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Ranking Visualizations of Correlation Using Weber's Law

Lane Harrison
November 13, 2014

Ranking Visualizations of Correlation Using Weber's Law

Paper presentation at IEEE VIS.

Paper: http://www.eecs.tufts.edu/~lane/files/harrison2014ranking.pdf

Lane Harrison

November 13, 2014
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  1. Ranking Visualizations of Correlation using Weber’s Law Lane Harrison, Fumeng

    Yang, Steven Franconeri*, Remco Chang Tufts University, *Northwestern University
  2. Model-based Evaluation M1 M2 M3 M4 M5 M3 M2 M4

    M1 M5 Models of performance can be compared directly and efficiently. Models are scalable and falsifiable. > > > >
  3. Model-based Evaluation M1 M2 M3 M4 M5 M3 M2 M4

    M1 M5 To be effective, models must be grounded in theory. > > > >
  4. Model-based Evaluation M1 M2 M3 M4 M5 M3 M2 M4

    M1 M5 To be effective, models must be grounded in theory. vs vs > > > >
  5. A model grounded in theory: The Perception of Correlation in

    Scatterplots Ron Rensink, Gideon Baldridge (2010) - Used psychophysiological methodologies.
  6. A model grounded in theory: The Perception of Correlation in

    Scatterplots Ron Rensink, Gideon Baldridge (2010) - Used psychophysiological methodologies. - Inferred just-noticeable differences for scatterplots depicting positive correlations.
  7. A model grounded in theory: The Perception of Correlation in

    Scatterplots Ron Rensink, Gideon Baldridge (2010) - Used psychophysiological methodologies. - Established that the perception of correlation in scatterplots can be modeled using Weber’s law. - Inferred just-noticeable differences for scatterplots depicting positive correlations.
  8. 0. 0.00 0.06 0.12 0.18 0.24 ;ĂͿƐĐĂƩĞƌƉůŽƚ͕ZĞŶƐŝŶŬ r 0.0 0.2

    0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ƽ භ from above from below JND Rensink plotted JND as a function of correlation (r) (bright room) (dark room) better worse
  9. 0. 0.00 0.06 0.12 0.18 0.24 ;ĂͿƐĐĂƩĞƌƉůŽƚ͕ZĞŶƐŝŶŬ r 0.0 0.2

    0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ƽ භ from above from below JND To see a difference in data with correlation of 0.3, the comparison r must be +/- 0.2. (dark room) (bright room) better worse
  10. ;ďͿƐĐĂƩĞƌƉůŽƚ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06

    0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ;ĐͿƐĐĂƩĞƌƉůŽƚƌĞŐƌĞƐƐŝŽŶ rA 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ 0.0 0.00 0.06 0.12 0.18 0.24 Because the trend of JND & correlation is linear… 0 0.00 0.06 0.12 0.18 0.24 ;ĂͿƐĐĂƩĞƌƉůŽƚ͕ZĞŶƐŝŶŬ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ƽ භ from above from below JND “The perception of correlation in scatterplots can be modeled using Weber’s Law.” (dark room) (bright room) better worse
  11. Weber's Law - sound, taste, weight, brightness, line-length - model

    for low-level perceptual discrimination ΔP = k * ΔI _ I
  12. Weber's Law - sound, taste, weight, brightness, line-length - model

    for low-level perceptual discrimination ΔP = k * ΔI _ I
  13. ΔP = k * ΔI I _ Actual intensity of

    Stimulus Change in Intensity Perceived diff
  14. ΔP = k * ΔI I _ Actual intensity of

    Stimulus Change in Intensity Perceived diff via experiment
  15. ;ďͿƐĐĂƩĞƌƉůŽƚ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06

    0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ;ĐͿƐĐĂƩĞƌƉůŽƚƌĞŐƌĞƐƐŝŽŶ rA 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ 0.0 0.00 0.06 0.12 0.18 0.24 0.00 0.06 0.12 0.18 0.24 ;ĂͿƐĐĂƩĞƌƉůŽƚ͕ZĞŶƐŝŶŬ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ƽ භ from above from below JND If the perception of correlation in scatterplots follows Weber’s law… better worse
  16. ;ďͿƐĐĂƩĞƌƉůŽƚ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06

