Junk Charts

Environmental science can use better graphics

Mike A. pointed me to two animated maps made by Caltech researchers published in LiveScience (here).

The first map animation shows the rise and fall of water levels in a part of California over time. It's an impressive feat of stitching together satellite images. Click here to play the video.

The animation grabs your attention. I'm not convinced by the right side of the color scale in which the white comes after the red. I'd want the white in the middle then the yellow and finally the red.

In order to understand this map and the other map in the article, the reader has to bring a lot of domain knowledge. This visualization isn't easy to decipher for a layperson.

Here I put the two animations side by side:

The area being depicted is the same. One map shows "ground deformation" while the other shows "subsidence". Are they the same? What's the connection between the two concepts (if any)?  On a further look, one notices that the time window for the two charts differ: the right map is clearly labeled 1995 to 2003 but there is no corresponding label on the left map. To find the time window of the left map, the reader must inspect the little graph on the top right (1996 to 2000).

This means the time window of the left map is a subset of the time window of the right map. The left map shows a sinusoidal curve that moves up and down rhythmically as the ground shifts. How should I interpret the right map? The periodicity is no longer there despite this map illustrating a longer time window. The scale on the right map is twice the magnitude of the left map. Maybe on average the ground level is collapsing? If that were true, shouldn't the sinusoidal curve drift downward over time?

The chart on the top right of the left map is a bit ugly. The year labels are given in decimals e.g. 1997.5. In R, this can be fixed by customizing the axis labels.

I also wonder how this curve is related to the map it accompanies. The curve looks like a model - perfect oscillations of a fixed period and amplitude. But one suppose the amount of fluctuation should vary by location, based on geographical features and human activities.

The author of the article points to both natural and human impacts on the ground level. Humans affect this by water usage and also by management policies dictated by law. It would be very helpful to have a map that sheds light on the causes of the movements.

Visualizing the Thai cave rescue operation

The Thai cave rescue was a great story with a happy ending. It's also one that lends itself to visualization. A good visualization can explain the rescue operation more efficiently than mere words.

A good visual should bring out the most salient features of the story, such as:

• Why the operation was so daunting?
• What were the tactics used to overcome those challenges?
• How long did it take?
• What were the specific local challenges that must be overcome?
• Were there any surprises?

In terms of what made the rescue challenging, some of the following are pertinent:

• How far in they were?
• How deep were they trapped?
• How much of the caves were flooded? Why couldn't they come out by themselves?
• How much headroom was there in different sections of the cave "tunnel"?

There were many attempts at visualizing the Thai cave rescue operation. The best ones I saw were: BBC (here, here), The New York Times (here), South China Morning Post (here) and Straits Times (here). It turns out each of these efforts focuses on some of the aspects above, and you have to look at all of them to get the full picture.

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BBC's coverage began with a top-down view of the route of the rescue, which seems to be the most popular view adopted by news organizations. This is easily understood because of the standard map aesthetic.

The BBC map is missing a smaller map of Thailand to place this in a geographical context.

While this map provides basic information, it doesn't address many of the elements that make the Thai cave rescue story compelling. In particular, human beings are missing from this visualization. The focus is on the actions ("diving", "standing"). This perspective also does not address the water level, the key underlying environmental factor.

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Another popular perspective is the sideway cross-section. The Straits Times has one:

The excerpt of the infographic presents a nice collection of data that show the effort of the rescue. The sideway cross-sectional section shows the distance and the up-and-down nature of the journey, the level of flooding along the route, plus a bit about the headroom available at different points. Most of these diagrams bring out the "horizontal" distance but somehow ignore the "vertical" distance. One possibility is that the real trajectory is curvy - but if we can straighten out the horizontal, we should be able to straighten out the vertical too.

The NYT article gives a more detailed view of the same perspective, with annotations that describe key moments along the rescue route.

If, like me, you like to place humans into this picture, then you have to go back to the Straits Times, where they have an expanded version of the sideway cross-section.

 

This is probably my most favorite single visualization of the rescue operation.

