Puzzling World

Here is a busy graphic representing the composition of the world's economy. Countries are given polygonal sections proportional to the relative size of their economies. Each sector is divided into three smaller regions: Most lightly colored is Agriculture, somewhat darker is Industry, darker yet, the sub-segment that is greatest for most countries, is Services. Starting with the largest (US) the polygons seem to be arranged in a rough Pareto-chart fashion from largest to smallest in a counter-clockwise fashion. Although, individual countries are hard to locate, those of similar size contributions are somewhat easy to compare. I found it fun to puzzle out comparisons that I found surprising, for example, US industry has about the same area as China's. Mathew Yglesias from Vox points out others:

You can see some cool things here.

• For example, compare the US and China. Our economy is much larger than theirs, but our industrial sectors are comparable in size, and China’s agriculture sector looks to be a little bit larger. Services are what drive the entire gap.

• The UK and France have similarly sized overall economies, but agriculture is a much bigger slice of the French pie.

• For all that Russia gets played up as some kind of global menace, its economy produces less than Italy. Put all the different European countries together, and Russia looks pathetic.

• You often hear the phrase “China and India,” but you can see here that the two Asian giants are in very different shape economically.

• The only African nation on this list, South Africa, has a smaller economy than Colombia.

This graphic has gotten criticism as being too busy, too unorganized, and too difficult to make comparison, among others. But I do like the puzzle-it-out quality of the graphic. It makes us work a little to understand and make comparisons. I especially like the quote from Andrew Gelman at Statistical Modeling, Causal Inference, and Social Science:

Paradoxically, the best thing about this graph may also be its worst: Its tricky, puzzle-like characteristic (it even looks like some sort of hi-tech jigsaw puzzle) makes it hard to read, hard to follow, but at the same time gratifying for the reader who goes to the trouble of figuring it out.

From howmuch, via Vox, via SM,CS and SS. 

Circles of Coal

 

Graphic from the print edition of the Washington Post on August 2, 2015 showing what proportion of a state's total electricity that comes from the burning of coal. Each state's circle represents 100% of the states electricity production. The inner black circle represents the percentage of the total electricity that is produced by coal. This is a nice display, but correctly interpreting such percentages from circles is difficult. Assessing "a lot" or "a little" is somewhat easy, but even correctly divining the 50% value, is something many find difficult and even counter-intuitive.

High school geometry likely taught you that an inner circle half the size of an outer circle is found by inscribing a square inside the outer circle and then inscribing an inner circle inside the square. This inner circle will have half the area of the outer circle.

The geometry is correct, but visually interpreting this black circle as half the area of the outer circle can be difficult. Shaded areas of squares might have worked better in the coal graphic. The Washington Post has more maps on other methods of electricity generation here.

Yakkity Yak...

Here is a larger view of the infographic from Alberto Lucas López showing the fascinating worldwide diversity of spoken languages. From the Infographic:

There are at least 7,102 known languages alive in the world today. Twenty-three of these languages are a mother tongue for more than 50 million people. The 23 languages make up the native tongue of 4.1 billion people. We represent each language within black borders and then provide the numbers of native speakers (in millions) by country. The colour of these countries shows how languages have taken root in many different regions.

Pie Rules

"There is no data that can be displayed in a pie chart, that cannot be displayed BETTER in some other type of chart," is a quote Wikipedia attributes to the late, great statistician John Tukey, (I've found no original source for the quote). It gets worse when Excel and/or graphic designers start adding chart junk of 3-D projections in hope of adding more visual interest.

Any reasonable comparisons in the above chart are impossible.

If you insist on using pie charts, Benjamin Starr at Visual News offers some history and sensible guidelines for using pie charts.

First, as the lead-in graphic above illustrates, display no more than five categories in a pie chart. Many small areas are difficult to compare.

Second, since wedges of a pie are difficult to compare side-by-side, Starr says don't use multiple pie charts for comparison. Use stacked bar charts instead, as shown above.

Third, make sure that the percentages add up to 100% and that all slices are drawn proportionately to the percentages they purport to represent.

And finally, order the slices from largest to smallest, starting at 12 o'clock and continuing either clockwise or counter-clockwise to aid in comprehension.

Of course, we've posted some pie charts here and had some fun with them.

Conditional Probability

Here is a clever, interactive, simulation display of conditional probability from Victor Powell, via flowingdata.

Balls fall from the sky, uniformly distributed across the display window. Some hit a red shelf of adjustable width. Here it is set at a width so that
P(A) = 20% of all the falling balls hit the red shelf.
Another lower blue shelf, overlapping a bit with the red one, is set so that
P(B) = 12% of the balls hit the blue shelf.
A mere P(A and B) = 6% of the balls hit both shelves, indicated by the mixture of red and blue to get purple. But, as the simulation says,
"If we have a ball and we know it hit the red shelf, there's a 30.0% chance it also hit the blue shelf" and 
"If we have a ball and we know it hit the blue shelf, there's a 50.0% chance it also hit the red shelf". 

Below are connected bars showing, by their length, the color composition of the dropped balls. We can easily see how these proportions are obtained by visually estimating that fraction that purple makes up of the balls that hit the red shelf. That is the ratio, purple / (red + purple) = 30% or what fraction purple makes up of the balls that hit the blue shelf. This is the ratio, purple / (purple + blue) = 50%.

Compositional Eating

Are you eating right? This site has dinner plates that graphically help you to keep to certain eating proportions. Of course, you must be careful not to pile-on and overload one section and skimp on others. The area devoted to your food choices might be a good reminder, but it's more the mass of each component that's important to your nutrition.

Cake Chart

You've heard of pie charts. Here are Cake Charts. The cake's decoration is designed to be the proportions of each cake's ingredients. As the site says, "Decoration becomes information."

Such data are called compositional data. The previous post had compositional data on national flags. Here is one of my research papers on modeling compositional data.