    0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ;ĐͿƐĐĂƩĞƌƉůŽƚƌĞŐƌĞƐƐŝŽŶ rA 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ 0.0 0.00 0.06 0.12 0.18 0.24 0.00 0.06 0.12 0.18 0.24 ;ĂͿƐĐĂƩĞƌƉůŽƚ͕ZĞŶƐŝŶŬ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ƽ භ from above from below JND What does the perception of correlation in other charts look like? better worse
  17. ;ďͿƐĐĂƩĞƌƉůŽƚ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06

    0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ;ĐͿƐĐĂƩĞƌƉůŽƚƌĞŐƌĞƐƐŝŽŶ rA 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ 0.0 0.00 0.06 0.12 0.18 0.24 0.00 0.06 0.12 0.18 0.24 ;ĂͿƐĐĂƩĞƌƉůŽƚ͕ZĞŶƐŝŶŬ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ƽ භ from above from below JND vs What does the perception of correlation in other charts look like? better worse
  18. ;ďͿƐĐĂƩĞƌƉůŽƚ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06

    0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ;ĐͿƐĐĂƩĞƌƉůŽƚƌĞŐƌĞƐƐŝŽŶ rA 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ 0.0 0.00 0.06 0.12 0.18 0.24 0.00 0.06 0.12 0.18 0.24 ;ĂͿƐĐĂƩĞƌƉůŽƚ͕ZĞŶƐŝŶŬ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ƽ භ from above from below JND What if the perception of correlation in other charts also follows Weber’s law? better worse
  19. ;ďͿƐĐĂƩĞƌƉůŽƚ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06

    0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ;ĐͿƐĐĂƩĞƌƉůŽƚƌĞŐƌĞƐƐŝŽŶ rA 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ 0.0 0.00 0.06 0.12 0.18 0.24 0.00 0.06 0.12 0.18 0.24 ;ĂͿƐĐĂƩĞƌƉůŽƚ͕ZĞŶƐŝŶŬ r 0.0 0.2 0.4 0.6 0.8 1.0 0.00 0.06 0.12 0.18 0.24 ƽ ƽ ƽ ƽ ƽ ƽ ƽ භ from above from below JND What if the perception of correlation in other charts also follows Weber’s law? vs better worse
  20. r = -1 r = -0.8 r = -0.3 r

    = 0.3 r = 0.8 r = 1 scatterplot parallel coordinates (pcp) stackedarea
  21. coordinates (pcp) stackedarea stackedline stackedbar r = -1 r =

    -0.8 r = -0.3 r = 0.3 r = 0.8 r = 1 scatterplot parallel coordinates (pcp) stackedarea
  22. radar line ordered line r = -1 r = -0.8

    r = -0.3 r = 0.3 r = 0.8 r = 1 scatterplot parallel coordinates (pcp) stackedarea
  23. stackedbar donut radar line r = -1 r = -0.8

    r = -0.3 r = 0.3 r = 0.8 r = 1 scatterplot parallel coordinates (pcp) stackedarea
  24. - n=1687 (AMT) - 9 charts - Normal data (in

    charts) - Between subjects - “Staircase” methodology - Kruskal-Wallis (overall) - Mann-Whitney 
 (post-hoc) - Bonferonni correction
 (p < 0.0036) Design Analyses
  25. scatterplot − positive r jnd 0.0 0.1 0.2 0.3 0.4

    0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • scatterplot − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • parallel coordinates − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • parallel coordinates − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • stackedarea − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • stackedarea − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedline − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedline − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedbar − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedbar − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • donut − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • donut − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • line − positive jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • line − negative jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • radar − positive jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • radar − negative jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • ordered line − positive jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • ordered line − negative jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • 1. Inferred JNDs from experiment data for each chart and for 
 positive/negative correlations.
  26. scatterplot − positive r 0.0 0.1 0.2 0.3 0.4 0.5

