Junk Charts

Doing legwork, doing justice

The New York Times brought attention to the Bronx courtrooms this weekend. (link) The following small-multiples chart effectively illustrates how the Bronx system is uniquely unproductive, compared to the other boroughs:

The above chart shows the outcomes. The next chart shows the possible cause.

It appeared that at any time of the day, at least one-third of the courtrooms are not actively conducting business. In fact, outside of the period between 10:30 and 12:30, and 2:30, less than half of the courtrooms have a judge present.

I want to draw your attention to the caption below the chart. It said: "The Times visited all 47 courtrooms at the Bronx County Hall of Justice in 30-minute intervals totally how many were open and actively in session, ..."

Too often, we analyze and plot whatever data has been collected conveniently by some machine. Such data frequently do not address the questions we'd like to answer. We let the data dictate our research question.

Most great work in statistics come from people who put in the effort to define their research goals first, and then manually collect the specific data needed to accomplish those goals.

 

Interpreting some charts about guns

Felix linked to a set of charts about guns in the U.S. (and elsewhere). The original charts, by Liz Fosslien, are found here.

I like the clean style used by Fosslien. Some of the charts are thought-provoking. Many of them may raise more questions than they answer. Here are a few that caught my eye.

A simplistic interpretation would claim that banning handguns is futile, and may even have an adverse impact on murder rate. However, this chart does not reveal the direction of causality. Did some countries ban handguns because they are reacting to higher violence? If that is the case, this chart is confirming that the countries with handgun bans are a self-selected group.

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The U.S. is an outlier, both in terms of firearm ownership and firearm homicides. This makes the analysis much harder because the U.S. is really in a class of its own. It's not at all clear whether there is a positive correlation in the cluster below, and even if there is, whether we can draw a straight line up to the U.S. dot is also dubious.

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Fosslien is being cheeky to deny us the identity of the other outlier, the country with few firearms but even higher death rate from intentional homicide. These scatter plots are great by the way to show bivariate distributions.

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I'd still prefer a line chart for this type of data but this particular paired bar chart works for me as well. The contents of this chart is a shock to me.

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I just don't get this one. Why is there a fan?

The electoral map sans the map

Xan G. has a must-read post comparing different ways of showing the electoral map. See here.

The key learning is something I often point out on this blog: geographical data can have a greater impact when it is unshackled from the map.

Xan pointed to a series of ideas that are improvements upon the map.

Here's an attempt to portray the election night as a horse race. This borrows an idea from the sports world where a baseball game can be portrayed with such a chart.

I love this sort of presentation. Similar to a baseball game, someone can look at this chart after the fact and experience the ups and downs of an Obama/Romney supporter without actually being there.

Then Xan spoils some of the fun by transforming the above into the following chart, which portrays Obama's win as a rout. All the suspense is gone!

As Xan explains it, he took Nathan Silver's predictions of "sure wins" and plotted those first. Thus, Obama started the night at almost 200 while Romney started with about 170.

While indeed the fun is gone, this is a more accurate view of this just-concluded election. I was a spoilt sport myself that night as I kept telling my friends that the only reason why Romney seemed close at the start was that the Red States generally have smaller populations, and thus took less time to count their votes. In addition, the Red States also tend to favor Republican candidates by very large margins so that the winner could be called early without counting most of the votes.

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I have other thoughts on the state of reporting on polls, which I'll cover in a later post.

How to fail three tests in one chart

The November issue of Bloomberg Markets published the following pair of pyramid charts:

This chart fails a number of tests:

Tufte's data-ink ratio test

There are a total of six data points in the entire graphic. A mathematician would say only four data points, since the "no opinion" category is just the remainder. The designer lavishes this tiny data set with a variety of effects: colors, triangles, fonts of different tints, fonts of different sizes, solid and striped backgrounds, and legends, making something that is simple much more complex than necessary. The extra stuff impedes rather than improves understanding. In fact, there were so many parts that the designer even forgot to add little squares on the right panel beside the category labels.

Junk Charts's Self-sufficiency test

The data are encoded in the heights of the pyramids, not the areas. The shapes of the areas are inconsistent, which also makes it impossible to decipher. The way it is set up, one must compare the green, striped triangle with two trapezoids. This is when a designer realizes that he/she must print the data labels onto the chart as well. That's when self-sufficiency is violated. Cover up the data labels, and the graphical elements themselves no longer convey the data to the readers. More posts about self-sufficiency here.

