Student Project: Understanding Numerical Graphics

This describes a project suitable for three students. Please let me ( know by Nov. 1 if you intend to undertake the project. Students who undertake the project are exempted from the final exam.

The assignment is focused on graphics depicting numerical relations, but it could be acceptable to contrast alternative graphical communication in another area. If you wish to do this, send a proposal for approval to the course instructor, John Nerbonne, at

Background: Understanding Graphics Depicting Numerical Relations

Tufte (The Visual Display of Quantitative Information, p.81) is scathing about graphics that display relations in forms fit for single variables. He describes these as "convoluted specimens" of "elliptical and eccentric communication". But more than fifteen years later the same sorts of graphical devices were used to describe what went wrong in the American presidential elections in Palm Beach, where the form of the ballot apparently led to significant miscasting of votes.

The Issue being Communicated

A voting ballot with an unusual form was used in Palm Beach, where a very conservative candidate, Pat Buchanan, received an unusual number of votes in the 2000 US Presidential Election. See (the beginning of) Matt Ruben's informative web site on the problem. Since we'll focus on the choice of graphic design used to illustrate the problem, it is not necessary (and probably not possible even for me) to try to understand all the various statistical analyses that have been published about this question. Briefly, analyses have tried to show that Buchanan received many more votes than one would expect based on the number of votes which candidates of similar political leanings received.

The Graphics

We take this to be a case where two variables (quantities) are compared, the number of votes for Buchanan on the one hand, and the number of votes, e.g., for Bush on the other. It is a standard case where a scatterplot, perhaps with a regression line, is normally used, just as Tufte (above) insists. See Michael Shamos's use of a scatterplot by Greg Adams on the last page of this powerpoint presentation on the Palm Beach predicament.

But not everyone has illustrated the issue using a scatterplot. For example Til Rosenband at MIT expression the ratio between the two votes as a single variable, and plots that in a bar chart.

The Communicative Effect

The task in this final project will be, not to determine how likely it is that voters miscast their votes because they misread the ballot, but rather to determine how well people (students) understand the argument that Buchanan probably received too many votes on the basis of the different numerical graphs.


The idea is to present similar groups of students with one of two graphs, for example, either as a single bar chart or as a scatterplot showing the variable values (vote counts or percentages). The students should get a chance to examine the graphics, after which they will be asked questions about the content. The purpose of the questions will be to check on how well the graphics convey the information that they are supposed to convey.


Since you wish to see what information is available from the graphics, you should not use the Palm Beach issue directly. If you used the Palm Beach issue, you might just elicit information about what people think about Palm Beach. A first task is then to make up an issue involving two quantities (perhaps student-staff ratio in different departments, or the thesis grade and the number of months taken to complete it). The graphs reporting on the issue should be significantly different, e.g., one a scatterplot (such as Adams used) and the other either a representation of single ratio between the two variables (such as Rosenband's) or perhaps a representation of the two variables in bar charts next to each other. It is essential that the graphics be as comparable as possible except for this design point. A second task is thus to redraw them.

It is essential that the graphics be as comparable as possible except for this design point. Second, the graphics should be accompanied by a small amount of prose (a caption), explaining the message the graphic is meant to support. Ideally, the caption would be the same for both forms of the graphic, but certainly as close as possible. The captions and graphs should definitely all be in the same language, and I would suggest that it be done in Dutch so that fluency in English is not a confounding factor.


The test should focus on whether the subjects have understood the issue as the graphics presents it. An important task is therefore to design the test questions. Aim for ten questions, and include some questions that are very easy (as a check that people are filling in the test seriously). For example, if the test were on the Palm Beach issue, suitable questions might be the following: Naturally, your test questionaire will not include the answers. You might prepare the graphics either on the web or on paper, but it's probably a good idea to have the questions on paper so that you'll have a record.

"Pilot runs"

It is a good idea to have a couple of people try your test before gathering data. This way you won't do a great deal of work, and then discover, only in the analysis that subjects misunderstood your questions, or that there was an error in the graph. Select people outside your group to try out the graphics and the test.

Collecting Data

Aim to have 40 subjects in total read the graphics and answer the questions, i.e., 20 for the one sort, and 20 for the other. Since you won't have a great deal of time to complete the study, I'd suggest that you approach students in the cafeteria. Note that we don't suspect that this group should be different with respect to their sophistication in graphical understanding. Flip a coin to decide which graphic they get so that they are assigned randomly to the one or other group. Once you have 20 students in one group, just let all the other subjects take the test for which you need more data. Do not explain the test in great detail, only that it's a test of effective communication, that you'll ask them to answer some questions about a graphical presentation, and that you'll measure how long it takes them to answer. You may refer them to this web site if they want further information.

Control the conditions under which people take the test. It is best to have them work in conditions where distractions are not great --- perhaps a quiet time of day. Let people look back at the graphic in order to answer the questions. It is essential that people work under roughly the same conditions.. If the test is interrupted, let it continue and record the data, but note that this has happen. It is best to collected enough data so that you don't need to include this questionable data in the analysis.

Let them take as long as they want (once they have been told that the time is also interesting). Measure and record the time with the test material. Thank the subjects when they're done. You may explain the experiment in more detail once they're done, if they ask for this.


Since you'll be dealing with two non-overlapping groups of subjects, you can analyse whether there is a difference in their average accuracy or speed by performing a t-test for independent samples on the two groups. This can be done easily in SPSS, and there are indications of how to do it available under the web site for the course in Toetsende Statistiek. This will be easiest for someone who has already taken that course. For someone who's already taken the course, it should also be straightforward to check on whether there's a relation between speed and accuracy by performing a linear regression analysis.


In your (group) report, you should explain the issue, including Tufte's ideas on this and perhaps the ideas of others you might find through a literature search. Describe why your experiment should have bearing on the issue, and in particular what you hope to prove or disprove.

Describe the graphics you use, and the test and include all of the material in the report. Describe the experiments, including any unexpected developments that might have influenced the outcome. Report on the statistical analysis, preferably in the standard way (known to those who've already taken the statistics course). Finally, discuss your results, and include suggestions for further experiments in a similar vein.


Nov. 4 Groups formed. Commitment to project instead of exam. Two alternative graphical representations made.
Nov. 11 Test materials developed. "Pilot" test run completed.
Nov. 18 50% of subjects completed.
Nov. 29 Reports due (5 pm).

Turn in your report by Nov. 29, 2002 at 5 pm

John Nerbonne
Last modified: Oct. 14, 2002