    0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • scatterplot − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • parallel coordinates − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • parallel coordinates − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • stackedarea − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • stackedarea − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedline − positive r 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedline − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedbar − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedbar − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • donut − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • donut − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • line − positive 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • line − negative jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • radar − positive jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • radar − negative jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • ordered line − positive jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • ordered line − negative jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • •
  27. scatterplot − positive r jnd 0.0 0.1 0.2 0.3 0.4

    0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • scatterplot − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • parallel coordinates − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • parallel coordinates − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • stackedarea − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • • stackedarea − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedline − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedline − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedbar − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • stackedbar − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • donut − positive r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • donut − negative r jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • line − positive jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • line − negative jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • radar − positive jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • radar − negative jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • ordered line − positive jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • ordered line − negative jnd 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 • • • • • • • • • • • • 2. Tested Weber-model fit using previously- established methodologies. 1. Inferred JNDs from experiment data for each chart and for 
 positive/negative correlations. model fit results 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 ordered line line radar stackedline stackedarea stackedbar donut scatterplot parallel coordinates scatterplot, Rensink positive negative JND rA
  28. model fit results 0.0 0.1 0.2 0.3 0.4 0.5 0.6

    0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 ordered line line radar stackedline stackedarea stackedbar donut scatterplot parallel coordinates scatterplot, Rensink positive negative JND rA less precise more precise
  29. model fit results 0.0 0.1 0.2 0.3 0.4 0.5 0.6

    0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 ordered line line radar stackedline stackedarea stackedbar donut scatterplot parallel coordinates scatterplot, Rensink positive negative JND rA less precise more precise
  30. model fit results 0.0 0.1 0.2 0.3 0.4 0.5 0.6

    0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 ordered line line radar stackedline stackedarea stackedbar donut scatterplot parallel coordinates scatterplot, Rensink positive negative JND rA Obtain rankings at each |r|
  31. r = -1 r = -0.8 r = -0.3 r

    = 0.3 r = 0.8 r = 1 scatterplot parallel coordinates (pcp) stackedarea
  32. 0.7 0.8 0.85 scatterplot (positive) scatterplot (negative) parallel coordinates (negative)

    parallel coordinates (positive) Symmetric Not Symmetric ✓ ✓ ✓ X 0.7 0.8 0.85 ✓ Differences reliably 
 perceived Differences
 (not) reliably 
 perceived X
  33. 0.7 0.8 0.85 scatterplot (positive) scatterplot (negative) parallel coordinates (negative)

    parallel coordinates (positive) Symmetric Asymmetric ✓ ✓ ✓ X 0.7 0.8 0.85 ✓ Differences reliably 
 perceived Differences
 (not) reliably 
 perceived X
  34. sp and pcp 0.0 0.1 0.2 0.3 0.4 0.5 0.6

    0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 parallelCoordinates scatterplot positive negative -PCP as good as scatterplots +PCP terrible
  35. To show correlations precisely in parallel coordinates plots, flip the

    axes to show as many negative correlations as possible. Design implication: scatterplot (positive) scatterplot (negative) parallel coordinates (negative) parallel coordinates (positive) scatterplot (positive) scatterplot (negative) parallel coordinates (negative)
  36. stackedarea, stackedline and stackedbar 0.0 0.1 0.2 0.3 0.4 0.5

    0.6 0.7 0.8 0.9 1.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 stackedline stackedarea stackedbar positive negative parallel coordinates (pcp) stackedarea stackedline stackedline stackedbar donut parallel coordinates (pcp) stackedarea stackedline stackedbar Worst Best OK
  37. Why does Weber’s law, which typically applies to low-level aspects

    of perception, work so well for modeling correlation?
  38. Theory-grounded models help build the science of visualization while providing

    actionable information to inform visualization design. To summarize: