A nice plot of densities, but what's behind the colors?

I came across this chart by Planet Anomaly that compares air quality across the world's cities (link). The chart is in long form. The top part looks like this:

The bottom part looks like this:

You can go to the Visual Capitalist website to see the entire chart.

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Plots of densities are relatively rare. The metric for air quality is micrograms of fine particulate matter (PM) per cubic meter, so showing densities is natural.

It's pretty clear the cities with the worst air quality at the bottom has a lot more PM in the air than the cleanest cities shown at the top.

This density chart plays looser with the data than our canonical chart types. The perceived densities of dots inside the squares do not represent the actual concentrations of PM. It's certainly not true that in New Delhi, the air is packed tightly with PM.

Further, a random number generator is required to scatter the red dots inside the circle. Thus, different software or designers will make the same chart look a bit different - the densities will be the same but the locations of the dots will not be.

I don't have a problem with this. Do you?

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Another notable feature of this chart is the double encoding. The same metric is not just presented as densities; it is also encoded in a color scale.

I don't think this adds much.

Both color and density are hard for humans to perceive precisely so adding color does not convey  precision to readers.

The color scale is gradated, so it effectively divided the cities into seven groups. But I don't attach particular significance to the classification. If that is important, it would be clearer to put boxes around the groups of plots. So I don't think the color scale convey clustering to readers effectively.

There is one important grouping which is defined by WHO's safe limit of 5 pg/cubic meter. A few cities pass this test while almost every other place fails. But the design pays no attention to this test, as it uses the same hue on both sides, and even the same tint changes on either side of the limit.

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Another notable project that shows densities as red dots is this emotional chart by Mona Chalabi about measles, which I wrote about in 2019.

 

Yet another off radar plot 2

In the last post, I described my experience reading the radar plot, by Bloomberg Graphics, that compares countries in terms of their citizens' post-retirement lives.

I used a different approach:

Instead of focusing on the actual time points (ages), my chart highlights the variance from the OECD averages.

The chart compares countries along three metrics: total life expectancy (including healthy and unhealthy periods), effective retirement age, and the number of healthy years in retirement, which is the issue of greatest interest.

From the above chart, France and Luxembourg have the same profiles. Their citizens live a year or two above the average life expectancy. They retire about 5 years earlier than average, and enjoy about 5 more years of healthy retirement.

Meanwhile, the life expectancy of Americans is about the same as the average OECD resident. Retirement also occurs around the same age as the OECD average. Nevertheless, Americans end up with fewer years of healthy retirement than the OECD average.

 

 

Yet another off radar plot

Bloomberg compares people's lives in retirement in this interesting dataviz project (link, paywall). The "showcase" chart is a radar plot that looks like this:

The radar plot may count as the single chart type that has the most number of lives. I'm afraid this one does not go into the hall of fame, either.

The setup leading to this plot is excellent, though. The analytical framework is to divide the retirement period into two parts: healthy and not so healthy. The countries in the radar plot are in fact ordered by the duration of the "healthy retirement period", with France leading the pack. The reference levels used throughout the article is the OECD average. On average, the OECD resident retires at age 64, and dies at age 82, so they spend 18 years in retirement, and 13 of them while "healthy".

In the radar plot, the three key dates are plotted as yellow, green and purple dots. The yellow represents the retirement age, the green, the end of the healthy period, and the purple, the end of life.

Now, take 10, 20, 30 seconds, and try to come up with a message for the above chart.

Not easy at all.

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Notice the control panel up top. The male and female data are plotted separately. I place the two segments next to each other:

It's again hard to find any insight - other than the most obvious, which is that female life expectancy is higher.

But note that the order for the countries is different for each chart, and so even the above statement takes a bit of time to verify.

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There are many structural challenges to using radar charts. I'll cover one of these here - the amount of non data-ink baggage that comes with using this chart form.

In the Bloomberg example, the baggage includes radial gridlines for countries, concentric gridlines for the years dimension, the country labels around the circle, the age labels in the middle, the color legend, the set of arrows that map to the healthy retirement period, and the country ranks (and little arrow) that indicate the direction of reading. That's a lot of information to process.