There are better cartoons of the specific diving actions, though. For example, the BBC has this visual that shows the particularly narrow part of the route, corresponding to the circular inset in the Straits Times version above.

The drama!

NYT also has a set of cartoons. Here's one:

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There is one perspective that curiously has been underserved in all of the visualizations - this is the first-person perspective. Imagine the rescuer (or the kids) navigating the rescue route. It's a cross-section from the front, not from the side.

Various publications try to address this by augmenting the top-down route view with sporadic cross-sectional diagrams. Recall the first map we showed from the BBC. On the right column are little annotations of this type (here):

I picked out this part of the map because it shows that the little human figure serves two potentially conflicting purposes. In the bottom diagram, the figurine shows that there is limited headroom in this part of the cave, plus the actual position of the figurine on the ledge conveys information about where the kids were. However, on the top cross-section, the location of the figure conveys no information; the only purpose of the human figure is to show how tall the cave is at that site.

The South China Morning Post (here - site appears to be down when I wrote this) has this wonderful animation of how the shape of the headroom changed as they navigated the route. Please visit their page to see the full animation. Here are two screenshots:

This little clip adds a lot to the story! It'd be even better if the horizontal timeline at the bottom is replaced by the top-down route map.

Thank you all the various dataviz teams for these great efforts.

 

 

 

Graphical advice for conference presenters - demo

Yesterday, I pulled this graphic from a journal paper, and said one should not copy and paste this into an oral presentation.

So I went ahead and did some cosmetic surgery on this chart.

I don't know anything about the underlying science. I'm just interpreting what I see on the chart. It seems like the key message is that the Flowering condition is different from the other three. There are no statistical differences between the three boxplots in the first three panels but there is a big difference between the red-green and the purple in the last panel. Further, this difference can be traced to the red-green boxplots exhibiting negative correlation under the Flowering condition - while the purple boxplot is the same under all four conditions.

I would also have chosen different colors, e.g. make red-green two shades of gray to indicate that these two things can be treated as the same under this chart. Doing this would obviate the need to introduce the orange color.

Further, I think it might be interesting to see the plots split differently: try having the red-green boxplots side by side in one panel, and the purple boxplots in another panel.

If the presentation software has animation, the presenter can show the different text blocks and related materials one at a time. That also aids comprehension.

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Note that the plot is designed for an oral presentation in which you have a minute or two to get the message across. It's debatable as to whether journal editors should accept this style for publications. I actually think such a style would improve reading comprehension but I surmise some of you will disagree.

Graphical advice for conference presenters

I've attended a number of talks in the last couple of days at the Joint Statistical Meetings. I'd like to offer some advice to presenters using graphics in their presentations.

Here is an example of the style of graphics that are being presented. (Note: I deliberately picked an example from a Google image search - this graphic was not used in a presentation but is representative of those I've seen.)

Here are some tips to make your graphic much more impactful:

• Use much larger font sizes. Typically, the same graphic published in a journal is used in the presentation. Other than the people sitting in the front row, no one can see any of the text, which means no one can understand anything. Most of us realize that for the bullet points on the slides, you have to pick a large font, say 20 points. The same goes for any labels or annotation on your graphics!
• Use much thicker lines, larger dots, etc. Similar to the above, if you'd like people in the second to the last rows to be able to see your chart, you must enlarge everything. (For R users, cex comes in handy.)
• Put a lot of text on the graphic itself. The graphic shown above has words but it lacks any context. In many of these presentations, the audience are statisticians, many of whom work in different industries or disciplines so we don't know what OpN, LIN, LIC mean. You may have explained this five slides prior but it's hard to expect the audience to remember. Why not just spell that out. Kendall's tau may be known to some in the audience but we still don't know - just based on what's on this chart - what correlation is being assessed. Any other text that helps explain what's on the chart should be added.
• Add an informative title. These presentations are only 20 minutes long, and you'll spend maybe one minute explaining the graphic to someone who hasn't read the paper. You should spell out what is the message of your graphic - then we can look at the evidence to see how you drew that conclusion. In this example, it seems like there is a story around Flowering.
• Avoid complex graphics. In a few occasions, the presenters show a grid of charts. These work well in a journal paper when we have time to figure out the layout. It's hard to grasp the message plus figure out how to read the chart all in a matter of a minute or so! Just like we recommend usually one message per slide, you should stick to one message per graphic used in an oral presentation.

