Great demonstration. It will be great to use with my grade 8 unit on graphing and misrepresentation! Thanks for sharing.

Love it! Well caught too.

I did miss that part of the SOTU address (although it’s interesting to Canadians, dinner was more pressing this evening), the part that I did enjoy the most (for part cynical hilarity and part thankfulness) was when the President said the following:

“Become a teacher. Your country needs you.”

Cynical hilarity because, in my neck of the woods at least, there are too many teachers and not enough jobs due to budget cuts and declining enrollment. Thankfulness for having the importance of teachers and the job they do put in the (inter)national spotlight for just a moment.

I’ll be making use of the circles next semester I’m sure, so thanks.

Actually doing a quick measurement of my own (I got slightly different numbers), it looks like they simply scaled the diameter in proportion to the GDP, which of course created an exponential relationship between the areas.

Not strictly accurate in a mathematical sense, but the eye does have a hard time telling the difference in areas of circles, so this is probably better at making the point than a mathematically accurate chart would be.

It seems that *all* of the disks relate to the GDPs by their diameter and not by their area. If you alter the US disk so that the sizes of the US GDP and China’s GDP are represented by area, you should also change the sizes of the disks representing French and German GDPs.

Of course, as Rhett suggested, those might not be disks. They could be spheres or domes, in which case the relations might be based on volume or surface area, though clearly if left as published by the White House, the relationships are based on the diameters.

My point is that if you are looking for clarity, you will need to replace the blue round-looking-things-whatever-they-are with bars with one axis the same for every GDP shown and the other axis varying, or remove them all together.

These definitely look Spherical… But if one were to argue the accuracy of the spheres. Would they be measuring
Surface Area, Volume, or even Mass. Mass could be argued to the point where the spheres are physically proportionate… That is to say density was involved in the calculations; then there would have to be a Legend explaining each Sphere’s properties.

I would hate to assume that this slide will be used by foreign countries as a motivational tool…, “This is a prime example why Americans fail in mathematical academics”.

But, I bet the designer of the graphic hadn’t thought this deep… Considering they were a probably a state worker on a paycut and returning from their 3rd furlough in one month.

Greg: “At issue here is the axiom that people interpret such graphs by perceiving the area of the various figures (rather than the diameter, say). I happen to believe this axiom, but I have no way of justifying it to someone who doesn’t … have any studies been done on this?”

I’m betting the opposite. Exactly because this happens all the time (infographics in USA Today, Newsweek, etc. on stuff like this or drink sizes, etc.) – designers consistently represent sizes by linear dimensions while trying to represent them with areas or volumes – I say that people perceive the size, not the area. I don’t think that the designers know the score and are trying to trick the public; I think they’re in the same boat.

Well this is all a step in the development of the brain, right? It is called the “conservation of quantities,” where if a child sees a wide glass of water poured into a narrow glass he/she will assume the narrow glass has “more” although one would think they would know it must be the same amount. Piaget says we figure this out prior to six years-old. I am not so optimistic.

What is a trillion anyway?

“Most trained graphics designers doing infographics have (or should have) read Tufte’s “The Visual Display of Quantitative Information”. That means that they either they do know the score and are being deceitful, or that they have not had even minimal training in their craft (that is, that the White House is hiring people known to be incompetent).”

Or perhaps they are their own intelligent individual and simply (gasp) disagree with Tufte.

Tufte says you shouldn’t use 2D objects to represent 1D quantities, but in practice it is often clearer to use these sorts of graphics. In the end it is all about conveying the information.

I love the irony of this and Obama’s talking points about education. This one little graphic can create a great discussion for any math class. Thanks for sharing!

This is so mathtastic OMG!

While the point about the size of the circles is certainly interesting, it is dwarfed in importance by this question:
Are the numbers accurate ?

Hmmm,

From a biological perspective, one has to consider osmosis as a potential path for inflating the circle: The heavy ink surrounding the circle would penetrate through and into the lighter ink inside the circle. We may have started with true dimensions and later on ended as presented here.