In the next post, I'll try a different visual form.

 

 

Here's a radar chart that works, sort of

In the same Reuters article that featured the speedometer chart which I discussed in this blog post (link), the author also deployed a small multiples of radar charts.

These radar charts are supposed to illustrate the article's theme that "European countries are racing to fill natural gas storage sites ahead of winter."

Here's the aggregate chart that shows all countries:

In general, I am not a fan of radar charts. When I first looked at this chart, I also disliked it. But keep reading because I eventually decided that this usage is an exception. One just needs to figure out how to read it.

One reason why I dislike radar charts is that they always come with a lot of non-data-ink baggage. We notice that the months of the year are plotted in a circle starting at the top. They marked off the start of the war on Feb 24, 2022 in red. Then, they place the dotted circle, which represents the 80% target gas storage amount.

The trick is to avoid interpreting the areas, or the shapes of the blue and gray patches. I know, they look cool and grab our attention but in the context of conveying data, they are meaningless.

Instead of areas, focus on the boundaries of those patches. Don't follow one boundary around the circle. Pick a point in time, corresponding to a line between the center of the circle and the outermost circle, and look at the gap between the two lines. In the diagram shown right, I marked off the two relevant points on the day of the start of the war.

From this, we observe that across Europe, the gas storage was far less than the 80% target (recently set).

By comparing two other points (the blue and gray boundaries), we see that during February, gas storage is at a seasonal low, and in 2022, it is on the low side of the 5-year average. 

However, the visual does not match well with the theme of the article! While the gap between the blue and gray boundaries decreased since the start of the war, the blue boundary does not exceed the historical average, and does not get close to 80% until August, a month in which gas storage reaches 80% in a typical year.

This is example of a chart in which there is a misalignment between the Q and the V corners of the Trifecta Checkup (link).

The question/message is that Europeans are reacting to the war by increasing their gas storage beyond normal. The visual actually says that they are increasing the gas storage as per normal.

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As I noted before, when read in a particular way, these radar charts serve their purpose, which is more than can be said for most radar charts.

The designer made several wise choices:

Instead of drawing one ring for each year of data, the designer averaged the past 5 years and turned that into one single ring (patch). You can imagine what this radar chart would look like if the prior data were not averaged: hoola hoop mania!

Simplifying the data in this way also makes the small multiples work. The designer uses the aggregate chart as a legend/how to read this. And in a further section below, the designer plots individual countries, without the non-data-ink baggage:

Thanks againto longtime reader Antonio R. who submitted this chart.

Happy Labor Day weekend for those in the U.S.!

 

 

 

Metaphors give and take

Another submission came in from Euro Twitter. The following chart is probably from Germany:

As JB noted, this chart explains a financial pyramid scheme. I believe the numbers on the left are participants while the numbers on the right are the potential ill-gotten gains per person. The longer the pyramid scheme lasts, the more people participate, the more money flows to the top.

The pyramid is a natural metaphor for visualizing pyramid schemes. The levels of the pyramid correspond to levels of a pyramid scheme - the newly recruited participants expand the base while passing revenues up the pyramid.

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The chart fails because it's not really a dataviz. There are exactly three bars that are scaled according to data. Everything else is presented as data labels.

Let's look at the two data series separately:

Each series is exponentially growing (in opposite directions). [Some of the data labels for participants may be incorrect.]

Unfortunately, the triangle is not a good medium to display exponential growth. In fact, the triangular structure imposes a linear growth constraint. The length of the base is directly proportional to the height from the top. As one traverses downwards level by level, the width of the base grows linearly - not exponentially.

To illustrate exponential growth, the edge of the triangle cannot be a straight line - it has to be s steep curve!

While natural, the pyramid metaphor is also severely restricting. The choice of chart form has unexpected consequences.

 

Funnel is just for fun

This is part 2 of a review of a recent video released by NASA. Part 1 is here.

The NASA video that starts with the spiral chart showing changes in average global temperature takes a long time (about 1 minute) to run through 14 decades of data, and for those who are patient, the chart then undergoes a dramatic transformation.