The larger lesson is that the chart that is perfect for publication in a journal is less than perfect for an oral presentation.

 

PS. Please see here for an example of how one can remake the above chart for use in a conference presentation.

Two good charts can use better titles

NPR has this chart, which I like:

It's a small multiples of bumps charts. Nice, clear labels. No unnecessary things like axis labels. Intuitive organization by Major Factor, Minor Factor, and Not a Factor.

Above all, the data convey a strong, surprising, message - despite many high-profile gun violence incidents this year, some Democratic voters are actually much less likely to see guns as a "major factor" in deciding their vote!

Of course, the overall importance of gun policy is down but the story of the chart is really about the collapse on the Democratic side, in a matter of two months.

The one missing thing about this chart is a nice, informative title: In two months, gun policy went from a major to a minor issue for some Democratic voters.

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 I am impressed by this Financial Times effort:

The key here is the analysis. Most lazy analyses compare millennials to other generations but at current ages but this analyst looked at each generation at the same age range of 18 to 33 (i.e. controlling for age).

Again, the data convey a strong message - millennials have significantly higher un(der)employment than previous generations at their age range. Similar to the NPR chart above, the overall story is not nearly as interesting as the specific story - it is the pink area ("not in labour force") that is driving this trend.

Specifically, millennial unemployment rate is high because the proportion of people classified as "not in labour force" has doubled in 2014, compared to all previous generations depicted here. I really like this chart because it lays waste to a prevailing theory spread around by reputable economists - that somehow after the Great Recession, demographics trends are causing the explosion in people classified as "not in labor force". These people are nobodies when it comes to computing the unemployment rate. They literally do not count! There is simply no reason why someone just graduated from college should not be in the labour force by choice. (Dean Baker has a discussion of the theory that people not wanting to work is a long term trend.)

The legend would be better placed to the right of the columns, rather than the top.

Again, this chart benefits from a stronger headline: BLS Finds Millennials are twice as likely as previous generations to have dropped out of the labour force.

 

 

 

 

Playfulness in data visualization

The Newslab project takes aggregate data from Google's various services and finds imaginative ways to enliven the data. The Beautiful in English project makes a strong case for adding playfulness to your data visualization.

The data came from Google Translate. The authors look at 10 languages, and the top 10 words users ask to translate from those languages into English.

The first chart focuses on the most popular word for each language. The crawling snake presents the "worldwide" top words.

The crawling motion and the curvature are not required by the data but it inserts a dimension of playfulness into the data that engages the reader's attention.

The alternative of presenting a data table loses this virtue without gaining much in return.

Readers are asked to click on the top word in each country to reveal further statistics on the word.

For example, the word "good" leads to the following:

 

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The second chart presents the top 10 words by language in a lollipop style:

The above diagram shows the top 10 Japanese words translated into English. This design sacrifices concise in order to achieve playful.

The standard format is a data table with one column for each country, and 10 words listed below each country header in order of decreasing frequency.

The creative lollipop display generates more extreme emotions - positive, or negative, depending on the reader. The data table is the safer choice, precisely because it does not engage the reader as deeply.

 

 

Lines, gridlines, reference lines, regression lines, the works

This post is part 2 of an appreciation of the chart project by Google Newslab, advised by Alberto Cairo, on the gender and racial diversity of the newsroom. Part 1 can be read here.

In the previous discussion, I left out the following scatter bubble plot.

This plot is available in two versions, one for gender and one for race. The key question being asked is whether the leadership in the newsroom is more or less diverse than the rest of the staff.

The story appears to be a happy one: in many newsrooms, the leadership roughly reflects the staff in terms of gender distribution (even though both parts of the whole compare disfavorably to the gender ratio in the neighborhoods, as we saw in the previous post.)

