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«1. GRAPH PEOPLE VERSUS TABLE PEOPLE We are grateful to Andrew Gelman for what can best be described as thought-provoking chutzpah, in its most ...»

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DISCUSSION ARTICLE

Comment

Michael FRIENDLY and Ernest KWAN

We consider Gelman’s claims about the relative merits of tables versus graphs from

a psychological perspective that emphasizes the role of data displays in the communication of quantitative results from authors to readers or viewers. From this perspective,

we consider these claims in relation to a cognitive distinction between graph people and

table people.

1. GRAPH PEOPLE VERSUS TABLE PEOPLE

We are grateful to Andrew Gelman for what can best be described as thought-provoking chutzpah, in its most positive sense. To reply in like manner, we write this in the firstperson, non-royal I.

Thus, I will begin with a bald assertion: there are two kinds of people in this world— graph people and table people. If you sit in your local Starbucks, or even in a departmental faculty meeting and gaze around, you will have trouble at first distinguishing them by sight.

But trust me—I have a Ph.D. in quantitative and cognitive psychology, so I should know what I am talking about. With a little training, you can do this, too.

Establishing this assertion scientifically is similar to what psychologists have done for over 100 years, using techniques of principal components analysis, factor analysis, and more recently, structural equation modeling, almost all of which we developed. As a result (e.g., McCrae and Costa Jr. 1987) we now know that nearly all the aspects of your personality can be summarized along five dimensions: the so-called Big 5: Openness to experience (appreciation for art, adventure, curiosity,... ); Conscientiousness (self-discipline, act dutifully,... ); Extraversion (positive emotions, seeking the company of others,... );

Agreeableness (compassionate and cooperative toward others); Neuroticism (experience unpleasant emotions easily, such as anger, anxiety, depression,... ).

With only a little bit of training, you will easily be able to classify Aunt Bertha, cousin Charles, your department chair, and others along such dimensions. If pressed, I will even

Michael Friendly is Professor, Psychology Department, York University, Toronto, ON, Canada (E-mail:

friendly@yorku.ca). Ernest Kwan is Assistant Professor, Sprott School of Business, Carleton University, Ottawa, ON, Canada (E-mail: ernest_kwan@carleton.ca).

© 2011 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America Journal of Computational and Graphical Statistics, Volume 20, Number 1, Pages 18–27 DOI: 10.1198/jcgs.2011.09166b COMMENT 19 admit that my academic forefathers established all this primarily with tables, though they

did use graphic methods of factor rotation extensively before the advent of analytic methods. As psychologists, we even invented a convenient acronym for you to remember this:

OCEAN.

So, my assertion is first that there is another underlying dimension, not of personality, but rather of cognition, underlying both the presentation of quantitative information in tables and graphs by authors and the understanding of this information by readers and viewers. What works best depends most strongly on the match between the requirements of a given task on the one hand, and the skills and orientation of reader or viewer on the other.

The second part of my assertion is that these distributions, in the general population, are at least strongly bimodal, if not fully two-point, discrete distributions—graph people versus table people. Thanks to the recent important developments in Bayesian computational statistics, I do not have to address the stronger, two-point claim here, given my prior.

My initial diagnostic impressions from reading Gelman’s article are recorded in my case notes: “As clear a case of graphic-denial as I’ve ever observed; ask about tabular-tendencies of parents and mentors; should we try the penile-erectile test with brief visual presentations of tables and graphs? What is the real question?”

WHAT IS THE QUESTION?

1.1 Gelman raises the question of why tables might be better than graphs (or not) with tongue firmly planted in cheek to stimulate discussion, and this is a worthy goal. As he overstates his case, this tabular-centric view invites the conclusion that almost any form of tabular presentation will suffice, as long as it is factually correct.

But in any debate, it is useful to know exactly “what is the question?” In as fine an example of the shifting-sands school of rhetoric as I have seen in a while, Gelman frames the comparison of tables and graphs in different ways, each nicely illustrated with ad hominem arguments: Graphical methods (cute toys) versus statistical modeling (serious statistics);

use of graphs in the statistical literature (ignored or under-used) versus data visualization (eye-catching fluff); use of graphs in applied social science (little serious role).

Part of this debate has a long history, largely centered on the nature of the task (look up a precise value? make comparisons? detect trends, differences or anomalies?); see the article by Gelman, Pasarica, and Dodhia (2002, sec. 2.1) for a brief summary. Here, I just want to call attention to a brief note by Karl M. Dallenbach (1963), the editor of the American Journal of Psychology from 1926–1967. Publication of graphs in this journal had always been difficult and deprecated (requiring expensive “line cuts”), and Dallenbach had been largely a table person. In this note, he reports an epiphany: a long-undetected error from an earlier article caused him to “deduce from that error some evidence regarding the relative value of tables and graphs in the presentation of experimental result.” From his evaluation





of this case he morphed to a graph person. He concluded:

All the evidence obtained from the reproduction of the study mentioned here indicates that the graphic method is ‘better’ than the tabular. Tables, since graphs are based on them, are necessary, but they are like background rocks, heavy and uninteresting. Graphs, on the other hand, spice the reports; clarify them, and make them interesting and palatable. (Dallenbach 1963, p. 702) 20 M. FRIENDLY E. KWAN AND I describe this here to give some comfort to Gelman and other table- or crypto-table people reading this. Although the evidence on the Big 5 traits of personality suggests that they are relatively immutable over one’s lifetime and may even have some genetic component, cognitive capacities are more mutable, so even a predisposition as a table person is subject to change.

1.2 MODES OF COMMUNICATION: WORDS, NUMBERS, PICTURES

A good deal of confusion disappears when one considers a graph or table as an act of (or attempt at) communication, similar to using words. Then, more interesting questions

arise:

• What is the communication goal?

