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[MUSIC]. 
In our third and final lecture on visual 

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perception, we'll be discussing how 
humans estimate magnitude. 

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If you'll recall from our earlier 
lectures on mapping quantitative data to 

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visual attributes. 
You can see how understanding common 

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misperceptions or inaccuracies in the 
visual system can be very helpful when it 

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comes to designing an effective 
visualization. 

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We're fortunate in that, there is a large 
body of psychophysic research that we can 

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draw on. 
All, right. 

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So, I'd like you to look at these two 
circles, and tell me what is your 

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impression of the difference in areas 
between the two circles. 

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I want you to come up with two numbers. 
First, your first impression. 

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And then what you think it is after 
considering it more. 

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Write down both numbers, both your first 
impression and your more detailed 

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analysis. 
So, what did you get, the correct answer 

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is 25. 
The idea of a Power Law for visual 

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perception was first mentioned in the 
19th century. 

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But Stanley Stevens in the mid 1950s, 
came up with a body of work to justify it 

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and he formalized the Power Law. 
His experimental results for perceptual 

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estimation give an exponent for length of 
pretty close to one, so in other words 

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fairly accurate. 
But in area 0.6 to 0.9, so you get some 

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underestimation and in volume 0.5 to 0.8 
even more underestimation. 

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So, in the previous slide even though the 
area differential was 25, most people 

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tend to say it's around 16. 
So, how close did you come? 

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And perhaps more importantly, how can you 
use this for designing visualizations 

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that will be accurate and effective? 
It turns out cartographers have already 

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known about this for quite some time. 
In the 1970s, J Flannery, a cartographer, 

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conducted a set of experiments and 
produced a set of empirical guidelines, 

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for how to represent quantitative 
information using area. 

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So, what cartographers do when presenting 
quantitative data, they'll use apparent 

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magnitude scaling. 
All right, let's consider a set of visual 

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attributes, and how good humans are at 
estimating magnitude. 

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This data comes from, again, from many 
decades of research in psychophysics. 

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It turns out that humans are most 
accurate, at estimating differences in 

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position if there is a common scale. 
If the scales are non-aligned, then 

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they're slightly less accurate, but still 
fairly accurate. 

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Then comes length, slope, and angle. 
And then much less accurate are area, and 

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even less so volume. 
And finally, humans are most inaccurate 

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at using color to judge magnitude. 
So, again we have evidence that, the hue, 

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saturation and value are not very good 
choices to use when estimating 

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quantitative, when representing 
quantitative data. 

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[BLANK_AUDIO] So, the conclusion to these 
three lectures on visual perception is 

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that what is currently known about visual 
perception can aid the design process. 

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Understanding the low level mechanisms of 
the visual processing system and using 

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that knowledge can result in improved 
displays