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S. E. Hassan, G. D. Barnett, R. W. Massof; Validating a New Metric for Assessing the Discriminability of Vehicular Gap Times Using Different Amounts of Sensory Information. Invest. Ophthalmol. Vis. Sci. 2008;49(13):4107.
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When crossing an unsignalized street, pedestrians must judge gaps in vehicular traffic to allow enough time for them to reach the other side of the street before an approaching vehicle reaches them. Due to a lack of psychometric methods for measuring the street-crossing decision variable, little is known how well pedestrians can judge differences in gap duration based on using visual and/or auditory information. The aim of this study was to validate a new metric for assessing the discriminability of different gap durations based on using different amounts of visual and auditory information.
Using a 5 point rating scale, safety ratings for vehicular gaps of different durations were measured along an unsignalized, two-lane street of one-way traffic. Safety ratings were collected from 32 subjects: 12 normally sighted, 10 visually impaired and 10 blind subjects for 7 different gap times under three sensory test conditions: (i) visual and auditory information; (ii) visual information only; and (iii) auditory information only. Receiver Operating Characteristic (ROC) curves were fitted for all possible gap pairs and sensory test conditions and the discriminability (d’) of the street-crossing safety decision variable for all gap pairs and sensory test conditions was calculated as the area under the ROC curve.
We found that our data conform to the three underlying principles of ROC analysis. Specifically, the underlying distributions of the decision variable are continuous, monotonic and are unbounded. Using the dissimilarity matrix of d’ values (which were computed relative to each of the other gap times), in a one -dimensional scaling model, we estimated the means of each distribution of the decision variable relative to a "center of gravity" (COG). When plotting the means of the distributions against gap time, the data are best described as an ogive function symmetric about the COG.
Our analysis of the data strongly suggests that ROC analysis can be successfully applied to assessing the contributions of auditory and visual information to street-crossing decision making. Our finding that an ogive function best describes the relationship between the means of the distributions of the decision variable and gap time suggests that the decision variable is not discriminable across gap times below and above a certain value (gap time). Thus all gap times below a certain value will all be classified by the subject as being "unsafe" and all gap times above a certain value will be classified as being "safe".
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