Why Tables are Really Much Better than Graphs1
Andrew Gelman2
28 October 2009

Abstract. The statistical community is divided when it comes to graphicalmethods and models. Graphics researchers tend to disparage models and to focus
on direct representations of data, mediated perhaps by research on perceptions but
certainly not by probability distributions. From the other side, modelers tend to
think of graphics as a cute toy for exploring raw data but not much help when it
comes to the serious business of modeling. In order to better understand thebenefits and limitations of graphs in statistical analysis, this article presents a
series of criticisms of graphical methods in the voice of a hypothetical old-school
analytical statistician or social scientist. We hope to elicit elaborations andextensions of these and other arguments on the limitations of graphics, along withresponses from graphical researchers who might have different perceptions ofthese issues.

1

To appear (with discussion) in Journal of Computational and Graphical Statistics. We thank the Instituteof Education Sciences for partial support of this work.
2
Department of Statistics and Department of Political Science, Columbia University,gelman@stat.columbia.edu, http://www.stat.columbia.edu/~gelman/

The benefits and limitations of statistical graphics
My purpose in writing this article is to elicit lively discussion of the uses of graphicalmethods in statistical analysis.
Graphs tend to be ignored or underused in much of the literature of statistics and appliedfields (see, for example, Gelman, Dodhia, and Pasarica, 2002, and Kastellec and Leoni,
2008), and the literature on graphical methods is small and is mostly separate from therest of statistics. The related field of data visualization has become increasingly
prominent in digital communication and the arts, but there the focus is typically on eyecatching design rather than on conveying statistical information.3
Here I would like to stimulate considerations of the connections between graphics andmore formal statistical analysis, along with a serious discussion of the drawbacks ofvisual presentation of quantitative information: if graphs really are so wonderful andunderused in applied statistics (as I in fact believe), what is holding people back from
integrating them much more into data analysis?
Following the revolution begun by Tukey (1970, 1977) and continued by Chambers et al.
(1983), Cleveland (1985), and Tufte (1983, 1990), graphical methods for exploratory data
analysis have generally been recognized to be a useful first step in any statistical study.
Beyond this, though, there is disagreement, with the dominant strain of appliedresearchers (at least in social science) feeling that, when the serious models come out, it’stime to put the graphical toys away. From the other direction, researchers in statisticalgraphics often disparage models and to focus on direct representations of data.
There is a lot of valuable work combining analytical modeling and graphical display (fora classical example, consider Daniel, 1959), but in much of the published work inpolitical science, economics, sociology, and other areas, graphics have little if any serious
role, being used to display some simple data summaries and never seen again, with
important findings displayed in tabular form.
Those of us who believe graphing to be important and even essential to research would
be well advised to think hard about why visual displays are not used more extensively inserious applied research. To this end, this article presents a series of attacks on graphicalmethods in the voice of a hypothetical old-school analytical statistician or social scientist.
Although this originated as an April Fool’s blog entry (Gelman, 2009a), I believe theseare strong arguments to be taken seriously—and ultimately accepted in some settings andrefuted in others. I welcome elaboration and discussion of these points by statisticians
and statistically-minded researchers in applied fields. I have my own answers to some ofthese objections but do not present them here, in the interest of presenting an open forum
for discussion.
3

For example, when the influential (and interesting) Flowing Data blog published a list of the “5 best datavisualization projects of the year” (Yau, 2008), a debate ensued over whether data visualizations should
aim for transparent communication of information (Gelman, 2009b,c) or for visual novelty and beauty(Yau, 2009).

