Engineering Psychology PSY 378F

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Engineering PsychologyPSY 378F

• University of Toronto
• Fall 2002
• L7 Spatial Displays Graphs

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Outline

• Spatial Displays and Analog Perception
• What Graphs Are, History
• Graph Guidelines
• Use Physical Dimensions Judged Without Bias
• Consider the Task
• Minimize the Number of Mental Operations
• Keep the Data-Ink Ratio High
• Code Multiple Graphs Consistently

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Spatial Displaysand Analog Perception

• In Spatial Displays, Sizes of Objects or
  Distances Between Them Used to Communicate
  Information
• Analog Perception Judgments of Magnitude
  (Distance, Position, Extent, Depth, Angle etc.)
• Contrast to Digital Displays
• 99 vs. 100 km/h

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Graphical Perception

• What is a Graph?
• A Paper or Electronic Analog Representation of
  Numeric Data with Multiple Data Points
• Originally developed by Playfair (1786), Lambert
  (1765), a political economist and a chemist,
  respectively

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Perceptual Biases and Illusions

• Variation of Poggendorf Illusion
• Solution Scales on Each Side

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Perceptual Biases and Illusions

• Cleveland (1985) Illusion--Joining Shortest
  Distances Rather than Vertical Distances
• Solution Plot the Difference Directly, Draw
  Vertical Gridlines

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Area and Volume in Graphs

• Area and Volume Commonly Used to Code Values in
  Graphs
• Area and Volume Judged Inaccurately (Cleveland)

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Proportion Judgments of 3D Bars

• Cyclical bias patterns occur when observers make
  proportion judgments with bars (Spence, 1990)
• Why? What is source of bias?

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Bias in Judgments of Area and Volume
Stevens Law ? aPb

• Seen in Magnitude Estimation (Assign Number to
  Magnitude of Stimulus Stevens, 1957)
• Area and Volume Show Response Compression
  (Stevens Exponent, ? lt 1)
• Color Saturation Shows Response Expansion (? gt 1)

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Power Model (Spence, 1990 Karmarkar, 1978)

• Power model claims bias seen in magnitude
  estimation affects proportion judgments
• The model provides a method for estimating
  Stevens exponent using proportion judgments

P aPb / (aPb aWb) Pb / (Pb Wb) Pb / Pb
(1-P)b
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Power Model Predictions

• When b lt 1, over-then-under
• When b gt 1, under-then-over
• Can account for one-cycle pattern, but not
  multi-cycle

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Cyclical Power Model(Hollands Dyre, 2000,
Psych Review)

• This more general model can account for
  multiple-cycle bias patterns
• Let P W R, where R is a reference value
• Multiple reference values may be available within
  a stimulus

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Cyclical Power Model(Hollands Dyre, 2000)

• With two reference points one cycle (same as
  power model)

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Adding Reference Points

• With three reference points two cycle

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Adding Reference Points

• With five reference points four cycle

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Fitting the Model to Judgments with Graphs

• Data from Spence (1990) fit by Hollands Dyre
  (2000)
• Two-Cycle Patterns
• Stevens Exponents a Bit Larger Than 0.8
  (Indicating that Area Judged at Least Part of the
  Time)

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Cyclical Power Model Evidence

• Hollands Dyre (2000)
• Conducted experiments to test two assumptions of
  CPM
• Experiment 1
• Changes in Stevens exponent obtained through
  magnitude estimation predicted exponents obtained
  from proportion judgments

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Cyclical Power Model Evidence

• Experiment 2
• Changing Available Reference Points (Tickmarks)
  Predicts Frequency of Cyclical Bias
• Overall Error (Distance from Horizontal Line)
  Reduced With More Reference Points

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Cyclical Power Model Extensions

• Same Graph, Different Continua
• Box-and-Whisker Plots Length and Area
• Box Overestimated When Box Small Underestimated
  When Large (Behrens et al., 1990)
• Solution Use Quartile Plot, Because Length Used
  to Code Values

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Response Method(Morton Hollands)

• Experiment 2
• 3 response methods line, dial, numeric
• No tickmarks on pies

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Morton Hollands Results

• 2 and 4 cycle model versions fit
• Best fitting version (largest R2) shown below
• No difference among ? values (0.8)

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Cyclical Power Model Conclusions

• Avoid Continua Whose Stevens Exponents Differ
  From One
• Increase the Frequency of Tickmarks in the Graph
• Possible to Make less Effective Perceptual
  Continua (e.g., Area) More Effective with More
  Reference Points
• Portray bars at similar depths in 3D bar graphs
  if accurate judgments are necessary or use 2D

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Task Dependency and the PCP

• Task Dependency The Choice of the Best Graph
  Type Depends on the Judgment Task
• Continuum of Tasks Point Reading, Local
  Comparisons, Global Comparisons, Synthesis

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Continuum of Tasks
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Proximity Compatibility Principle

• If task requires high processing proximity there
  should be high display proximity.
• If a task requires low processing proximity there
  should be low display proximity (Wickens
  Carswell, 1995).
• Or,
• For integrated tasks, use more integrated
  displays
• For specific, point reading tasks, use separated
  displays

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PCP Applied to Graphs

• Carswells (1988, 1992a) Metanalysis
• Each Study Classified by Task
• Performance in Task Evaluated as to Whether
  Consistent with PCP Prediction

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PCP Applied to Graphs

• Increasing Benefit of Integrated Graphs as Tasks
  Require More Integration (Consistent with PCP)

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PCP Applied to Graphs

• Result Confirmed by More Recent Studies Using
  Multiple Tasks (e.g., Gillie Berry, 1994
  Hollands Spence, 1992, Liu Wickens, 1992,
  Wickens et al., 1994, 1995)

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Cleveland vs. PCP

• Cleveland McGill (1984) Hierarchy Applies to
  More Focused Tasks--therefore subsumed by PCP
• Metanalysis by Carswell (1992b) Supports this
  Conclusion

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Minimizing Mental Operations

• Fewer Operations will Reduce Processing Time and
  Reduce Likelihood of Error
• Two Factors Affect Graph Reading Performance
• 1. Number of operations necessary given a
  particular task-graph combination
• 2. Effectiveness of the perceptual features used
  as input for the operations
• Predicts Task Dependent Results (underlies PCP)

Sum Summation (heightA, heightB) Ratio
estimation (heightA,Sum)
B
Ratio estimation (heightA, heightAB)
B
A
A
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The Data-Ink Ratio

• Amount of ink not used to depict data should be
  kept to a minimum (Tufte, 1983)
• Unnecessary non-data ink slows search for values
• Gillan Richman (1994) found empirical support
  for the data-ink ratio concept
• Judgments were slower and less accurate with
  extra ink

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Multiple Graphs

• Coding variables
• Focused judgments of variable coded across graphs
  difficult
• Mental representation of coded variables (B and
  C) qualitative
• Mental representation of variable on x-axis is
  quantitative (Shah Carpenter, 1995)

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Multiple Graphs

• Keep format of multiple graphs as consistent as
  possible
• Identify each graph Identify changing element
• Local and global optimality

Causes of Death Among 25-44 Yr. Olds (Tufte, 1997)
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General Summary

• Spatial Displays and Analog Perception
• What Graphs Are, History
• Graph Guidelines
• Use Physical Dimensions Judged Without Bias
• Consider the Task
• Minimize the Number of Mental Operations
• Keep the Data-Ink Ratio High
• Code Multiple Graphs Consistently