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Forgive me if this is outside of the scope of Cross Validated, but it seemed relevant on the visualization front. As described here (page 3) there exists a phenomenon when gauging the distance between two lines on a plot to compare the shortest distance between the two lines, rather than the vertical distance. This leads to underestimation of the distance between lines at certain gradients. To illustrate, the following graphic is from the aforementioned link:

enter image description here

The difference on the y-axis between these two lines is uniform across all x values, and yet the difference appears to shrink. I am curious as to whether this phenomenon has an official name and if so, whether there is any kind of canonical reference paper/citation describing the phenomenon in more detail?

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  • $\begingroup$ Yes, this one often causes issues; the appearance of shrinkage is of course due to our tendency to perceive not the vertical distance, but at (roughly speaking) something closer to the normals to the curves. I can't say I know the name of the effect though. $\endgroup$
    – Glen_b
    Commented Apr 23, 2013 at 22:51
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    $\begingroup$ Cleveland and McGill (1985) discuss this issue (p831) "... the difficulty of detecting vertical distances between curves" but don't explicitly name it. This blogpost calls it the "tilted baseline problem". $\endgroup$
    – Glen_b
    Commented Apr 23, 2013 at 23:13
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    $\begingroup$ Interesting question, but perhaps most appropriate for the Cognitive Sciences stack exchange? $\endgroup$
    – Jake Westfall
    Commented Apr 24, 2013 at 1:30

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This psycho-visual problem is the consequence of the mind making effective bisquare approximations when thinking about "distance". It is most often addressed by plotting the variable of interest, in this case the difference, as its own variable. Personally I would put this into a subplot with y-axis label as "difference between domestic and international" or such.

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It would be interesting to see what the Cognitive Sciences stack exchange calls it, and I am not an expert in this, but I have been reading on it recently, and I think you would be justified in calling it a "subjective contour illusion".

The textbook Vision Science focuses on illusory contours like Kanizsa's Triangle, where viewers perceive a white triangle in an image that shows only lines and pac men: Kanizsa's Triangle

It seems to me that mentally filling in the area between the two curves is just what is going wrong when viewers underestimate the gap between the lines in your example. If it doesn't have a better name already, let's call it a subjective contour illusion.

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  • $\begingroup$ I don't see the connection. Read Glen_b's comments to the original question, it is typical the reader does not estimate vertical distances, but the nearest point of the two curves. $\endgroup$
    – Andy W
    Commented May 1, 2013 at 0:24
  • $\begingroup$ When I looked at the figure above of Kaniza's triangle on my laptop the stackexchange background was more visible, emphasizing the vertical lines and breaking the illusion. I think this is a demonstration of the connection, but I agree that it is not definitively connected. Glen_b references Cleveland's work; his 1985 book The elements of graphing data names a different challenge "the angle contamination of slope judgements" (p. 245). Following this and his taxonomy of graphical perception tasks (p. 235), we could call the phenomenon above "the slope contamination of length judgements". $\endgroup$
    – Abraham D Flaxman
    Commented May 2, 2013 at 16:59
  • $\begingroup$ But "subjective contour illusion" sounds cooler. $\endgroup$
    – Abraham D Flaxman
    Commented May 2, 2013 at 17:00

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