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I find that in many cases, either a table or a plot will do an equally good job of presenting numeric information. Does anyone have any advice or even rules about when to prefer using a table over a plot and vice versa? I'm referring to tables and plots in the context of academic journal articles.

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I generally prefer plots as they are easier to interpret at a glance. Only use tables when there is lots of information which is hard to put in a plot – nivag Aug 14 '14 at 9:01

I would say: Use tables if the actual values are of importance and use plots if trends (or similar things) are important.

The rationale is simply that one cannot extract actual values of a function at specific places from plot. Vice verse its much simpler to see linear growth or periodicity from a plot than from a table.

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I would add that when both the actual values and the geometrical form are important it is convenient to provide both of them. – Alexey Popkov Aug 14 '14 at 12:23
Tufte offers suggestions for making the precise numeric data extractable from plot while still showing the relationships. – dmckee Aug 15 '14 at 20:12

As @Dirk says, it's often quite useful to preserve the numeric values - that's the motivation for tabulating data. However, plots have the advantage of being able to easily visualize trends in data.

If you have a set grid of x and y co-ordinates, with each pair of co-ordinates having a numeric value, you can sort of do both.

Here is an example. The trends in the data are made much clearer by plotting and colour-coding the data, but the numeric information is preserved. As a result the readability of the numbers isn't perfect, but (depending on your data) you can sometimes have the best of both worlds.

enter image description here

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More often than not, "it's often quite useful to preserve the numeric values" is only true from the perspective of the author, though. :/ – Raphael Aug 14 '14 at 19:21
what is the name of your program? – Ooker Sep 19 '14 at 13:12
@Ooker PGFPlots for LaTeX. See Jake's answer to this question to see how you can do a plot like mine. I just followed his example and added the text annotations using nodes at each set of co-ordinates. – Moriarty Sep 19 '14 at 16:14

In addition to the other answers, I think it depends on how much data you are trying to show. Personally, I like to use tables when I can. If you have only three data points, a figure wastes a lot of space and ink. Tufte calls this the Data-ink ratio. In his book, he recommends:

Above all else, show the data.

So, if you have hundreds of data points, you would show a figure, unless the exact data values matter (in which case it is rather a reference table). But if you have only a handful of points, it is more efficient to display the data in a table. Unless, as other answers point out, you want to visualise a particular relation or trend — then a visualisation is again more appropriate.

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I strongly disagree with your answer. It's one thing to argue that some very limited cases might justify a table. It's another thing entirely to advocate tables as a default choice. I find the later position completely out of sync with current practices in both statistics and scientific publishing. I would suspect that Tufte would in fact disagree with your opinion and he certainly never advocated “using table when [you] can”. – Relaxed Aug 14 '14 at 23:51
I don't know if current practices in statistics and scientific publishing are to use graphics by default, and if it is, I don't know if that is a good thing. Personally, I often see graphs where I would rather see tables (in particular in the powerpoint/excel world), but rarely the opposite. Maybe it's a matter of taste. – gerrit Aug 15 '14 at 2:52
Personally, I do often regret not seeing better plots (dotplots, boxplots, small multiples, plots with the raw data and key indices of central tendency and variability, better ordering when there are several categories, etc.) instead of bar and pie charts but I almost never find myself wishing a table, no. Raw data I would sometimes like, of course, but that's something else. As I explained above what is both currently recommended and very much to my own taste is good plots + raw data and other materials available online. – Relaxed Aug 16 '14 at 13:51

If you are able to do it, use plots, period. What little purpose tables used to have is currently best served by online supplementary material, either on the journal's website or your own.

If you have more than a couple of constants/data points (which would not require a table either), numbers are very difficult to read and (good) plots are much better for human consumption (I don't think this is merely a matter of taste; while I am not an expert there is quite a lot of research on this).

If actual values are actually useful to someone, a table is in fact a very poor way to provide them as anybody wishing to use them must go through a time-consuming and error-prone data entry process. What should actually be done in this case is making the data themselves available electronically. A table is not a decent alternative to that, not anymore.

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I respectfully disagree. If you have three values it is possible to use a plot, but it is neither efficient nor helpful. In fact, any table can be converted into a plot, but the reverse is not true. – gerrit Aug 14 '14 at 15:36
@gerrit Fair point but I would argue you don't need a table in this case either. A sentence will do… More generally, I am being provocative to stress the point but I do think tables are overused left-overs of another time and plots are almost always better. – Relaxed Aug 14 '14 at 15:39
Three is an extreme case. But if the three values are the major result of the research, one might want it to stand out more clearly by having a table. – gerrit Aug 14 '14 at 15:41
@gerrit I still find it difficult to imagine what such a number could be (a theoretical constant?). In my field, a major result would depend on several experiments and have error bars or variability around it so even if the point estimate is important, there is still value in presenting it in context. – Relaxed Aug 14 '14 at 15:43
True, three results + corresponding errors compromise more than three pieces of information. Of course the article (or presentation, or poster) provides context, but I think summarising the results in a table is still valuable. Some explanation in the caption, and then "see text for discussion". That's how I would do it. – gerrit Aug 14 '14 at 15:52

Are the specific values really, really meaningful and relevant? Do they have meaning outside of the sandbox? Are you, for example, publishing new measurements of fundamental constants? No? Then, most likely, the actual numbers have no business being in your article extended abstract.

