Overview: Graphical Analysis

You have certainly heard the expression, a picture is worth a thousand words. While this may be an overstatement, it is often very useful to describe a relationship between phenomena in visual form. If you are interested in a broader treatment of the issue of presenting information visually, I would suggest three books by Edward Tufte: The Visual Display of Quantitative Information, Envisioning Information, and Visual Explanations. Tufte's message is clear: text, tables, and graphics should be viewed as alternatives - each with its strengths and weaknesses which is why they continue to coexist. The pages of his books are filled with a number of fascinating examples of success and failure in presenting information graphically. Three of my favorites which will be discussed in class are the tabular representation of information presented in the John Gotti trial, the graphical representation of data on the London cholera epidemic of 1854 developed by John Snow, and the presentation of the data on O-ring failures that provides some insight into the space shuttle Challenger disaster of 1986.

One of the most popular techniques for visually displaying quantitative information is the graph, but you know that if you have opened an introductory economics textbook or read the financial sections of newspaper or magazines. Unfortunately, my experience has clearly indicated that there is a considerable amount of information lost in the translation between words and graphs. Stated somewhat differently, it has become painfully clear to me that graphs are often misunderstood by students. On the input side, graphs often get in the way of student's learning of economics rather than aiding in their learning, and on the output side, graphs seldom add to the quality of student presentations / writing.

And this is not peculiar to Economics. Richard Bowen, a Psychology researcher who has seen much the same thing in his discipline, has actually written an interesting little book, Graph It! How to Make, Read, and Interpret Graphs. In his book he talks of Graphicacy, graph literacy, as the goal for his readers. He recognizes, however, that to achieve this goal he will need to help many overcome Graphobia, the fear of graphs, and motivate others to make the investment in developing the skills necessary to create and interpret graphs. Fortunately, these skills will pay off well beyond any one college course since more and more data is being presented in quantitative form and very often the data is presented graphically.

The difficulty that many people have with graphs is not surprising once you realize how recently we 'discovered' graphs. Until the 1800s graphical design was dependent upon a direct analogy to the physical world. The first graphics were maps. When you look at a sheet of paper, it is fairly easy to make the transition from movements right-left and up-down to physical movements north-south and east west where the grid lines substitute for latitude and longitude. We tend to order things spatially and thus it was a natural to develop maps that mimicked that order. For example, look at the map of the URI campus at Kingston. Once you get yourself orientated to the north, if you turn to the right you will be able to look at the map and see what you will be looking at. If you are looking North while standing in Chafee and then turn to the right you will see Woodward and Tyler Hall, which is just what you see in the map. You will also see that Tyler is about twice as far from Chafee as Woodward so not only is direction retained, so is concept of distance (URI map).

Similarly, if you have a map of the Kingston area surrounding URI (the star), you will find that Wickford is to the northeast of campus and that Newport is approximately twice as far in the easterly direction. If you are looking for some mapping programs, you may want to try the US Census and Mapquest.

When did we begin to see high quality maps? One of the earliest maps was produced in China in 1137 - nearly 400 years before comparable maps were produced in Western Europe. It was not until the late 1600's, however, that we began to see the emergence of data maps-a map to which we added data. The reason it took so long may - a combination of cartographic and statistical tools. An example of a data map that is available electronically today appears below. What is missing is the legend, but we can see that there is 'something' that sets apart the Northeast, and area extending from Virginia to New Hampshire, and California as well as the lower Mississippi delta region (Arkansas, Mississippi, and Louisiana).

Median Family Income: by State

Eventually, however, we were able to extend the reach of our visual representation of information beyond space to time and by 1786 we saw our first time-series graph in The Commercial and Political Atlas, by William Playfair. Now we could visualize the passage of time with a graph-just as we had been able to envision the passage of space. Just as we could say that the movement from Kingston to Newport was twice the move from Kingston to Wickford, now we can say that the movement from 1970 to 1980 was half the distance of the move from 1970 to 1990.

Our ability at ordering time allowed us to translate time-series relationships fairly easily into time-series graphs that help us to 'see' the relationship between interest rates and time. In the graph below, the reader can easily see that interest rates peaked in 1980 and have been following a cyclical pattern downward.

Occasionally, we can combine space and time in one graph. One very impressive example would be Charles Minard's graphical depiction of Napoleon's march into Russia which we will talk about in class.

The final advance in the graphical display of information was to move beyond space and time to relational graphics. Again it was Playfair who "broke free of the analogies to the physical world and drew graphics as designs-in-themselves." The implication was that 'any variable quantity could be placed in relationship to any other variable quantity, measured for the same units of observation."

The examples of these relational graphs from your economics books are numerous, although as Tufte pointed out, these graphs are not too frequent in the popular press. When he examined 15 news publications for the years 1974-1980, it was in Japan and Germany where we saw highest use of relational graphics, but even here the number of statistical graphics that were based on more than one variable, but were not time-series or maps, ranged between 5 and 10 percent. One of my favorites, The Economist, had only 2 percent while the New York Times and Time had .5 percent and 0 percent.

In a similar review of college and high school textbooks, Tufte found relational graphics to be significantly more common in a number of disciplines-ranging up to 77 percent in the high school text, Chemical Principles by William Masterton and Emil Slowinski to 82 percent in the college text, Statistics: A Guide to the Unknown by Judith Tanurnum. Among the three economics texts reviewed, relational graphics accounted for 16 percent of the statistical graphics in the classic college text by Samuelson, about midway between what he found in two high school texts.

It's now time to try your hand at data graphics which Tufte describes as visually display quantities by means of the combined use of points, lines, a coordinate system, numbers, symbols, words, shading, and color." As it turns out, it is a good thing that the creator of the graph has so many dimension to use since in the majority of cases what we are interested in representing are multivariate relationships on sheets of paper-what Tufte calls the flatlands.

When you see a graph, you should think that behind this graph is a table of numbers and that the creator of the graph was attempting to make it easier for the reader to see the story / pattern that existed in the data. As Bowen indicates, "Graphs are intended to make it easy to read, understand, and remember a relationship found in a set of data." To get there, however, we need to look a little more closely at the mechanics of the various graphs. You should review the Outline that describing the various types of graphs that you might create or be asked to interpret.