With a sleight of hand, the chart went from a set of circles to a funnel. Here is a look:

What happens is the reintroduction of a time dimension. Imagine pushing the center of the spiral down into the screen to create a third dimension.

Our question as always is - what does this chart tell readers?

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The chart seems to say that the variability of temperature has increased over time (based on the width of the funnel). The red/blue color says the temperature is getting hotter especially in the last 20-40 years.

When the reader looks beneath the surface, the chart starts to lose sense.

The width of the funnel is really a diameter of the spiral chart in the given year. But, if you recall, the diameter of the spiral (polar) chart isn't the same between any pairs of months.

In the particular rendering of this video, the width of the funnel is the diameter linking the April and October values.

Remember the polar gridlines behind the spiral:

Notice the hole in the middle. This hole has arbitrary diameter. It can be as big or as small as the designer makes it. Thus, the width of the funnel is as big or as small as the designer wants it. But the first thing that caught our attention is the width of the funnel.

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The entire section between -1 and + 1 is, in fact, meaningless. In the following chart, I removed the core of the funnel, adding back the -1 degree line. Doing so exposes an incompatibility between the spiral and funnel views. The middle of the polar grid is negative infinity, a black hole.

For a moment, the two sides of the funnel look like they are mirror images. That's not correct, either. Each width of the funnel represents a year, and the extreme values represent April and October values. The line between those two values does not signify anything real.

Let's take a pair of values to see what I mean.

I selected two values for October 2021 and October 1899 such that the first value appears as a line double the length of the second. The underlying values are +0.99C and -0.04C, roughly speaking, +1 and 0, so the first value is definitely not twice the size of the second.

The funnel chart can be interpreted, in an obtuse way, as a pair of dot plots. As shown below, if we take dot plots for Aprils and Octobers of every year, turn the chart around, and then connect the corresponding dots, we arrive at the funnel chart.

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This NASA effort illustrates a central problem in visual communications: attention (what Andrew Gelman calls "grabbiness") and information integrity. On the one hand, what's the point of an accurate chart when no one is paying attention? On the other hand, what's the point of a grabby chart when anyone who pays attention gets the wrong information? It's not easy to find that happy medium.

How does the U.K. vote in the U.N.?

Through my twitter feed, I found my way to this chart, made by jamie_bio.

This is produced using R code even though it looks like a slide.

The underlying dataset concerns votes at the United Nations on various topics. Someone has already classified these topics. Jamie looked at voting blocs, specifically, countries whose votes agree most often or least often with the U.K.

If you look at his Github, this is one in a series of works he produced to hone his dataviz skills. Ultimately, I think this effort can benefit from some re-thinking. However, I also appreciate the work he has put into this.

Let's start with the things I enjoyed.

Given the dataset, I imagine the first visual one might come up with is a heatmap that shows countries in rows and topics in columns. That would work ok, as any standard chart form would but it would be a data dump that doesn't tell a story. There are almost 200 countries in the entire dataset. The countries can only be ordered in one way so if it's ordered for All Votes, it's not ordered for any of the other columns.

What Jamie attempts here is story-telling. The design leads the reader through a narrative. We start by reading the how-to-read-this box on the top left. This tells us that he's using a lunar eclipse metaphor. A full circle in blue indicates 0% agreement while a full circle in white indicates 100% agreement. The five circles signal that he's binning the agreement percentages into five discrete buckets, which helps simplify our understanding of the data.

Then, our eyes go to the circle of circles, labelled "All votes". This is roughly split in half, with the left side showing mostly blue and the right showing mostly white. That's because he's extracting the top 5 and bottom 5 countries, measured by their vote alignment with the U.K. The countries names are clearly labelled.

Next, we see the votes broken up by topics. I'm assuming not all topics are covered but six key topics are highlighted on the right half of the page.

What I appreciate about this effort is the thought process behind how to deliver a message to the audience. Selecting a specific subset that addresses a specific question. Thinning the materials in a way that doesn't throw the kitchen sink at the reader. Concocting the circular layout that presents a pleasing way of consuming the data.

