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See http://yvonnejansen.me/size/ for more material such as the raw experiment data as well as the data analysis scripts in R.

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- 1. A Psychophysical Investigation of Size as a Physical Variable Yvonne Jansen Kasper Hornbæk
- 2. Data Physicalizations "a physical artifact whose geometry or material properties encode data." Atelier Brückner, German Age Pyramid, 2013
- 3. Data Communication "a physical artifact whose geometry or material properties encode data." Data source: dataphys.org Data Physicalization
- 4. Data Communication Hans Rosling, gapminder.com Presentations
- 5. Data Communication Presentations Exhibitions Joyce Hsiang & Bimal Mendis, The City of 7 Billion, 2011-2013 Atelier Brückner, German Age Pyramid, 2013
- 6. Loren Madsen, Chicago crime rates, District 5 police station, 2014 Presentations Exhibitions Public Installation
- 7. Data Physicalizations Physical VariablesVisual Variables Data Visualizations
- 8. How should we encode data?
- 9. Data Visualization Tableau's Show Me feature [Source: onlinehelp.tableau.com] 1980s ranking of visual variables! ! ! (Cleveland & McGill 1982-1987, Mackinlay 1986, Spence 1990) 1926 circle vs bars debate (e.g., Eels 1926, Croxton & Stryker 1927, Croxton & Stein 1932) bibliography under yvonnejansen.me/size
- 10. Data Physicalization Image source: Kahrimanovic et al, 2010 Psychology & Psychophysics experiments 1970 Baird, Psychophysical Analysis of Visual Space 2010 Kahrimanovic et al., haptic volume perception 1969 Stanek, volume and surface judgments e.g.,
- 11. sequential presentation size 10 size ? size ? …
- 12. Source: balanceandmobility.com Source:mv.cvc.uab.es Chin rests (see Baird 1970) Free head movements
- 13. Instructions matter how large is the smaller shape (compared to the larger)? how large appears the smaller shape? [Teeghtsoonian, The Judgment of Size, 1965]
- 14. ratio between heights How should we describe size? 11 cm 3 cm
- 15. ratio between ? How should we describe size?
- 16. ratio between (in the store) diameters 6 cm 2 cm 33 % How should we describe size?
- 17. (in the store) diameters 113 cm3 4.2 cm3 33 % 3.7 % How should we describe size? ratio between ("commonly") volumes
- 18. (in the store) diameters ("commonly") volumes (also possible) surface areas 113 cm2 12.6 cm2 33 % 3.7 % 11.1 % How should we describe size? ratio between
- 19. How should we encode data physically? Joyce Hsiang & Bimal Mendis, The City of 7 Billion, 2011-2013
- 20. Research Questions 1. How accurately are elementary shapes estimated? 3. Are estimates systematically biased? 2. How similar are estimates between individuals?
- 21. Experiment
- 22. Bars Spheres
- 23. Bars Spheres see dataphys.org/list
- 24. 28 pairs 7 sizes diameters 1.2-7cmheights 1-15cm 10 participants
- 25. Estimation Methods Ratio estimation e.g., Cleveland & McGill (1984) Constant sum e.g., Spence (1990)
- 26. 2 methods Constant sum e.g., Spence (1990) represents larger shape shorter shape Ratio estimation e.g., Cleveland & McGill (1984)
- 27. Task "Indicate the percentage of the quantity represented by the smaller shape relative to the larger shape."
- 28. "Divide the line such that the left part represents the quantity represented by the left shape and the right part represents the quantity of the right shape.” Task quantity represented by larger shape …shorter shape
- 29. Results
- 30. bar sphere 0 25 50 75 100 0 25 50 75 100 constantsumratioestimation 0 25 50 75 100 0 25 50 75 100 true ratio estimatedratio method shape estimatedratio true ratio
- 31. bar sphere 0 25 50 75 100 0 25 50 75 100 constantsumratioestimation 0 25 50 75 100 0 25 50 75 100 true ratio estimatedratio method shape estimatedratio true ratio y = xa (Stevens’ law)
- 32. bar sphere 0 25 50 75 100 0 25 50 75 100 constantsumratioestimation 0 25 50 75 100 0 25 50 75 100 true ratio estimatedratio method shape estimatedratio true ratio y = xa (logistic curve) (Stevens’ law) y = 1 10 b+a·log 1 x −1 + 1
- 33. bar sphere 0 25 50 75 100 0 25 50 75 100 constantsumratioestimation 0 25 50 75 100 0 25 50 75 100 true ratio estimatedratio method shape estimatedratio true ratio y = xa y = 1 10 b+a·log 1 x −1 + 1 (logistic curve) (Stevens’ law)
- 34. Accuracy
- 35. Accuracy bars: ratio between heights spheres: ratio between volumes, diameters, and surface areas
- 36. absolute discrepancy (in percent) Accuracy 2D bars (Spence) 3D bars (height) diameter1.6 surface diameter volume 0 5 10 15 20 (error bars indicate 95% bootstrapped conﬁdence intervals)
- 37. Bias in Estimates residuals
- 38. Bias in Estimates −50 −25 0 25 50 0 25 50 75 100 ratio between volumes (in %) residuals volume-based encoding Spheres
- 39. Bias in Estimates −50 −25 0 25 50 0 25 50 75 100 ratio between volumes (in %) residuals −50 −25 0 25 50 0 25 50 75 100 ratio between diameters (in %) residuals volume-based encoding diameter-based encoding
- 40. −50 −25 0 25 50 0 25 50 75 100 ratio between surfaces areas (in %) residuals Bias in Estimates −50 −25 0 25 50 0 25 50 75 100 ratio between volumes (in %) residuals volume-based encoding surface-based encoding
- 41. estimates ~ linear Take Aways – Bars response curves similar across people
- 42. Take Aways – Bars ● ● ● ● ● ● line (H) length line (V) length bar height box height cylinder height bar (RE) height 0 2 4 6 Spence(1990) lower accuracy than 2D bars but still < 5%
- 43. Take away - Spheres Encoding in volumes misleading representations✘ diameter only marginally better surface area ✘ much better (but still more overestimations)
- 44. Take away - Spheres Encoding in volumes misleading representations✘ diameter only marginally better surface area ✘ much better (but still more overestimations) supported by haptic perception studies (Kahrimanovic et al, 2010) see bibliography under yvonnejansen.me/size
- 45. Open Questions / Future Work Other physical shapes Interactions between vision and touch Large range of absolute sizes
- 46. Raw data, R scripts, and additional charts at yvonnejansen.me/size (work in progress) yvja@di.ku.dk Comments, questions, requests

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