–  –  –

• Was the communication effective?

Thus, a given scientific result or statistical analysis can be conveyed in different forms—words, numbers (p-values, parameter estimates, or tables), or pictures (graphs or diagrams)—for different purposes (analysis or presentation), to achieve different communication goals (exploration, detection, comparison, aesthetics, or rhetoric). Moreover, this view suggests that communication is an activity directed from a source (author) to a target (reader or viewer) and therefore the communication mode should be tailored to the audience in order to achieve the desired goal.

In fact, we can take this further, and consider the proposition that the majority of human communication involves, to a fair approximation, different relative proportions of the three primary ingredients: words, numbers, and pictures. Figure 1 shows some examples that help to position graphs and tables in a wider context. I freely admit that this is just a cute toy and it is not based on any data. But it does show that (in my view) tables occupy a rather lonely position, and I would have been foolish to try to present this view in a table.

Most statisticians and applied researchers know implicitly how this works. In the analysis stage, you use a collection of statistical and graphical methods both to summarize the data (often in tables of numbers) and to expose it (in graphs); you make notes (in words) regarding what you have seen and come to believe. At this stage, you are both the author and viewer, and the communication goal is the “Aha!” experience—you have found something noteworthy. In a conference presentation, you have only 20 minutes to convince your audience that what you have found is indeed interesting, so you need to focus on the “Wow!” experience. If you are smart, you will use a larger proportion of incisive visual displays, not all of the words you could have used on your slides, and tables of numbers only as necessary. Finally, you want to publish your findings, so you need to think of the communication goals and audience anew, but particularly the editors and reviewers who will decide whether you publish or perish. This goal should help decide the mix of words, numbers, and pictures in what you write and submit. Of course, through all of this is another layer: are you a graph person, or a table person? What about your audience?

COMMENT 21 Figure 1. Modes of communication, as composed of words, numbers, and pictures, displayed in trilinear coordinates. Each point shows the (fictitious) composition of a given communication form, referred to the vertices representing 100%. The online version of this figure is in color.

2. USE OF GRAPHS AND TABLES IN SCIENTIFIC PUBLICATION

Gelman asserts that “graphs tend to be ignored or underused in much of the literature of statistics and applied fields,” but this view is highly selective and ignores a growing body of research on the role of graphs (and of tables) in the construction and communication of science, as well as trends in the history of data visualization. From the previous section, it should be clear that use of graphs or tables in journal publication represents just a slice of the communication goal—intended audience tableau, but let us see where this takes us.

In a classic article Cleveland (1984) surveyed the use of graphs in 14 disciplines for the years 1980–1981, selecting 57 journals (4–5 in each area), with 50 articles selected randomly from each journal. Given that page space in journals is a limited resource, he measured the “fractional graph area” (FGA), or proportion of the total area of all journal pages devoted to graphs. Cleveland was careful in his tabulations, excluding figures such as apparatus illustrations, theoretical diagrams, etc.: “a figure was judged to be a graph if it had scales and conveyed quantitative information,” so the FGA measure represented the amount of text displaced by graphs.

The results, presented in a dotplot (Cleveland 1984, fig. 3) compared journals in natural science, mathematical science, and social science. For example, the average graph use in natural science journals (chemistry: 0.18; physics: 0.17) vastly exceeded that in social science journals (economics: 0.025; sociology: 0.01).

More recently, other authors have taken up the more detailed study of the use of graphs versus tables across and within disciplines. Noteworthy here are articles by Smith, Best, and collaborators (Smith et al. 2000, 2002) where they asked respondents to rate each of the disciplines from the Cleveland study on a 1–10 scale, distinguishing “soft” science at the low end from “hard” science at the high end. As shown in Figure 2(A), use of graphs (in terms of FGA) across disciplines was nearly perfectly correlated with the rated hardness of the discipline.

22 M. FRIENDLY E. KWAN AND

–  –  –

Figure 2. Proportion of journal page area devoted to graphs, in relation to rated hardness.

(A) For seven scientific disciplines; (B) for 10 psychology journals. (Source: Smith et al. 2002, fig. 1.) It should therefore not be surprising to Gelman that graph use in political science (somewhere between sociology and economics in hardness) is at the lower end of the continuum.

If he is to “take a lead from our most prominent social science colleagues,” he would do somewhat better to follow the exemplars set in psychology than in the dismal science of economics. As well, he (Gelman, Pasarica, and Dodhia 2002) and others in political science (Kastellec and Leoni 2007) have amply demonstrated some impressive ways in which tabular displays of even complex statistical models and model comparisons can be turned into graphic ones that preserve the essential information and make the results far more apparent.

What might be surprising is that this strong positive relation between graph use and “hardness” also applies within subfields of a given discipline. In psychology, journals range from the soft side (J. Counseling Psychology, J. Educational Psychology) to the harder side (J. Experimental Psychology, Behavioral Neuroscience). In a parallel study, Smith et al.

(2000) obtained ratings of hardness for 10 psychology journals and also calculated graph use (FGA) for 156 articles distributed across these journals. Their results (Figure 2(B)) show nearly as strong a relation between hardness and graph use within psychology as the relation across disciplines.

The icing on this cake is shown in Figure 3, which shows the comparison between use of graphs and tables across these subfields of psychology. As rated hardness increases, area devoted to tabular displays decreases. This inverse relation is not unexpected, but the magnitude of the effect might be: in the two softest journals, the ratio of graph use to table use was about 1 :10; among the hardest-rated journals, this ratio approached 10 :1. It is also noteworthy that the total space devoted to data displays (tables and graphs) was more nearly constant, averaging about 14% of total page area; nevertheless, there was a smaller tendency for data display area to increase with rated hardness (r = 0.35).



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