The Problem with Pictorial Proportional Charts

Pictures are great. People understand them. When someone sees a picture of a house, they are likely to recognize it as just that: a house. Similarly, when someone sees a picture of a small house next to a large house, they will immediately determine some kind of proportional relationship between the two houses. This is one reason why we see pictorial charts in books, magazines and newspapers (oh, right, and on the internet too). Robert Harris, in Information Graphics, points out a number of other benefits of pictorial charts:

• To make the document more interesting and appealing.
• To make the material more understandable to a greater number of people [they are not language-dependent].
• To improve communication in situations where the appearance of an item is better known than the name.
• To facilitate easier reading of a chart or graph by including information to orient the reader that otherwise might have been shown in a legend or note.

I can get behind these points (though, it should be said that if a chart is not needed, it probably should not be added simply to “make the document more interesting and appealing”). Pictures may be understood faster than bar charts, where the reader must trace the horizontal and vertical axes to their respective labels in order to determine what (and how much) is being represented.

That doesn’t mean we should always use pictures though. In fact, we should be careful with them. A picture can be too specific or too general, inadvertently leaving out  some part of the dataset in the mind of the reader. (Who is this guy, anyway? I don’t look like that guy!). Pictures and icons can also be tricky because of different accepted traditions and conventions. A good rule of thumb might be: if you aren’t sure the picture clearly represents your data set, don’t use it.

One particularly popular—yet often misleading—form of pictorial chart is the proportional chart or diagram. Here are some examples… and thoughts on how we could do better.

Oh, my. What do we have here? From Arkin’s Graphs: How to Make and Use Them (1936), these are… well, oranges. The orange on the left represents “44,319 carloads of oranges”; the orange on the right represents “84,944 carloads of oranges”. I wonder if it the US Department of Commerce retained a single car for 10 years explicitly to facilitate this orangey comparison. That seems likely enough.

But in all seriousness, this is a pictorial proportional diagram that isn’t entirely necessary (except as an example of what not to do, as the author has used it). Generally, readers cannot estimate volume based on a diagram nearly as well as they can other visual variables. What about you? When you first saw this, did you look at it and think, “Golly, they sold 1.9 times more carloads of oranges in 1931!”? Or did you simply think, “Hmm… more oranges 10 years later.”

These ladies make the orange chart look like a work of information visualization genius. Arkin stands behind this one, suggesting that it is a stronger graphic since the volume of the figures is used to make the comparison and the pictures are representative of the data they depict (that is, the appearance of the women varies based on age bracket). Sexism of the trans-generational shopping bag aside, charts of this type have another problem to contend with. If volume of a simple shape is difficult to ascertain, deducing it from a complex or irregular shape is nearly impossible. Schmid (Handbook of Graphic Presentation guy) lists a number of common shapes which are particularly difficult to read in this context: humans (d’oh!), ships, automobiles, houses (whoops!) and domestic animals.

Our old buddy, Brinton weighs in on this topic too. He explains the problem with a specific method: “Charts of this kind with men represented in different sizes are usually so drawn that the data are represented by the height of the man. Such charts are misleading because the area of the pictured man increases more rapidly than his height. Considering the years 1696-1700, the pictured minister has about two and one half times the height of the man representing public service. The minister looks over important because he has an area of more than six times that of the man drawn to represent public service. This kind of graphic work has little real value.” Right on, Brinton.

A reoccurring theme in all of the pieces I’ve read on these charts is that: a. they are really easy to read, but b. they are often accidentally misleading, so c. the shapes used should be as uncomplicated as possible. It makes me think… you know what shape is really uncomplicated? A bar… you know, as in “bar chart”. Ha. Nothing is perfect.

That said, some intriguing alternatives to these somewhat awkward proportional charts have gained popularity of late. Some of you may remember one viral graphic from 2009 showing what $1 trillion looks like. While I’m sure there are arguments against using 2.5D space in this graphic (oblique pie charts are the worst, right!?), I actually find that it emphasizes the point. It gives the reader the ability to say, “Gosh! That money is as far as the eye can see!” Perhaps more to the point, if the author attempted creating this graphic in 2D, there would be some major readability issues due to scale. Imagine all of those palettes stacked vertically in one row. Yikes.

After all, the pictorial chart is not unlike most charts, graphs and maps. Compromises need to be made. As long as those compromises are managed well and the readers are aware of them, they are generally quite effective.

ps. I do enjoy this planet and star size comparison video.

pps. Odd timing: immediately after posting this, I saw that information aesthetics had a moderately related post today entitled Social Compare: Visually Compare the Size of Objects and Concepts. Check it out.

ppps. Bonus chart, from Manual of Charting (1924). Hogs, Rubber and Houses. Veritable peas in a roaring 20s pod.

