Pyramid Perversion – More Junk Charts

by Stubborn Mule on 12 March 2010 · 24 comments

Food pyramid charts

Knowing the reaction it would elicit, an old friend of mine sent me a link to an article entitled “Shocking Graphic Reveals Why a Big Mac Costs Less Than a Salad”, which featured the chart pictured here. I did indeed find the graphic shocking, but not for the reason the headline writer intended. The graphic in question, taken from the Consumerist which in turn had taken it from Good Medicine*, shows a pair of charts comparing the levels of subsidies different food types receive in the US compared to recommended dietary intake of corresponding food groups. Needless to say, the foods receiving the largest subsidies are the ones that should be consumed in the smallest proportions and the conclusion: no wonder Americans are getting fatter.

The idea that the US government’s agricultural policies appear to be producing decidedly unhealthy outcomes is one I have been reading about in the fascinating book The Omnivore’s Dilemma: A Natural History of Four Meals (its tale of the sex-life of corn alone makes it worth the price) and so this was not what I found shocking about the graphic. What shocked me was the travesty of data visualization used in the graphic: pyramid charts.

It should not be surprising that charts like this are becoming increasingly common since so many charting tools try to lure you into using them. The screenshot below shows the options that the current version of Microsoft Excel offers under the heading “Column” charts. I would argue that everything below “2-D Column” should be banned from the arsenal of the thinking chart-user. These variants on three-dimensional graphics all represent the trap “chart junk”: fancy extra details that, at best, add nothing to the information being conveyed and, at worst, result in distortion. Cones and pyramids fall well into the distortion category.

No doubt echoes of the “food pyramid” trope made the choice of pyramids an irresistible temptation for the Consumerist. The problem is that the data is represented by the height of each segment of the pyramid, but we tend to perceive the apparent volume of each layer. As a result, the layers near the top appear much smaller that they should relative to the lower layers**. This serves to drastically exaggerate how little government funding in the US is directed to fruits, vegetables, nuts and legumes. Using a more prosaic bar chart instead shows that, while the funding of meat and dairy is certainly far greater, the ratios are not as extreme as the pyramid suggests.

US Food Subsidies chart

The bar chart has the added advantage of making it easier to gauge the funding proportion for each category. Also, having each layer stacked one on top of another makes it harder to compare one figure with another. The bar chart eliminates the need for moving the shapes around in your mind in an attempt to make these comparisons. Note how close the funding levels are for grains compared to sugar, oil, starch and alcohol, while the pyramid chart  makes the funding of grains look significantly higher.

The original graphic compensates by quoting each of the figures, but this defeats the purpose of using a chart. If your chart does not make the numbers evident, use a table instead! The extent of the distortion that the pyramids produce is even more apparent in the case of the recommended diet data. While the recommended intake of sugar, oil and salt is certainly low, on the bar chart this category is no longer vanishingly small.

Recommended Diet Chart

Another visualisation alternative would be to use pie charts. While pie charts do have a bad reputation in statistical and scientific circles, and are often used and abused in many a business presentation, they allow more straightforward comparisons of the contributions categories make to the whole. In the pie chart it is much easier to see at a glance that vegetables and fruit should make up about a third of a regular diet, while protein combined with sugar, oil and salt should make up about a quarter. On the other hand, it is harder to use a pie chart to scan numerical values. For that purpose, the bar chart excels (no pun intended). So when choosing a chart to represent data, it is essential to first decide what aspect of the data you are aiming to highlight.

Diet Pie ChartThe pyramid charts were indeed intended to shock, but there was no need for the authors of the post to resort to misleading exaggeration. The figures should be allowed to speak for themselves. Even when using dispassionate bar charts, it remains clear that the US government is funneling a disproportionate amount of money into the types of food Americans are already over-consuming.

You might also be interested in these posts on charts.

* Thanks to Greg for the updated source.
** As a commenter on Lifehacker observed, this distortion would also occur in 2-D triangles, so it’s due to the shape rather than the 3-D nature of the charts. Having said that, the 3-D versions are far more common and indeed Excel only gives the 3-D options.

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{ 20 comments… read them below or add one }

1 Mark L March 13, 2010 at 7:54 am

An excellent and insightful discussion, Mule. However the very last sentence doesn’t quite follow from the data. A food type having a low dietary recommendation level is not the same thing as the food type being over-consumed.

Also, your subsidy data is presumably in total dollars spent — if the varied cost of a serving of different food types is considered, I imagine the mismatch would be lessened.

2 Stubborn Mule March 13, 2010 at 8:09 am

Mark: Good points. The most that we can conclude is that the US governments spending mix may be leading to some distortions. As you say, it would be interesting to reweight the subsidy data as $ per serving.

3 Stubborn Mule March 13, 2010 at 8:21 am

Actually, it is not as simple as that. In The Omnivore’s Dilemma the say that 63% of corn produced in the US is used as feed for livestock, so this effectively means that much of the grain subsidy from the US Government is actually a meat and dairy subsidy.

4 Marco March 13, 2010 at 11:43 am

Hi Stubborn,

You made some good points here, about the way a pyramid conveys a distorted message.

