[MUSIC]. 
In our third and final lecture on visual 
perception, we'll be discussing how 
humans estimate magnitude. 
If you'll recall from our earlier 
lectures on mapping quantitative data to 
visual attributes. 
You can see how understanding common 
misperceptions or inaccuracies in the 
visual system can be very helpful when it 
comes to designing an effective 
visualization. 
We're fortunate in that, there is a large 
body of psychophysic research that we can 
draw on. 
All, right. 
So, I'd like you to look at these two 
circles, and tell me what is your 
impression of the difference in areas 
between the two circles. 
I want you to come up with two numbers. 
First, your first impression. 
And then what you think it is after 
considering it more. 
Write down both numbers, both your first 
impression and your more detailed 
analysis. 
So, what did you get, the correct answer 
is 25. 
The idea of a Power Law for visual 
perception was first mentioned in the 
19th century. 
But Stanley Stevens in the mid 1950s, 
came up with a body of work to justify it 
and he formalized the Power Law. 
His experimental results for perceptual 
estimation give an exponent for length of 
pretty close to one, so in other words 
fairly accurate. 
But in area 0.6 to 0.9, so you get some 
underestimation and in volume 0.5 to 0.8 
even more underestimation. 
So, in the previous slide even though the 
area differential was 25, most people 
tend to say it's around 16. 
So, how close did you come? 
And perhaps more importantly, how can you 
use this for designing visualizations 
that will be accurate and effective? 
It turns out cartographers have already 
known about this for quite some time. 
In the 1970s, J Flannery, a cartographer, 
conducted a set of experiments and 
produced a set of empirical guidelines, 
for how to represent quantitative 
information using area. 
So, what cartographers do when presenting 
quantitative data, they'll use apparent 
magnitude scaling. 
All right, let's consider a set of visual 
attributes, and how good humans are at 
estimating magnitude. 
This data comes from, again, from many 
decades of research in psychophysics. 
It turns out that humans are most 
accurate, at estimating differences in 
position if there is a common scale. 
If the scales are non-aligned, then 
they're slightly less accurate, but still 
fairly accurate. 
Then comes length, slope, and angle. 
And then much less accurate are area, and 
even less so volume. 
And finally, humans are most inaccurate 
at using color to judge magnitude. 
So, again we have evidence that, the hue, 
saturation and value are not very good 
choices to use when estimating 
quantitative, when representing 
quantitative data. 
[BLANK_AUDIO] So, the conclusion to these 
three lectures on visual perception is 
that what is currently known about visual 
perception can aid the design process. 
Understanding the low level mechanisms of 
the visual processing system and using 
that knowledge can result in improved 
displays