My rationale is: you are telling a story. Elements that don't serve to make a (major) plot point or at least support it have to go. Nobody will look at the numbers if their values are not relevant or support a point you are trying to make.

Now, there is data that does not lend itself well to the usual plots you can make (line plots, histogramms, bar charts, ...). Sometimes, a table is all you can do, especially if the data has no useful scale in at least one dimension. For example, assume we have investigated four methods in four scenarios and have collected some quality measure; the bigger the number, the better the method worked in that scenario.

enter image description here

What do we see in this table? Nothing, without really reading which may be a waste of time, given that the numbers may not mean anything on their own.

What is the story we want to tell? Maybe something like this: Methods one and three are complementary and excell in their respective strong scenarios; you should pick one of them if you know which category your application falls into. Method two is somewhat useable in all cases but worse than the specialists; use it if you don't know what you have at hand. Never use the fourth method, it's always bad.

We can improve the table so that it supports that story at one glance by normalising the data (I assume a linear scale from 0 to 250 here) and giving visual indication of "good", "meh" and "bad".

enter image description here

Now, the layout of the table can be improved and maybe you want to swap columns so that the complementary methods are neighbours. It is hard to show variances with this visualisation. Furthermore, the choice of colors can be debated (red/green may have different meanings in different cultures; also they can not be distinguished by a sizable portion of all readers).

Still, I think the example serves to support my point: be creative when representing data, with a focus on supporting the narrative of the article and less on dumping data (there's other places for that).

There is plenty of literature on visualising data but I'm not intimately familiar with any, so I'll just point you towards some blogs:

They have plenty of inspiring examples.

One further TeXnical note: it's possible to draw small inline-style plots (called sparklines, apparently) with which you could potentially fill a table.

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Really intuitive – Ooker Sep 19 '14 at 13:20
Great examples and links ! – Moritz Sep 26 '15 at 20:37

I find that in many cases, either a table or a plot will do an equally good job of presenting numeric information.

Strictly speaking, a plot does NOT present numerical information because it is just a picture. The purpose of a plot is to show geometrical form of some dependence(s) when this form is important. It is impossible to recover original numerical information from such picture. The requirement of reproducibility of scientific results requires to provide all necessary information needed to reproduce the results described in the paper. Most journals do not allow publishing large tables of numerical data but they allow to publish supplementary information online which can contain huge tables in TXT format. It is good idea to supply such information and it is free.

The topic of effective visual presentation of information is subject of infographics:

Ben Fry. Visualizing Data (2008)

Cleveland W.S. The Elements of Graphing Data (1985, 1994)

Cleveland W.S. (1993): A Model for Studying Display Methods of Statistical Graphics. // Journal of Computational and Graphical Statistics, 2(4): 323-343.

Tufte E.R. The Visual Display of Quantitative Information (2001)

Wilkinson L. The Grammar of Graphics (2005)

and others.

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Thanks for the answer, but I think that just posting references is not a good way to answer a question. Use those references and links to support your answer to the question. Even if your answer is an abstract of all those links. – Enthusiastic Student Aug 14 '14 at 15:54
Note that Tufte discusses strategies for preserving the precises numeric data in a plot. – dmckee Sep 27 '15 at 2:01
@dmckee Again, plot is just a figure and does not contain numeric data. If the plot is available as a high-quality vector figure, such figure is described using numbers and then it is possible to discuss how precisely the vector data represent original numeric data. But it is a very bad habit to mix numeric data and figures: numeric data usually is presented in tables and allows to create any visual representation you wish, while figure is just a figure - what can you do with it? – Alexey Popkov Sep 27 '15 at 5:39
Er ... Perhaps you don't recall the form that Tufte shows for exposing the precise numeric values in a plot, but I really meant that. A plot with the raw data. The best of both worlds. – dmckee Sep 27 '15 at 5:45
@dmckee Can you provide a reference? If it is in the book "Tufte E.R. The Visual Display of Quantitative Information", please tell which figure do you mean? – Alexey Popkov Sep 27 '15 at 6:00

Readers and listeners tend to read without no more that 16 or about items on the figure during presentation, so a good table should not be larger that 4x4 or about. This is relatively small size. Use plots if you need to present more data.

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Good advice, I think. Does this apply to articles as well? – Raphael Aug 19 '14 at 15:57

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