A statistical law in the perception Psychophysics = the study of how - - PDF document

A statistical law in the perception

• f risks and physical quantities in

traffic

Accident Analysis and Prevention, 82, 2015, 36-44 Rune Elvik, Institute of Transport Economics

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Psychophysics – a field of study with long traditions

Psychophysics = the study of how physical phenomena are perceived by humans Can be extended to the perception of more abstract phenomena like probabilities or risks Can be linked to the basic characteristics of utility functions as developed in economic theory Founded in 1860 by Gustav Theodor Fechner The law-like relationships he found have been named «Fechner’s law»

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Fechner’s law

Small quantities (rare events, low probabilities) are

• verestimated (perceived as heavier, more frequent, etc.

than they really are) Large quantifies (common events, high probabilities) are underestimated (perceived as lighter, less frequent, etc. than they really are) As a result, the scale for perceived quantities is a compressed version of the real scale (ranges from 2 to 30, rather than 1 to 100) The extreme points of the scale are ill-defined

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10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100 Perceived quantity or probability Actual quantity or probability

A general law of perception of physical amounts and probabilities

Small quantities or low probabilities are

• verestimated

Large quantities or high probabilities are underestimated The curve showing perceived quantity or probability is compressed, i.e. flatter than

• bjective quantities or probabilities

The curve showing perceived probability is ill-defined at extreme values; these may be perceived as 0 or 1

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A classic study (Lichtenstein et al. 1978)

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y = -0.0123x2 + 0.9957x + 10.11 R² = 0.9917 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 Perceived stopping distance (metres) Actual stopping distance (metres)

Relationship between actual and perceived stopping distance as assessed by pedestrians intending to cross the road. Based on Sun et al. 2015, figure 4

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y = 0.6617x + 100.45 R² = 0.9002 0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 0.0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 400.0 Perceived distance needed (metres) Actual distance needed (metres)

Relationship between actual and perveived distance (metres) needed to

• vertake. Based on Gordon and Mast 1968

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70 70 70 40 40 40 40 41.4 44.5 50.5 53.4 10 20 30 40 50 60 70 80 0.08 17 34 Speed (miles per hour) Time spent at higher speed (70 miles per hour) - minutes

Speed adjustment as a function of speed adaptation. Based on Schmidt and Tiffin 1969

Initial speed Target speed Chosen speed Instruction: Accelerate to 40 miles per hour (from standstill) Instruction: Slow down to 40 miles per hour

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y = 0.9213e-0.016x R² = 0.8847 0.000 0.200 0.400 0.600 0.800 1.000 1.200 0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 Accuracy of speed adjustment (1.00 = perfect adjustment) Duration of exposure to 70 miles/hour

Accuracy of speed adjustment as a function of duration of exposure to higher speed

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y = 11.735ln(x) + 27.026 R² = 0.589 50 100 150 200 250 300 350 50 100 150 200 250 300 350 Stated speed (kilometres per hour) Actual speed (kilometres per hour)

Relationship between actual and perceived speed needed to save a stated travel time (e.g. 50 minutes). Based on Svenson 2009

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y = 105.1e0.0025x R² = 0.7997 50 100 150 200 250 300 350 400 450 500 50 100 150 200 250 300 350 400 450 500 Perceived increase in risk (percent; 400 = risk increases fourfold) Actual increase in risk (percent; 400 = risk increases fourfold)

Actual and perceived increase in risk of injury accident associated with increased speed. Based on Svenson 2009

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y = 0.1116x + 5.1749 R² = 0.2738 0.00 0.01 0.10 1.00 10.00 100.00 1000.00 0.00 0.01 0.10 1.00 10.00 100.00 1000.00 Perceived risk of apprehension (per 1,000 drivers) Actual risk of apprehension (per 1,000 drivers)

Relationship between actual and perceived risk of apprehension for traffic violations

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y = 1.5711e0.0217x R² = 0.8194 0.10 1.00 10.00 100.00 1000.00 0.10 1.00 10.00 100.00 1000.00 Perceived fatality rate (log scale; safest mode = 1.0) Actual fatality rate (log scale; safest mode = 1.0)

Relationship between actual and perceived fatality rate for seven modes of

• transport. Based on Elvik and Bjørnskau 2005, figure 1

Aviation Rail Bus Boat Car Walking Cycling Motorcycle

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100 1000 10000 100000 1000000 10000000 100000000 100 1000 10000 100000 1000000 10000000 Logarithm of monetary valuation Logarithm of number of cases

Relative valuation of different damages/injuries in four countries

Norway Great Britain Germany Sweden Fatal Serious Slight Damage-only Page 15 y = 1.1781x0.0636 R² = 0.9161 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40 2.60 2.80 3.00 10000 20000 30000 40000 50000 60000 70000 Score for happiness (1.00 = minimum; 3.00 = maximum) Equivalent income per household member (US dollars)

Function fitted to data points relating income to happiness in the United States 1994-1996. Based on Frey and Stutzer (2002)