Junk Charts's Trifecta checkup

The juxtaposition of two candidates' positions on two entirely different issues does not yield much insights. One is an economic issue, one is military in nature. Is this a commentary of the general credibility of the candidates? or their credibility on specific issues? or the investors' attitude toward the issues? Once the pertinent question is clarified, then the journalist needs to find the right data to address the question. More posts about the Trifecta checkup here.

Minimum Reporting Requirements for polls

Any pollster who doesn't report the sample size and/or the margin of error is not to be taken seriously. In addition, we should want to know how the sample was selected. What does it mean by "global investors"? Did the journalist randomly sample some investors? Did investors happen to fill out a survey that is served up somehow?

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The following bar charts, while not innovative, speak louder.

Purple politicial speech

I enjoy looking at the New York Times' summation of National Convention speeches via visualization. (link)

It's a disguised word cloud combined with a bubble chart with a little bar chart thrown in for good measure.

The size of the bubble is the total number of mentions of particular words or phrases. So the bubbles tell us the importance of specific concepts in aggregate of two parties.

It's the split within each bubble that represents the relative emphasis by party. Helpfully, the bubbles are sorted from left to right with the most Democratic words on the left. This splitting uses a bar chart paradigm. The diameter of the bubble is being partitioned, not the areas of the segments.

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I wanted to see this as a straight-out word cloud. In the following, I use the red-blue-purple color gradient to indicate the Republican-Democratic bias, and the size of the words to indicate the number of mentions.

This word cloud is created using the Wordle tool, advanced options. My colleague John helped me pick the colors. (By the way, I don't like the insertion of small words within large letters, like what happened here inside the O in Obama.)

Also, I'd line the colors up so that the red words are on one side, blue on the other and purple in the middle. I'd need a different tool to be able to exercise this type of control.

A winning graphic of early voting

This pair of WSJ charts I like very much.

The article talks about the effect of early voting during Presidential elections in the States. People are allowed to mail in their votes as early as 2 months before the November 6 election.

The chart on the right identifies all the states that allow early voting, and in particular, it highlights (in orange) the seven battleground states that allow early voting. This shows the designer keenly aware of what's important and what's not important on the chart. The states are ordered by the first date of voting, instead of alphabetically. (I do have a question about why several of the gray lines towards the bottom of the chart do not reach November 6. Probably because mail-in voting is closed prior to Election Day in some states...)

If the data were to be available, a nice addition to this chart is to include the distribution of early votes over time. It's useful to see if North Carolina voters tend to spread their mail-in votes evenly over the 2 month period, or if most of them get sent close to Election Day, or some other pattern. Changing the bar chart to a dot plot and using the density of dots to indicate frequency would work fine here.

Instead of the first date of voting, the chart would be more informative if it plots the average date of voting (among mail-in voters). This is because the first date of voting is an extreme value and there may be few voters who vote on that day. If we have to pick one number to represent all early voters, we should pick the one with the average (or median) voting time. Again, this is constrained by whether such data is publicly released.

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The chart on the left is also well executed. The title should include the additional fact that only battleground states are depicted. I'd also extend the vertical axis to 100% since the data are proportions. The beauty of this presentation is that it functions on several levels, whether you are interested in knowing that not much changed in Iowa from 2004 to 2008, or the fact that almost 8 of 10 mail-in votes in Colorado were early votes, or that in both Colorado and North Carolina, the proportion of mail-in votes more than doubled between 2004 and 2008.

Neither of these are fancy charts, but they pack quite a bit of useful information.

 

No sorting and lack of structure undermine a chart

Reader Daniel L. isn't impressed with this page of charts about gay rights in the U.S., from the Guardian paper (London). (link)

 

The use of circles to organize data has a long history, stretching back at least to the Nightingale rose, which turns the time dimension into a circle. Andrew doesn't like this concept (e.g. here), neither do I.  Here is something similar by McCandless (link) that has appeared on this blog.

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Take the following set of charts showing the legislative differences by region of the country.

Since states within region are categories with no order, there is no easy way to order the states. This is made worse by the categorical nature of the other variable: the legislative posture on marriage, civil union and domestic partnership is very messy data with no order either.

The regions can be sorted reasonably by the "average" permissiveness but this chart shows no concern over sorting at all.

About the only easy read from this set of charts is the observation that the Northeast states are most permissive while the Southeast statements are most restrictive. Anyone who has casual exposure to this social issue knows this without needing a chart.

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The key to clarifying this chart is to clarify the underlying structure, particularly the structure of the permissiveness variable. Dissecting the data reveals that there are only five possible postures (Banned all three rights, Banned marriage but allows one of the other rights, Allow civil unions, Allow marriage, and No information).  The following data table conveys the data with minimal fuss:

 

 

Look what I found: two amazing charts

While doing some research for my statistics blog, I came across a beauty by Lane Kenworthy from almost a year ago (link) via this post by John Schmitt (link).