The arguments I lay out are, briefly, that graphs are a distraction from more serious
analysis; that graphs can mislead in displaying compelling patterns that are notstatistically significant and that could easily enough be consistent with chance variation;that diagnostic plots could be useful in the development of a model but don’t belong in
final reports; that, when they take the place of tables, graphs place the careful reader one
step further away from the numerical inferences that are the essence of rigorous scientificinquiry; and that the effort spent making flashy graphics would be better spent on thesubstance of the problem being studied.
Some problems with graphs
Graphs are gimmicks, substituting fancy displays for careful analysis and rigorous
reasoning. It's basically a tradeoff: the snazzier your display, the more you can get awaywith a crappy underlying analysis. Conversely, a good analysis doesn't need a fancy
graph to sell itself. The best quantitative research has an underlying clarity and asubstantive importance whose results are best presented in a sober, serious tabular
display. And the best quantitative researchers trust their peers enough to present theirestimates and standard errors directly, with no tricks, for all to see and evaluate. Let'sleave the dot plots, pie charts, moving zip charts, and all the rest to the folks in themarketing department and the art directors of Newsweek and USA Today. As scientists
we're doing actual research and we want to see, and present, the hard numbers.
To get a sense of what's at stake here, consider two sorts of analyses. At one extreme arecontrolled experiments with clean estimate and p-value, and well-specified regressions
with robust standard errors, where the p-values really mean something. At the otherextreme are descriptive data summaries—often augmented with models such as
multilevel regressions chock full of probability distributions that aren't actually justified
by any randomization, either in treatment assignment or data collection--with displays ofall sorts of cross-classified model estimates. The problem with this latter analysis is notreally the modeling—if you state your assumptions carefully, models are fine—but thedisplay of all sorts of numbers and comparisons that in no way are statisticallysignificant.
For example, consider a research article with a graph showing three lines with different
slopes. It's natural for the reader to assume, if such a graph is featured prominently in thearticle, that the three slopes are statistically significantly different from each other. But
what if no p-value is given? Worse, what there are no point estimates are no standard
errors to be found? Let alone the sort of multiple comparisons correction that might beneeded, considering all the graphs that might have been displayed? Now, I'm not
implying any scientific misconduct—and, to keep personalities out of this, I've refrained
from referring to the article that I'm thinking about here—but it's sloppy at best andstatistical malpractice at worst to foreground a comparison that has been presented withno rigorous--or even approximately rigorous--measure of uncertainty. And, no, it's not an
excuse that the researchers actually "believe" their claim. Sincerity is no defense. There'sa reason our forefathers developed p-values and all the rest, and let's remember thosereasons.
To flip this discussion around, what are sorts of graphs do we commonly see in statistics
textbooks? Residual plots, influence diagrams, quantile-quantile plots . . . a bunch of
cookbook routines that have little to do with exploratory data analysis as it might bepracticed. In addition, it doesn’t usually make sense to include diagnostic plots inpublished articles: if the plot reveals a problem, the model should be fixed, whereas if noproblem is found, the graph is typically not very informative and so there’s no point in
displaying it.
The positive case for tables
So far I've explained my aversion to graphs as an adornment to, or really a substitute for,scientific research. I've been bothered for a while by the trend of graphical displays injournal articles, but only in writing this piece right here have I realized the real problem,
which is not so much that graphs are imprecise, or hard to read, or even that theyencourage us to evaluate research by its "production values" (as embodied in fancy
models and graphs) rather than its fundamental contributions, but rather that graphs are
inherently a way of implying results that are often not statistically significant. (And all
but the simplest graphs allow so many different visual comparisons, that even if certain
main effects actually do past the p-value test, many many more inevitably won't. Sometechniques have been developed to display multiple-comparisons-corrected uncertainty
bounds, but these are rarely included in graphs for the understandable reason that theymagnify visual clutter.)But enough about graphs. Now I'd like to talk a bit about why tables are not merely anecessary evil but are actually a positive good.
A table lays down your results, unadorned, for the readers—and, most importantly,
scientific peers—to judge. Good tables often have lots of numbers. That's fine—different
readers may be interested in different things. A table is not meant to be read as anarrative, so don't obsess about clarity. It's much more important to put in the exact
numbers, as these represent the most important summary of your results, estimated local
average treatment effects and all the rest.
It's also helpful in a table to have a minimum of four significant digits. A good choice isoften to use the default provided by whatever software you have used to fit the model.
Software designers have chosen their defaults for a good reason, and I'd go with that.
Unnecessary rounding is risky; who knows what information might be lost in the foolishpursuit of a "clean"-looking table?
There is also the question of what words should be used for the rows and columns of thetable. In tables of regressions, most of the rows represent independent variables. Here, I
recommend using the variable names provided by the computer program, which are
typically abbreviations in all caps. Using these abbreviations gets the reader a little closer

to your actual analysis and also has the benefit that, if he or she wants to replicate yourstudy with the same dataset, it will be clearer how to do it. In addition, using these raw
variable names makes it more clear that you didn't do anything shifty such astransforming or combining your variables before putting them in your regression.
We'd do well to take a lead from our most prominent social science colleagues—the
economists—who have, by and large, held the line on graphics and have insisted on
tabular presentations of results in their journals. One advantage of these norms is that,when you read an econ paper, you can find the numbers that you want; the authors ofthese articles are laying it on the line and giving you their betas. Beyond this, thestandardization is a benefit in itself: a patterned way of presenting results allows theexpert readers--who, after all, represent the most important audience for journal articles-to find and evaluate the key results in an article without having to figure out new sorts ofdisplays. Less form, more content: that's what tables are all about. If you've foundsomething great and you want to share it with the world, sure, make a pretty graph andput it on a blog. But please, please, keep these abominations out of our scientific journals.
B-b-b-but . . .
Yes, you might reply, sure, graphics are manipulative tricks and tables are the best. But
doesn't the ambitious researcher need to make graphs, just to keep up with everybody
else, just to get his or her research noticed? It's the peacock's tail all over again—I don't
want to waste my precious time making fancy 3-D color bar charts, but if I don't, mywork will get lost in the nation's collective in-box.
To this I say, No! Stand firm! Don't bend your principles for short-term gain. We're all inthis together and we all have to be strong, to resist the transformation of serious social
science into a set of statistical bells and whistles. Everything up to and including orderedlogistic regression is OK, and it's fine—nay, mandatory—to use heteroscedasticityconsistent standard errors. But No to inapporpriate models and No to graphical displaysthat imply research findings where none necessarily exist.
Beyond this, even in the short term I think there are some gains from going graph-free.
The time you save not agonizing over details of graphs can be instead be used to think
more seriously about your research. Undoubtedly there's a time substitution: effort spenttinkering with graphs (or, for that matter, blogging) is effort not spent collecting data,
working out models, proving theorems, and all the rest. If you must make a graph, try
only to graph unadorned raw data, so that you're not implying you have anything you
don't. And I recommend using Excel, which has some really nice defaults as well as
options such as those 3-D colored bar charts. If you're gonna have a graph, you might aswell make it pretty. I recommend a separate color for each bar—and if you want to throw
in a line as well, use a separate y-axis on the right side of the graph.
I’m sure there are a lot of other problems with statistical graphics that I’ve missed. You
can take it from here.

References
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Cleveland, W. S. (1985). The Elements of Graphing Data. Pacific Grove, Calif.:
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Daniel, C. (1959). Use of half-normal plots in interpreting factorial two-level
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