commercial and Political Atlas, 1786
- 6. Stocks Human Vitals Sensor Data Learning Curves https://en.wikipedia.org/wiki/Learning_curve_(machine_learning)
- 7. Visualization Analysis and Design by Tamara Munzner
- 12. Increased Variability Increased visual weight may capture attention Increased salience may bias average estimates
- 18. Line graph Points equally spaced along the x-axis Research questions
- 19. Line graph Points equally spaced along the x-axis Points spaced along the arc of the line Experiment 1 Experiment 2 Research questions
- 20. Bias Towards Areas of Higher Variability Experiments Results
- 22. Stimuli Base series generated from geometric Brownian motion
- 23. Stimuli Base series generated from geometric Brownian motion Add noise based on y-position Low variability High variability
- 24. Stimuli Base series generated from geometric Brownian motion Add noise based on y-position
- 25. Stimuli Base series generated from geometric Brownian motion Scale Add noise based on y-position
- 26. Stimuli Parameters: • Seed • Low and high variability levels • Mirrored or not mirrored ...
- 27. Experiment 1 2 ⨉ 2 0.15 Variability 0.4 Variability Variability Upper Variability Lower All within subject 140 Participants 48 trials per participant
- 28. 140 Participants Experiment 1 Experiment 2 2 ⨉ 2 0.15 Variability 0.4 Variability Variability Upper Variability Lower 2 ⨉ 2 0.4 Variability Variability Upper Variability Lower 0 Variability ⨉ 3 Line Point Arc Point All within subject Variability and upper vs lower within subject Mark type between subject 48 trials per participant 420 Participants 48 trials per participant
- 29. Hypotheses H1: Estimation error will be signi fi cantly di ff erent than zero. H2: There will be signi fi cantly more estimation error for trials with higher variability compared to lower variability. H3: Estimation error will be observed in the direction of the increased variability. H4: There will be signi fi cantly more estimation error for trials with higher variability than no additional variability. H5: The least variability-overweighting will occur in graphs with points that are equally spaced along the x-axis.
- 31. Bias Towards Areas of Higher Variability Experiments Results
- 32. Experiment 1 Is there a bias?
- 33. Experiment 1 Is there a bias?
- 34. Experiment 1 Is there a bias?
- 35. Experiment 2 Does the mark type a ff ect the bias?
- 36. Experiment 2 Does the mark type a ff ect the bias?
- 37. Experiment 2 Does the mark type a ff ect the bias?
- 38. Additional analyses in the paper We asked participants for their strategies and looked at how strategies a ff ect estimation error. We can model estimation error for arbitrary line graphs based on the true average and the average of the points drawn along the arc.
- 39. Limitations of unbalanced and few stimuli Thanks to Steve Haroz for pointing out this issue! We used the same 12 seeds for each participant rather than a new seed for each stimulus. This introduces biases.
- 40. Limitations of unbalanced and few stimuli Thanks to Steve Haroz for pointing out this issue! 9/12 stimuli seeds have true averages below 0.5 ➡ when using responses of 0.5, the error distributions ideally overlap These should be the same Our normalization (Section 4.2) ensures that these are the same
- 41. Materials available at osf.io/aupbk/ Average Estimates in Line Graphs are Biased Toward Areas of Higher Variability domoritz@cmu.edu or vis.social/@dom