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Unfortunately, there are a few execution problems with this scatter plot.

First, take a look at the vertical axis labels on the right side. The labels inform the leadership axis. The mid-point showing 50-50 (parity) is emphasized with the gray band. Around the mid-point, the labels seem out of place. Typically, when the chart contains gridlines, we expect the labels to sit right around each gridline, either on top or just below the line. Here the labels occupy the middle of the space between successive gridlines. On closer inspection, the labels are correctly affixed, and the gridlines  drawn where they are supposed to be. The designer chose to show irregularly spaced labels: from the midpoint, it's a 15% jump on either side, then a 10% jump.

I find this decision confounding. It also seems as if two people have worked on these labels, as there exists two patterns: the first is "X% Leaders are Women", and second is "Y% Female." (Actually, the top and bottom labels are also inconsistent, one using "women" and the other "female".)

The horizontal axis? They left out the labels. Without labels, it is not possible to interpret the chart. Inspecting several conveniently placed data points, I figured that the labels on the six vertical gridlines should be 25%, 35%, ..., 65%, 75%, in essence the same scale as the vertical axis.

Here is the same chart with improved axis labels:

Re-labeling serves up a new issue. The key reference line on this chart isn't the horizontal parity line: it is the 45-degree line, showing that the leadership has the same proprotion of females as the rest of the staff. In the following plot (right side), I added in the 45-degree line. Note that it is positioned awkwardly on top of the grid system. The culprit is the incompatible gridlines.

 

The solution, as shown below, is to shift the vertical gridlines by 5% so that the 45-degree line bisects every grid cell it touches.

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Now that we dealt with the purely visual issues, let me get to a statistical issue that's been troubling me. It's about that yellow line. It's supposed to be a regression line that runs through the points.

Does it appear biased downwards to you? It just seems that there are too many dots above and not enough below. The distance of the furthest points above also appears to be larger than that of the distant points below.

How do we know the line is not correct? Notice that the green 45-degree line goes through the point labeled "AVERAGE." That is the "average" newsroom with the average proportion of female staff and the average proportion of leadership staff. Interestingly, the average falls right on the 45-degree line.

In general, the average does not need to hit the 45-degree line. The average, however, does need to hit the regression line! (For a mathematical explanation, see here.)

Note the corresponding chart for racial diversity has it right. The yellow line does pass through the average point here:

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In practice, how do problems seep into dataviz projects? It's the fact that you don't get to the last chart via a clean, streamlined process but that you pass through a cycle of explore-retrench-synthesize, frequently bouncing ideas between several people, and it's challenging to keep consistency!

And let me repeat my original comment about this project - the key learning here is how they took a complex dataset with many variables, broke it down into multiple parts addressing specific problems, and applied the layering principle to make each part of the project digestible.

 

 

A look at how the New York Times readers look at the others

The above chart, when it was unveiled at the end of November last year, got some mileage on my Twitter feed so it got some attention. A reader, Eric N., didn't like it at all, and I think he has a point.

Here are several debatable design decisions.

The chart uses an inverted axis. A tax cut (negative growth) is shown on the right while a tax increase is shown on the left. This type of inversion has gotten others in trouble before, namely, the controversy over the gun deaths chart (link). The green/red color coding is used to signal the polarity although some will argue this is bad for color-blind readers. The annotation below the axis is probably the reason why I wasn't confused in the first place but the other charts further down the page do not repeat the annotation, and that's where the interpretation of -$2,000 as a tax increase is unnatural!

The chart does not aggregate the data. It plots 25,000 households with 25,000 points. Because of the variance of the data, it's hard to judge trends. It's easy enough to see that there are more green dots than red but how many more? 10 percent, 20 percent, 40 percent? It's also hard to answer any specific questions, say, about households with a certain range of incomes. There are various ways to aggregate the data, such as heatmaps, histograms, and so on.

For those used to looking at scientific charts, the x- and y-axes are reversed. By convention, we'd have put the income ranges on the horizontal axis and the tax changes (the "outcome" variable) on the vertical axis.

