[MUSIC]. 
Last time, we talked about data types, 
dimensions and how to map data to visual 
attribute based on the number of data 
dimensions. 
Clearly there's a large design space for 
this visual encoding. 
Information visualization is about 
choosing the most effective visual 
encoding for a given data set. 
In this lecture, we're going to describe 
how to do that. 
We saw earlier that there are different 
data types. 
And those can be mapped to a set of 
visual attributes. 
And some mapping are better than others. 
So now we have a challenge. 
How do we pick the best mapping of all 
possibilities? 
So in order to do this we're going to 
follow three basic principles. 
Importance ordering, expressiveness and 
consistency. 
This was first described by Jock McKinley 
in 1986. 
So importance ordering has to do with 
encoding the most important information 
in a most perceptually active way. 
Expressiveness has to do with depicting 
all the data and only the data. 
And finally consistency means the 
property of the image, the visual 
attributes should match the properties of 
the data. 
I'll go into more detail on how to do 
this on the following slides. 
We'll start with importance ordering. 
We've seen this slide before. 
Now as we discussed earlier, decades of 
research have taught us that certain 
visual attributes more accurately 
represent quantitative data to the human 
brain. 
Mackinlay defined expressiveness in the 
following manner: he said a set of facts 
is expressible in a visual language if 
the sentences: i.e the visualizations in 
the language express all the facts in the 
set of data and only the facts in the 
data. 
So what does this mean? 
Well, using color hue we cannot express 
the fact that one item is greater than 
another. 
So color hue simply can't represent 
ordinal data. 
Ordinal or quantitative data. 
So color hues simply can't represent 
ordinal or quantitative data. 
It's best you use phenomenal data. 
On the other hand you don't want to 
express facts that are not in the data. 
So a length is interpreted as a 
quantitative value. 
In this incorrect use of a bar chart, the 
length of the bars say something untrue 
about the data. 
So on the x axis we have the national 
origin of these cars, now on the y axis 
the make and model. 
Now the length of the bars suggests an 
ordering on the axis. 
So it implies that somehow Germany is 
greater than the USA. 
So therefore using bars for nominal data 
is an incorrect choice. 
Number three, we have consistency. 
The properties of the image, the visual 
attributes should match the properties of 
the data. 
What this means, is you don't want to do 
something like mapping one dimensional 
data to two or three dimensional visual 
representations. 
This diagram represents why that is not a 
good idea. 
So here we have the price per barrel of 
oil represented as the height of a three 
dimensional barrel. 
You can see the obvious problem here. 
Look at 1974. 
The price is $10.95 and then for 1979, 
the price is $13.34. 
Well this is less than a 30% increase. 
And yet the 1979 barrel looks 
significantly larger than the 1974 
barrel. 
So clearly this is an inconsistent 
representation. 
The three-dimensional representation is 
implying something false about the 
underlying data. 
Let's move to a data encoding exercise. 
Here we have a data set of cars. 
We have the model on the first column. 
The country of origin, the year, the 
number of cylinders, the horsepower, the 
miles per gallon and finally the weight 
in pounds. 
I would like you to create a 
visualization that encodes all seven 
dimensions in this data set. 
Make the perceptually appropriate choices 
and be prepared to explain. 
I will describe the steps you need to do 
and show you Bertin's examples once more. 
So step one the terminal which columns 
represents nominal, ordinal or quantative 
data. 
Step two review the transvisual 
attributes on the next slide and assign 
the most perceptually appropriate choices 
to each data set. 
Step three create a visualization that 
encodes as many of the seven dimensions 
as you can. 
Don't worry if you can't get all of them 
but, but do try to do so. 
To review here are Bertin's visual 
attributes. 
Position, size, value, texture, color, 
orientation and shape. 
Are you done? 
Here's one attempt made by one of my 
students. 
So this is an attempt at encoding seven 
variables from the cars dataset in a 
single visualization. 
So this student chose to put two of the 
quantitative variables, horsepower and 
miles per gallon on the x and y axis. 
The third ratio data weight he encoded 
with area of the marks. 
Not a bad choice since you, you can only 
put two of those ratio variables on axes. 
He also chose to encode cylinders, which 
are quantitative integral data by using 
the shape of the mark. 
And then finally he used color hue for 
the region, Europe, Japan or US. 
And color value or lightness for the 
year. 
Additionally in his visualization you can 
mouse over each of the marks and the name 
of the model of the car would pop-up. 
So, what do you think of this 
visualization? 
What works, what doesn't and what could 
you do better? 
I'll leave that critique as an exercise 
for you.