649week05 → Variables and Axes
Jasper Liu shared a learning experience with me that I’d like to pass on. You may recall that Jasper described some information for his Pure Visibility project and said he planned to depict it in three dimensions. He showed several pictures of labeled 3D axes, listing the information he planned to show as the axis labels. I objected to this on the basis that some of the information was nominal and some was ordinal (see Agresti, 2002), so their locations in three dimensions would introduce some ambiguity. Here’s a sample of the information, scores for terms in three search engines.
Jasper’s response was to first plot some data to demonstrate what he had in mind. This is a crucial step. It’s often the case that our mental picture of a planned representation glosses over some practical limitations. When we draw a concrete picture and supply it with data we often see game-changing details. Such was the case for Jasper’s data. Here’s how it looked, plotted as 3D data.
Jasper was dissatisfied with this picture and, significantly, looked at Card (1999), page 60, where the editors say “Static presentations often use retinal properties such as color to add an additional variable to a visual structure.” Reading this, he was apparently struck by the insight that he could use color to distinguish between search engines and greatly simplify the representation to the following picture. As we discuss the normative perspective, it might be helpful to look back at Jasper’s process.
This learning experience really hit home for me and has a lot to do with Leanna’s comment on ‘prescriptive perspectives’ and how she says that the “normative perspective in information visualization has to do with popularizing and standardizing basic principles”. I feel that this case is a great example of how such prescriptions should be used as a starting point and treated as “heuristics” to arrive at the best place to start iterating your design ideas. This is especially visible in constructing network graphs from a complex data set. Many times establishing nodes and edges is a matter of context, but other times it is more an issue of visual clarity. The process of constructing usable network graphs from a large and/or complex data-set is so inherently iterative in this respect. It may not be possible to clearly view all the data in one graph, but starting with simple decisions such as what to assign to nodes, and what assign to edges, whether the graph is directed or undirected, and how to layout the graph all must all be explored in order to arrive at the most optimal set of visualizations. This is interesting to me because while some arrangements are optimal due to the context surrounding the data, other cases might favor arrangements based more upon avoiding ambiguity; such as in the example above. However, ‘prescriptive perspectives’ provide a baseline place to start structuring how to express your data by following tried and true methods. The same thing applies to usability heuristics used in evaluation; this method is discount and statistically is not the best, but the PROCESS of working through the heuristic itself provides great reflexive data.
Nominal variables are used to distinguish categories that differ in quality. Sometimes the categorical data is ordered, though no numerical value measures it accurately. The search engine is more like an ordinal variable. The importance of different SE is different. The website ranks first only in MSN may be not as good as another website ranks first only in Google. As is said in Agresti2002 p4, “Analysts often treat ordinal variables as qualitative, using methods for nominal variables. But in many respects, ordinal variables more closely resemble interval variables than they resemble nominal variables. They possess important quantitative features: Each category has a greater or smaller magnitude of the characteristic than another category.”
For example, in City A, 30% people hold Bachelor’s degree, all others don’t have a college degree.
While, in City B, 30% people hold Master’s degree, all others don’t have a college degree.
It is obvious that City B’s overall education level is higher than City A, because of the ordinal nature of education variable.
How about the following case:
Bachelor’s degree Master’s degree
City A 20% 10%
City B 30% 5%
How to compare the education level?
The possibile solution might require analysts to “utilize the quantitative nature of ordinal variables by assigning numerical scores to categories”. “This requires good judgment and guidance from researchers” (Agresti2002 p4)
Color is an effective method to distinguish nominal variables, but lacks sufficient ability to represent ordinal variables. An additional element is required for effective representation. Let’s come back to the case of Search Engine. Google, Yahoo, MSN are not equal to each, each of them has their own weight. Using three different colors as is shown in the picture above is not really appropriate. It would be better if different widths are used for each of the columns to represent the weight of search engine. And the overall traffic is the area, instead of the height of that column.