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Ranking Charts: Marital Happiness & US State Population

In addition to the clock graph, another form of graphic that seems to have been quite popular in the early 1900s is the Ranking (or Rating) Chart. Here, I have plucked two examples. The first is from Calvin Schmid’s Handbook of graphic presentation (1954) and the second from our old friend Brinton’s Graphic Methods for Presenting Facts (1914). In a ranking chart, items or categories are placed in order (generally in a vertical fashion) based on frequency or magnitude. In the case of our first chart, marital grievances are ranked in descending order according to intensity for both husbands and wives. To see if there is any relation, a line is drawn that connects identical grievances from each list. The further the line deviates from horizontal, the less agreement the two parties have on that particular grievance. (Perhaps there should have added another line: “way partner ranked grievances”.)

I quite like this graphic… at least partly because it appears as if not a whole lot has changed in terms of Marital Happiness since 1938. We still hear these types of complaints about our friends’ partners (no, I’m not talking about anyone particular. gosh!). Modern-day additions might be “uses smart phone at dinner table” or “hasn’t changed relationship status on Facebook”. Otherwise, these grievances seem—as David Byrne might say—”same as they ever were”. One question here though: what has the author encoded in the line type that is connecting the two lists? Level of agreement? It’s tough to say.

Here is a time series ranking chart showing state and territory population in the US from 1860 to 1900. Some trends can be seen in this chart: steady high population in NY, PA, OH and IL, while some Midwestern and Western states have growing population. I have to wonder, though: is this data better suited for a set of maps in small multiples? I find this web of tangled lines fairly difficult read. Nevertheless, unlike some forms of charts and graphs, I believe an effective ranking chart may not necessarily have an immediate impact on the reader. Instead, further inspection may be required. With a simple glance at the Marital Happiness chart, for example, a reader may not be able to deduce much of anything. But with closer look, he or she might start notice that lines appear to be straighter at the top and bottom of the chart, with the middle looking more criss-crossy. Without knowing the exact grievances, the reader is able to deduce that at least husbands and wives can more or less agree on the BIG and small stuff… right? Right?

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The Hated Clock Graph

The proto-infovis specialist, Willard Brinton, has gotten his fair share of attention on the blogosphere over the last few years. With good reason too—this guy was way ahead of the game, writing about proper methods to be implemented while authoring maps, charts and graphs. Much of his writing, though, is pretty thinly veiled personal opinion. His map pin chapter in Graphic Methods for Presenting Facts (1914) reveals an extreme phobia of “the janitor’s feather duster.” So it should come as no surprise that he might have a few non-scientifically-based asides. Above is one such aside, a rant against the clock graph: This type of chart should be banished to the scrap heap. Wow. Such hatred for such a seemingly harmless graphic.

I’ll admit it; I first saw this graphic (and the comment about rectangular graphics being easier to make and read) months ago. And it’s been on my mind since. I just couldn’t figure out why Brinton would have so much distain for it. To be honest – as long as the variation between observations is not minute (in which case, why would there be a graphic to begin with?) – I actually quite like the look of this type of graphic. It’s decently easy identify a seasonal trend, is it not? But then I ran across Charts and Graphs (1925), by Karl Karsten. And look at what he has to say about these graphs.

As a chart, this is worthless. Great. So this really piqued my interest. What is the deal with these clock graphs!? And why don’t I hate them when I really, really… should? Well, it turns out some are more successful than others. Check out some examples (all pre-1970).

 

Arthur Lockwood, in Diagrams: a visual survey of graphs, maps, charts and diagrams for the graphic designer, refers to these two images as “diagrams”, the first showing temperatures throughout the year and the second showing “employment of working hours on a weekly basis for a group of sample farms in Finland”. Successful or not, it’s pretty clear that Finnish farmers are really into the earth’s crust (though I’m not sure that’s the point). Is it this kind of muddled graphic that fueled Brinton and Karsten’s hatred? I look at this lower image and think I may have been caught up in the aesthetic novelty of the others if I was actually getting ready to defend the clock graph… because, I’m sorry, this Finnish Farmer graph is unnecessarily difficult to read.

 

From Calvin Schmid’s Handbook of Graphic Presentation (1954), here’s another clock graph. I think this one mostly works… but now I’m starting to agree with Brinton. Does the polar coordinate system really add anything to this data set? And as for Karsten’s hatred… well, if you root around a bit more in his book, you’ll find the following two clock graphs.

 

 

I think the bottom graph is fairly well readable. But the top one gets a little muddy. Does it have too many subsets of data? It might not, if there is any meaningful correlation. But is there? To me, it simply looks like this department store sells more stuff on Saturdays in December. Do we need a graph for that? And if we do, do we need it to be a clock?

I still think there is a place for these charts. I really do. But after looking closer at those made during the age of Brinton and Karsten, I completely understand the distain.

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