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Activity Number:
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478
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Type:
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Contributed
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Date/Time:
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Thursday, August 7, 2008 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Statistical Graphics
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| Abstract - #301840 |
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Title:
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Resultant-Vector Banking of Graphical Displays: Geometry and Statistical Properties
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Author(s):
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Saptarshi Guha*+ and William Cleveland
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Companies:
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Purdue University and Purdue University
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Address:
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Dept. Of Statistics, West Lafayette, IN, 47907,
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Keywords:
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banking to 45 degrees ; graphical displays ; aspect ratio ; graphical perception
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Abstract:
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The aspect ratio of a two-dimensional graph is critical when slopes are judged to determine how one variable depends on another, carried out by assessing the orientations of line segments. Theory and experiment have demonstrated that judgments are enhanced by banking to 45 degrees: the aspect ratio is chosen so that the absolute values of the orientations are centered on 45 degrees. A new approach to centering has a geometric motivation. Take the segments on the graph with any aspect ratio and think of them as vectors at an origin pointing into Quadrant I with polar angles equal to the absolute values of their orientations. Choose the aspect ratio on this construction so that the resultant vector has an angle of 45 degrees. Resultant-vector banking provides an excellent centering, geometrical insight into banking, and simple formulas that allow tractable theoretical study.
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