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Now, let me talk about the things that need more work.

I'm not convinced that he got his message across. What is the visual telling us? Half of the cricle are aligned with the U.K. while half aren't so the U.K. sits on the fence on every issue? But this isn't the message. It's a bit of a mirage because the designer picked out the top 5 and bottom 5 countries. The top 5 are surely going to be voting almost 100% with the U.K. while the bottom 5 are surely going to be disagreeing with the U.K. a lot.

I did a quick sketch to understand the whole distribution:

This is not intended as a show-and-tell graphic, just a useful way of exploring the dataset. You can see that Arms Race/Disarmament and Economic Development are "average" issues that have the same form as the "All issues" line. There are a small number of countries that are extremely aligned with the UK, and then about 50 countries that are aligned over 50% of the time, then the other 150 countries are within the 30 to 50% aligned. On human rights, there is less alignment. On Palestine, there is more alignment.

What the above chart shows is that the top 5 and bottom 5 countries both represent thin slithers of this distribution, which is why in the circular diagrams, there is little differentiation. The two subgroups are very far apart but within each subgroup, there is almost no variation.

Another issue is the lunar eclipse metaphor. It's hard to wrap my head around a full white circle indicating 100% agreement while a full blue circle shows 0% agreement.

In the diagrams for individual topics, the two-letter acronyms for countries are used instead of the country names. A decoder needs to be provided, or just print the full names.

 

 

 

 

 

 

Dreamy Hawaii

I really enjoyed this visual story by ProPublica and Honolulu Star-Advertiser about the plight of beaches in Hawaii (link).

The story begins with a beautiful invitation:

This design reminds me of Vimeo's old home page. (It no longer looks like this today but this screenshot came from when I was the data guy there.) In both cases, the images are not static but moving.

The tour de force of this visual story is an annotated walk along the Lanikai Beach. Here is a snapshot at one of the stops:

This shows a particular homeowner who, according to documents, was permitted to rebuild a destroyed seawall even though officials were supposed to disallow reconstruction in order to protect beaches from eroding. The property is marked on the map above. The image inside the box is a gif showing waves smashing the seawall.

As the reader scrolls down, the image window runs through a carousel of gifs of houses along the beach. The images are synchronized to the reader's progress along the shore. The narrative makes stops at specific houses at which point a text box pops up to provide color commentary.

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The erosion crisis is shown in this pair of maps.

There's some fancy work behind the scenes to patch together images, and estimate the boundaries of th beaches.

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The following map is notable for its simplicity. There are no unnecessary details and labels. We don't need to know the name of every street or a specific restaurant. Removing excess details makes readers focus on the informative parts. 

Clicking on the dots brings up more details.

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Enjoy the entire story here.

I made a streamgraph

The folks at FiveThirtyEight were excited about the following dataviz they published last week two weeks ago, illustrating the progression of vote-counting by state. (link) That was indeed the unique and confusing feature of the 2020 Presidential election in the States. For those outside the U.S., what happened (by and large) was that many Americans, skewing Biden supporters, voted by mail before Election Day but their votes were sometimes counted after the same-day votes were tallied.

 

A number of us kept staring at these charts, hoping for a how-to-read-it explanation. Here is a zoom-in for the state of Michigan:

To save you the trouble, here is how.

The key is to fight your urge to look at the brown area. I know, it's pretty hard to ignore the biggest areas of every chart. But try to make them disappear.

Focus on the top edge of the chart. This line gives the total number of votes counted so far. In Michigan, by hour 12, about 2.4 million votes were counted, and by hour 72, 2.8 million votes were on the book. This line gives the sum of the two major parties' vote totals [since third parties got negligible votes in this election, I'm ignoring them so as to simplify the discussion].

Next, look at the red and blue areas. These represent the gap in the number of votes between the two parties' current vote totals. If the area is red, Trump was leading; if blue, Biden was leading. Each color flip represents a lead change. Suppress the urge to interpret red as the number or share of Trump votes.

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What have we learned about the vote counting in Michigan?