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The text labels do not describe the data patterns on the chart so much as they offer additional information. To see this, remove the labels as I have done below. Try adding the labels based on what is shown on the chart.

Perhaps it's possible to illustrate those insights with a set of charts.

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While reading this chart, I kept wondering how those 25,000 households were chosen. This is a sample of  households. The methodology is explained in a footnote, which describes the definition of "middle class" but unfortunately, they forgot to tell us how the 25,000 households were chosen from all such middle-class households.

The decision to omit the households with income below $40,000 needs more explanation as it usurps the household-size adjustment. Also, it's not clear that the impact of the tax bill on the households with incomes between $20-40K can be assumed the same as for those above $40K.

Are the 25,000 households is a simple random sample of all "middle class" households or are they chosen in some ways to represent the relative counts? It's also useful to know if they applied the $40K cutoff before or after selecting the 25,000 households. 

Ironically, the media kit of the Times discloses an affluent readership with median household income of almost $190K so it appears that the majority of readers are not represented in the graphic at all!

 

Wheel of fortune without prizes: the negative report about negativity

My friend, Louis V., handed me a report from Harvard's Shorenstein Center, with the promise that I can make a blog post or two from it. And I wasn't disappointed.

This report (link) caught some attention a few months ago because of the click-bait headline that the media is "biased" against Trump in his first 100 days. They used the most naive definition of "bias". The metric is the amount of coverage that is "negative," with the unspoken standard that the media should be 50% negative.

In the court of law, it is already established that, for example, a loan company cannot be sued for racial bias simply because the rejection rate of loans for black Americans is higher than that of white Americans. Similarly, a university is not necessarily biased against black applicants even if the proportion of black students is found to be below the national proportion of black Americans (in a statistically significant way).

The appropriate amount of negative coverage is a function of the content of the President's actions, which is a hard standard to nail down, much harder than the two examples shown above - which just says that such an analysis is futile from start to finish. Let alone the irony of generating a negative media headline criticizing the negative tone of media coverage.

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Now let's turn to their use of visuals. The following pair of pie charts is used to show the differences in coverage between U.S. and European media.

These pie charts are inspired by Wheel of Fortune, without the prizes. 

Notice how our attention is caught by certain colors (red, orange, etc.) and the size of the slices. The largest red slice is labeled "Other Foreign/Defense" in the U.S. pie chart, although it did not merit a mention in the accompanying writeup so it's not clear what that category means.

Instead of ordering the slices by their sizes, the design puts the larger slices as far apart as possible. Further, each color is used twice in a mirrored way, causing us to infer an association between categories that don't exist.

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There are lots of conventional ways to display this data better. I decided to experiment with word clouds (using the Wordle tool).

Here is one in which the color indicates whether the coverage is American or European. Each word appears twice, and in proximity to one another for comparison.

One can directly compute a discrepancy metric between the two regions. This next chart shows the difference in importance accorded each topic by American versus European media:

 

 

Lines that delight, lines that blight

This WSJ graphic caught my eye. The accompanying article is here.

The article (judging from the sub-header) makes two separate points, one about the total amount of money raised in IPOs in a year, and the change in market value of those newly-public companies one year from the IPO date.

The first metric is shown by the size of the bubbles while the second metric is displayed as distances from the horizontal axis. (The second metric is further embedded, in a simplified, binary manner, in the colors of the bubbles.)

The designer has decided that the second metric - performance after IPO - to be more important. Therefore, it is much easier for readers to know how each annual cohort of IPOs has performed. The use of color to map to the second metric (and not the first) also helps to emphasize the second metric.

There are details on this chart that I admire. The general tidiness of it. The restraint on the gridlines, especially along the horizontal ones. The spatial balance. The annotation.

And ah, turning those bubbles into lollipops. Yummy! Those dotted lines allow readers to find the center of each bubble, which is where the values of the second metrics lie. Frequently, these bubble charts are presented without those guiding lines, and it is often hard to find the circles' anchors.

That leaves one inexplicable decision - why did they place two vertical gridlines in the middle of two arbitrary years?