But, from my point of view, there are three additional questions/observations about the data itself, the most convenient form of representing it, and its origins.

First question: what on Earth is a “serve”? How many serves are there in a banana? What about a grilled chicken? Are serves the same for kids and adults? The fact that a serve is not clearly defined is troublesome. The original article seems to assume that people know what it means. I find this assumption cavalier.

As one is left to guess what a “serve” means, the first supposition that comes to mind is that it’s some standard weight (say, X grams for an adult); another possible answer is that it’s a volume measure (say, Y cubic centimeters, or “cups”, “table spoons” and such for an adult). You’ll notice the resulting quantities of food depend on whether we consider weight or volume: a 100 g of bread is more voluminous than 100 g of cheese; a cup of rice weights more than a cup of water.

In other words: on the basis of “serves”, the recommended intake pyramid only tells me that I should be eating a bit “more” grains than vegetables and fruits, not precisely how much more.

But the Federal financing pyramid does tell how much more money is put in each type of food production: meat and diary receives about 7 times the same amount of funding than sugar, oil, alcohol and starch

On the basis of the information conveyed by the charts, I would say, the only thing one could infer is that, for example, more subsidies should be going to grains than to protein production (and, of course, there is what you mention about grains being also inputs in protein production). As this is not the case, there is something “strange” here. But I cannot possibly conclude how much more money should be allocated to grain production, or taken from protein production.

The second question is this: wouldn’t it be better to represent the two variables (recommended intake and Federal funding as percentages) in a single chart? Say, a bar chart where, next to the recommended daily intake, is the proportion of Federal funding.
The third observation: the Consumerist post (which was only the chart itself, no comment whatever!) shows something I find extremely annoying. What are the sources of the data?

5 Greg March 20, 2010 at 9:01 am

Just so you know, the graphic didn’t originate from Consumerist, it originated here:

6 Stubborn Mule March 20, 2010 at 11:20 am

Greg: thanks for the original source. I’ll update the post accordingly.

7 Chris March 20, 2010 at 3:22 pm

I’m intrigued by this post (I despise poor representations of data), but I wonder about this bit:

“The problem is that the data is represented by the height of each segment of the pyramid, but we tend to perceive the apparent volume of each layer.”

Is there any evidence that people actually misperceive cone/pyramid charts?

8 Stubborn Mule March 20, 2010 at 11:11 pm

Chris: Good question. There are a lot of studies on graph perception that test things like accuracy and speed of perception of different chart types. Unfortunately very little is freely available online. William S. Cleveland, the author of The Elements of Graphing Data has done a fair amount of work in this area, although I doubt he would have looked at pyramid charts as they would fall into the category he dismisses as “pop charts” (not to be taken seriously). Still, I will have a hunt around for some studies.

9 Stubborn Mule March 20, 2010 at 11:13 pm

I should also emphasise (as I have now in the post) that the most significant distortion comes from the tapering up to a point rather than the 3D effect itself. 2D triangular charts would be just as bad. Perception of the pyramids is likely be guided more by the cross-sectional area than the full volume of each layer.

10 Chris March 21, 2010 at 3:46 am

Yes, I can certainly see how the tapering combined with the smaller numbers results in distortion–I mean, you’re basically representing the differences between values in two ways: the up-and-down scale, as one intends, but also the horizontal. Please do post here if you find a study of this–I’d be interesting in seeing to what extent people misinterpret these kinds of things.

11 papawow March 21, 2010 at 4:06 am

I read that article, “Shocking Graphic Reveals Why a Big Mac Costs Less Than a Salad”, and wondered the EXACT same thing – that the data seems to be distorted because of the volume of the pyramid!

Your post clarifies why 3D charts should be avoided, something I had never thought much about. I read the other link and I will be severing all ties to pie charts as well, no matter how delicious they may be…


12 Evan March 21, 2010 at 9:54 am

This chart drove me up the wall, too. It’s especially galling, since it’s easy to make a very good comparative bar chart, for example:

13 Stubborn Mule March 21, 2010 at 10:20 am

Evan: thanks for the link. That is an elegant and far better chart.

14 Marco March 21, 2010 at 6:36 pm

From Greg’s post one sees the problems that can arise when no sources are given…

15 Stubborn Mule March 21, 2010 at 9:14 pm

Marco: I know it is foolish to expect academic publishing standards of blogs, but a bit more referencing would be nice!

16 CapitalC March 22, 2010 at 2:16 pm

If the Egyptians never built the pyramids, would we still have pyramidal charts? Hrmm…

17 Stubborn Mule March 22, 2010 at 2:30 pm

CapitalC: perhaps in that case they may just have looked a little more Mayan.

18 CapitalC March 22, 2010 at 2:42 pm

Touché! ;)

19 Ibrahim | March 23, 2010 at 2:20 am

Agreed. Well put!

20 Coffee Break Science March 23, 2010 at 3:44 am

Thanks for this post – I had just been writing about why people make unhealthy food choices, and nearly used this diagram to make my case.

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