How embarrassing is the cost effectiveness of U.S. health care spending?

When a chart is executed well, no further words are necessary.

I'd only add that the other countries depicted are "wealthy nations".

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Even more impressive is this next chart, which plots the evolution of cost effectiveness over time. An important point to note is that the U.S. started out in 1970 similar to the other nations.

Let's appreciate this beauty:

• Let the data speak for itself. Time goes from bottom left to upper right. As more money is spent, life expectancy goes up. However, the slope of the line is much smaller for the US than the other countries. There is no need to add colors, data labels, interactivity, animation, etc.
• Recognize what's important, what's not. The US line is in a different color, much thicker and properly made the foreground of the chart.
• Rather than clutter up the chart, the other 19 lines are anonymized. They all have the same color and thickness, and all given one aggregate label. This is an example of overcoming loss aversion (see this post for more): it is ok to suppress some of the data.
• The axis labeling is superb. Tufte preaches this clean style. There is no need to use regularly-spaced axis labels... use data-informed labels. Unfortunately, software is way behind on this issue. You can do this in R but that's about it.

 

Light entertainment: Spinning wheel at the fun fair

@TheChadd submitted the following chart via Twitter.

I don't know if "fun fairs" mean the same thing to me as to you but that's where I got introduced to spinning wheel games. You stand 10 feet away from a multi-colored pie chart,  you are supposed to throw darts (or other objects) at the circle, you win gigantic teddy bears if you hit the narrow wedge and maybe a sweet if you hit the big wedge.

To add to the fun, the pie chart is made to spin around slowly.

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Well, we are at the fun fair and here is the spinning pie chart:

To see the real thing, click here.

Notice that this game has an extra level of difficulty; it spins both clockwise and counterclockwise.

Have a great weekend.

A reader's guide to a New York Times graphic

The New York Times chose to present the poll results from Super Tuesday in the following chart (link):

It took me a bit of time to take in what this chart has to offer. To save your troubles, I've drawn up a reader's guide:

The graphic is a disguised scatter plot with one axis being Romney's share minus Santorum's share and the other axis being the total share of all other candidates. This is an "uneven canvass" in the sense that the data are much more likely to fall into a small part of the chart area (the orange shaded region).

If the reader just wants to know which segments of the electorate favors Romney v. Santorum, the chart is pretty effective at pointing to the answer. It is quite challenging to learn much else about the data.

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Here are the results for Ohio, plotted as a stacked bar chart, with three segments in each bar (Romney's share, Santorum's share and the share of all other candidates).

 This more standard presentation conveys much more of the underlying information. The trade-off is that the reader has to try harder to figure out the answer for each segment of voters.

 

[PS: 3/13/2012]:

Thanks to several readers for your comments. I went back to look at the NYT graphic again, and can confirm that it is a ternary chart. The chart area is indeed an equilateral triangle with three equal sides.

What threw me off was the axis labels, particularly the Santorum and Romney labels which give the impression that there is a zero mid-point and some kind of share data along the  east-west axis. If this were true, then the chart could not be a ternary plot because Romney and Santorum shares are not mirror images.

In a ternary plot, we must identify Romney, Santorum, and "Other candidates" as the three vertices. The way this chart is labelled, it invites readers to drop a perpendicular line to the horizontal axis to read Santorum's share (e.g.). That doesn't work. Trying to fish the data out of a ternary plot is always challenging. You pick the vertex corresponding to the data series you want, say Romney's share. Then you take the side opposite that vertex. Now draw lines parallel to that side -- as you approach the Romney vertex, Romney's share goes from 0% to 100%. The following chart shows this:

For ternary plots, it's easier to go with the hand-waving principle that the closer you are to the vertex, the greater the weight of that vertex. So with the abortion data point, we see that it is much closer to the Santorum corner than the other two corners.

The vertical line for "other candidates" is also misleading. To read the share of votes that went to other candidates, one has to followS either the OR side or the SO side of the triangle. Basic geometry will show that going up the vertical line will not produce the share of "other candidates".

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Lastly, here is a scatter plot representation of the data using the Romney-Santorum difference as the horizontal axis and the share of all others as the "other candidates":

The pattern of dots on this chart looks very similar to the ternary chart (that is one other reason why I thought the original graphic was a scatter plot.) However, the two plots are distinct entities. For the scatter plot, the horizontal axis goes from -100% to +100% while the vertical axis can only go from 0% to 100%.