As I stirred on the circle, the small circle inflated too. :) Give it some time and the optical/mental illusion combined with cellular reorganization of eye nerve cells may place the presentation on entirely different path.

BUT, that is just a thought at 3:12 p.m. I may be just not thinking mathematically.

Best,

Actually, this is the truly correct way, in the data visualization research world, to size comparative spheres/circles. (They should be proportional by radius, NOT area.)

The reason for this is a matter of how we perceive size. For example, a circle that has twice the AREA of another, does not look twice as large – it looks only about 1/3 larger. However, if a circle has twice the diameter, it is perceived by the viewer as having twice the volume.

Sometimes to effectively show data, you don’t always have to follow the mathematical rules. In any case, comparing circular sizes should generally be avoided because of this dichotomy.

(Main source for this is in the excellent Wall Street Journal guide to data visualizations:
http://www.amazon.com/Street-Journal-Guide-Information-Graphics/dp/0393072959)

I showed students your original slide with the US GDP blocked out and had them guess what the value in the black box should be. One of my groups did make a circle the size of China’s circle and then duplicate it four times placing these neatly in the US circle and come up with a value of 5 X china’s GDP. What a great Graphic!! More fuel to the fire of why every citizen in the US needs to know mathematics if we are going to keep our democracy alive.

Created some great discussion.

Used it as my warm up. Instead of the Normal ACT PREP Question.
Great discussion followed.

The area principle states that “the area occupied by a part of the graph should correspond to the magnitude of the value it represents. Violations of the area principle are a common way to lie (or, since most mistakes are unitentional, we should say err) with Statistics.” Taken from Stats, Modeling the World by Bock, Belleman, DeVeaux, 3rd edition.

Here’s a similar infographic that accompanies a Roanoke Times feature on children with autism spectrum disorders:

http://www.roanoke.com/news/images/012110autism/graphic_increase/autism.html

And my forum post pointing out the inaccuracy:

http://cs.roanoke.com/forums/p/1080/16416.aspx#16416

I hope that what Catherine says isn’t true, because these circles are very misleading. The misrepresentation is not helpful to the average citizen in the way that, say, the London Underground map is to travelers.

Thanks for the clarification. I will continue to make fun of the White House now.

Way to go!

Isn’t the first “for classroom use” suggestion just a kind of pseudocontext?

Years ago (1983) Edward Tufte wrote a book, _The Visual Display of Quantitative Information_, in which he showed that graphs using 2-D objects tend to be read by _area_, not by diameter. Hence, 2-D objects proportional by diameter exaggerate differences. Whether Obama’s staff, or he himself, noticed the distortion, or chose to keep it in because it apparently made their point better, is unclear. People not versed in the use & abuse of graphics, including many/most non statistics-using professions, fall into this trap frequently, but it has been known for a long time.

To be fair, Obama didn’t botch it, the designers of the graphic did. However as others have pointed out, the radii are correct and while technically it’s the area that is important, it’s become such a common mistake outside of proper statistical graphics that it’s become acceptable (like a lot of grammatical errors).
Also, I’d have used a bar chart.

But… the facts are correct. The graphic debatably isn’t. But that’s not Obama’s fault.

What a great “catch” on your part. Typical use of “eye candy” to exaggerate a point. As others have said, this will make a great warm-up lesson for my middle school math students:)

We should take pity on the person responsible for that SOTU chart, they must have taken AP Stats back in high school, as this chart from college board would suggest (they did the same thing!)
College Board AP Math and Science Improvement
For Science, I get the ratio of the number of students getting 3’s or better in ’01 compared to ’10 to be 0.467, and for the circles I get the ratio of the diameters to be 0.471, but the ratio of the areas would be ~0.22
I’m but a lowly physics teacher, but now Dan has me seeing the world in ‘math.’