Counting significantly slowed after the 12th hour. Trump raced to a lead on Election Day, and around hour 20, the race was dead even, and after that, Biden overtook Trump and never looked back. Throughout most of this period, the vote lead was small compared to the total votes cast although at the end, the Biden lead was noticeable.

If you insist on interpreting the brown area, it is equal to twice the vote total of the second-place candidate, so it really isn't something you want to look at.

Just for contrast, here is the chart for Iowa:

Trump led from beginning to end, with his lead widening slightly as more votes were counted.

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As I was stewing over this chart, a ominous thought overcame me. Would a streamgraph work for this data? You don't hear much about streamgraphs here because I rarely favor them (see this long-ago post) but let's just try one and see.

(These streamgraphs were made in R using the streamgraph package. Post-processing was applied to customize the labeling.)

This chart conveys all the key points listed before. You can see how the gap evolved over time, the lead flips, which candidate was in the lead, and the total mass of votes counted at different times. The gap is shown in the middle.

I can't say I'm completely happy with the streamgraph - I hope readers don't care about the numbers because it's hard to evaluate a difference when it's split two ways on either side of the middle axis!

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If you come up with a better idea, make sure to leave a comment.

 

 

 

 

Election visuals 4: the snake pit is the best election graphic ever

This is the final post on the series of data visualization deployed by FiveThirtyEight to explain their election forecasting model. The previous posts are here, here and here.

I'm saving the best for last.

This snake-pit chart brings me great joy - I wish I came up with it!

This chart wins by focusing on a limited set of questions, and doing so excellently. As with many election observers, we understand that the U.S. presidential election will turn on so-called "swing states," and the candidates' strength in these swing states are variable, as the name suggests. Thus, we like to know which states are in play, and within these states, which ones are most unpredictable.

This chart lines up all the states from the reddest of red up top to the bluest of blue at the bottom. Each state is ranked by the voting margin predicted by 538's election forecasting model. The swing states are found in the middle.

Since each state confers a fixed number of electoral votes, and a candidate must amass 270 to win, there is a "tipping" state. In the diagram above, it's Pennsylvania. This pivotal state is neatly foregrounded as the one crossing the line in the middle.

The lengths of the segments correspond to the number of electoral votes and so do not change with the data. What change are the sequencing of the segments, and the color shading.

This data visualization is a gem of visual story-telling. The form lends itself to a story.

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The snake-pit chart succeeds by not doing too much. There are many items that the chart does not directly communicate.

The exact number of electoral votes by state is not explicit, nor is it easy to compare the lengths of bending segments. The color scale for conveying the predicted voting margins is crude, and it's not clear what is the difference between a deep color and a light color. It's also challenging to learn the electoral vote split; the actual winning margin is not even stated.

The reality is the average reader doesn't care. I got everything I wanted from the chart, and I ain't got the time to explore every state.

There is a hover-over effect that reveals some of the additional information:

One can keep going on. I have no idea how the 40,000 scenarios presented in the other graphics in this series have been reduced to the forecast shown in the inset. But again, those omissions did not lessen my enjoyment. The point is: let your graphics breathe.

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I'm thinking of potential variations even though I'm fully satisfied with this effort.

I wonder if the color shading should be reversed. The light shading encodes a smaller voting margin, which indicates a tighter race. But our attention is typically drawn first to the darker shades. If the shading scheme is reversed, the color should be described as how tight the race is.

I also wonder if a third color (purple) should be introduced. Doing so would require the editors to make judgment calls on which set of states are swing states.

One strange thing about election day is the specific sequence of when TV stations (!) call the state results, which not only correlates with voting margin but also with time zones. I wonder if the time zone information can be worked into the sequencing of segments.

Let me know what you think of these ideas, or leave your own ideas, in the comments below.

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I have already praised this graphic when it first came out in 2016. (link)

A key improvement is tilting the chart, which avoids vertical state labels.

The previous post was written around election day 2016. The snake pit further cements its status as a story-telling device. As states are called, they are taken out of the picture. So it works very well as a dynamic chart on election day.

I'm nominating this snake-pit chart as the best election graphic ever. Kudos to the FiveThirtyEight team.