How effective visualization brings data alive

Back in 2009, I wrote about a failed attempt to visualize regional dialects in the U.S. (link). The raw data came from Bert Vaux's surveys. I recently came across some fantastic maps based on the same data. Here's one:

These maps are very pleasing to look at, and also very effective at showing the data. We learn that Americans use three major words to describe what others might call "soft drinks". The regional contrast is the point of the raw data, and Joshua Katz, who created these maps while a grad student at North Carolina State, did wonders with the data. (Looks like Katz has been hired by the New York Times.)

The entire set of maps can be found here.

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What more evidence do we need that effective data visualization brings data alive... the corollary being bad data visualization takes the life out of data!

Look at the side by side comparisons of two ways to visualize the same data. This is the "soft drinks" question:

 

 

 And this is the "caramel" question:

 

 The set of maps referred to in the 2009 post can be found here.

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Now, the maps on the left is more truthful to the data (at the zip code level) while Katz applies smoothing liberally to achieve the pleasing effect.

Katz has a poster describing the methodology -- at each location on the map, he averages the closest data. This is why the white areas on the left-side maps disappear from Katz's maps.

The dot notation on the left-side maps has a major deficiency, in that it is a binary element: the dot is either present or absent. We lost the granularity of how strongly the responses are biased toward that answer. This may be the reason why in both examples, several of the heaviest patches on Katz's maps correspond to relatively sparse regions on the left-side maps.

Katz also tells us that his maps use only part of the data. For each point on his maps, he only uses the most frequent answer; in reality, there are proportions of respondents for each of the available choices. Dropping the other responses is not a big deal if the responses are highly concentrated on the top choice but if the responses are evenly split, or well-balanced say among the top two choices, then using only the top choice presents a problem.

 

 

Advocacy graphics

Note: If you are here to read about Google Flu Trends, please see this roundup of the coverage. My blog is organized into two sections: the section you are on is about data visualization; the other section concerns Big Data and use of statistical thinking in daily life--click to go there. Or, you can follow me on Twitter which combines both feeds.

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Because the visual medium is powerful, it is a favorite of advocates. Creating a chart for advocacy is tricky. One must strike the proper balance between education and messaging. The chart needs to present the policy position strongly and also enlighten the unconverted with useful information.

In my interview with MathBabe Cathy O'Neil (link), she points to this graphic by Pew that illustrates where death-penalty executions have been administered in the past two decades in the U.S. (link) Here is a screenshot of the geographic distribution for 2006:

The chart is a variant of the CDC map of obesity, which I discussed years ago. At one level, the structure of the data is the same. Each state is evaluated on a particular metric (proportion obese, and number of executions) once a year. Both designers choose to roll through a sequence of small-multiple maps.

The key distinction is that the obesity map encodes the data in color while the executions map encodes data in the density of semi-transparent, overlapping dots, each dot representing a single execution.

Perhaps the idea is to combat one of the weaknesses of color encoding: humans don't have an instinctive sense of the mapping between a numerical scale and a color scale. If the color transitions from yellow to orange, how many more executions would that map to? By contrast, if you see 200 dots instead of 160, we know the difference is 40.

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The switch to the dots aesthetic introduces a host of problems.

Density, as you recall from geometry class, is the count divided by the area. High density can be due to a lot of executions or a very small area. Look at Delaware (DE) versus Georgia (GA). The density of red appears similar but there have been far fewer executions in Delaware.

This is a serious mistake. By using dot density, the designer encourages readers to think in terms of area of each state but why should the number of executions be related to area? As Cathy pointed out, a more relevant reference point is the population of each state. An even cleverer reference point might be the number of criminals/convictions in each state.

Another design issue relates to the note at the bottom of the chart (shown on the right). Here, the designer is fighting against the reader's knowledge in his/her head. It is natural for a dot on a map to represent location and yet the spatial distribution of the dots here provide no information. Credit the designer for clarifying this in a footnote; but also let this be a warning that there are other visual representation that does not require such disclaimers.

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I am confused by why dots appear but never disappear. It seems that the chart is plotting cumulative counts of executions from 1977, rather than the number of executions in each year, as the chart title suggests. (If you go to the Pew website, you find a version with "cumulative" in the title; when they produced the animated gif, they decided to simplify the title, which is a poor decision.)

It requires a quick visit to Wikipedia to learn that there was a break in executions in the 70s. This is a missed opportunity to educate readers about the context of this data. Similarly, a good chart presenting this data should distinguish between states that have banned the death penalty and states that have zero or low numbers of executions.

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A great way to visualize this data is via a heatmap. Here, I whipped up a quick sketch (pardon the sideway text on the legend):

I forgot to add the footnote listing the states where the death penalty is banned. Also can add an axis labeling to the side histogram showing counts.

 

 

Some chart types are not scalable

Peter Cock sent this Venn diagram to me via twitter. (Original from this paper.)

For someone who doesn't know genetics, it is very hard to make sense of this chart. It seems like there are five characteristics that each unit of analysis can have (listed on the left column) and each unit possesses one or more of these characteristics.

There is one glaring problem with this visual display. The area of each subset is not proportional to the count it represents. Look at the two numbers in the middle of the chart, each accounting for a large chunk of the area of the green tree. One side says 5,724 while the other say 13 even though both sides have the same areas.

In this respect, Venn diagrams are like maps. The area of a country or state on a map is not related to the data being plotted (unless it's a cartogram).

If you know how to interpret the data, please leave a comment. I'm guessing some kind of heatmap will work well with this data. 

Beautiful spider loses its way 2

A double post today.

In the previous post, I talked about NFL.com's visualization of football player statistics. In this post, I offer a few different views of the same data.

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The first is a dot plot arranged in small multiples.

Notice that I have indiced every metric against the league average. This is shown in the first panel. I use a red dot to warn readers that the direction of this metric is opposite to the others (left of center is a good thing!)

You can immediately make a bunch of observations:

• Alex Smith was quite poor, except for interceptions.
• Colin Kaepernick had similar passing statistics as Smith. His only advantage over Smith was the rushing.
• Joe Flacco, as we noted before, is as average as it goes (except for rushing yards).
• Tyrrod Taylor is here to remind us that we have to be careful about backup players being included in the same analysis.

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The second version is a heatmap.

This takes inspiration from the fact that any serious reader of the spider chart will be reading the eight spokes (dimensions) separately. Why not plot these neatly in columns and use color to help us find the best and worst?

Imagine this to be a large table with as many rows as there are quarterbacks. You will able to locate the red (hot) zones quickly. You can also scan across a row to understand that player's performance relative to the average, on every metric.

I like this visualization best, primarily because it scales beautifully.

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The final version is a profile chart, or sometimes called a parallel coordinates plot. While I am an advocate of profile charts, they really only work when you have a small number of things to compare.