Election visuals 2: informative and playful

In yesterday's post, I reviewed one section of 538's visualization of its election forecasting model, specifically, the post focuses on the probability plot visualization.

The visualization, technically called  a pdf, is a mainstay of statistical graphics. While every one of 40,000 scenarios shows up on this chart, it doesn't offer a direct answer to our topline question. What is Nate's call at this point in time? Elsewhere in their post, we learn that the 538 model currently gives Biden a 75% chance of winning, thrice that of Trump's.

In graphical terms, the area to the right of the 270-line is three times the size of the left area (on the bottom chart). That's not apparent in the pdf representation. Addressing this, statisticians may convert the pdf into a cdf, which depicts the cumulative area as we sweep from the left to the right along the horizontal axis.  

The cdf visualization rarely leaves the pages of a scientific journal because it's not easy for a novice to understand. Not least because the relevant probability is 1 minus the cumulative probability. The cdf for the bottom chart will show 25% at the 270-line while the chance of Biden winning is 1 - 25% = 75%.

The cdf presentation is also wasteful for the election scenario. No one cares about any threshold other than the 270 votes needed to win, but the standard cdf shows every possible threshold.

The second graphical concept in the 538 post (link) is an attempt to solve this problem.

If you drop all the dots to an imaginary horizontal baseline, the above dotplot looks like this:

There is a recent trend toward centering dots to produce symmetry. It's actually harder to perceive the differences in heights of the band.

The secret sauce is to put down 100 dots, with a 75-25 blue-red split that conveys the 75% chance of a Biden win. Imposing the pdf line from the other visualization, I find that the density of dots roughly mimics the probability of outcomes.

It's easier to estimate the blue vs red areas using those dots than the lines.

The dots are stuffed toys. Clicking on each dot reveals a map showing one of the 40,000 scenarios. It displays which candidate wins which state. For example, the most extreme example of a Trump win is:

Here is a scenario of a razor-tight election won by Trump:

This presentation has a weakness as well. It gives the impression that each of the dots is equally important because they are the same size. In reality, the importance of each dot is proportional to the height of the band. Since the band is generally wider near the middle, the dots near the middle are more likely scenarios than the dots shown on the two edges.

On balance, I like this visualization that is both informative and playful.

As before, what strikes me about the simulation result is the flatness of the probability surface. This feature is obscured when we summarize the result as 75% chance of a Biden victory.

Election visuals: three views of FiveThirtyEight's probabilistic forecasts

As anyone who is familiar with Nate Silver's forecasting of U.S. presidential elections knows, he runs a simulation that explores the space of possible scenarios. The polls that provide a baseline forecast make certain assumptions, such as who's a likely voter. Nate's model unshackles these assumptions from the polling data, exploring how the outcomes vary as these assumptions shift.

In the most recent simulation, his computer explores 40,000 scenarios, each of which predicts a split of the electoral vote, from which the winner of the election can be determined. The model's outcome is usually summarized by a winning probability, which is just the proportion of scenarios under which one candidate wins.

This type of forecasting was responsible for the infamous meltdown in 2016 when most of these models - Nate's being an exception - issued extremely confident predictions that Hillary Clinton wins with 95% or higher probability. Essentially, the probability distribution collapses to a point. This is analogous to an extremely narrow confidence band, indicating almost zero uncertainty about the event. It was as if almost all of the 40,000 scenarios predicted Clinton to be the winner.

The 538 data team has come up with various ways of visualizing the outputs of the model (link). The entire post is worth reading. Here, I'll highlight the most scientific, and direct visual representation, which is the third display.

We start by looking at the bottom of the two charts, showing the predicted electoral votes won  by Democratic challenger Joe Biden, in each of the 40,000 scenarios. Our attention is directed to the thick line that gives the relative chance of Biden's electoral-vote tally. This line is a smoothed summary of the columns in the background, which show the number of times the simulation produces each electoral-vote count.

The highlighted, right side of the chart recounts scenarios in which Biden becomes President, that is to say, he wins more than 270 electoral votes (out of 538, doh). The faded, left side represents scenarios in which Biden is defeated and Trump wins a second term.

The reason I focused on the bottom chart is that the top chart is merely a mirror image of this one. Just reflect the bottom chart around the vertical axis of 270 electoral votes, change the color scheme to red, and swap annotations related to Trump and Biden, and you get the other chart. This is because the narrative has excluded third-party and write-in candidates, leaving us with a zero-sum situation.

Alternatively, one can jam both charts into one, while supplying extra labels, like this:

I prefer the denser single chart because my mind wanders away searching for extra meaning when chart elements are mirrored.

One advantage of the mirrored presentation is that the probability profiles of the potential Trump or Biden wins can be directly compared. We learn that Trump's winning margins are smaller, rarely above 150, and never above 250.

This comparison is made easier by flipping left side of the chart onto the right side:

Those are three different visualizations using the same chart form. I'd have to run a poll to figure out which is the best. What's your opinion?

Putting vaccine trials in boxes

Bloomberg Businessweek has a special edition about vaccines, and I found this chart on the print edition:

The chart's got a lot of white space. Its structure is a series of simple "treemaps," one for each type of vaccine. Though simple, such a chart burns a few brain cells.

Here, I've extracted the largest block, which corresponds to vaccines that work with the virus's RNA/DNA. I applied a self-sufficiency test, removing the data from the boxes. 

What proportion of these projects have moved from pre-clinical to Phase 1?  To answer this question, we have to understand the relative areas of boxes, since that's how the data are encoded. How many yellow boxes can fit into the gray box?

It's not intuitive. We'd need a ruler to do this task properly.

Then, we learn that the gray box is exactly 8 times the size of the yellow box (72 projects are pre-clinical while 9 are in Phase I). We can cram eight yellows into the gray box. Imagine doing that, and it's pretty clear the visual elements fail to convey the meaning of the data.

Self-sufficiency is the idea that a data graphic should not rely on printed data to convey its meaning; the visual elements of a data graphic should bear much of the burden. Otherwise, use a data table. To test for self-sufficiency, cover up the printed data and see if the chart still works.

***

A key decision for the designer is the relative importance of (a) the number of projects reaching Phase III, versus (b) the number of projects utilizing specific vaccine strategies.

This next chart emphasizes the clinical phases:

 

Contrast this with the version shown in the online edition of Bloomberg (link), which emphasizes the vaccine strategies.

If any reader can figure out the logic of the ordering of the vaccine strategies, please leave a comment below.

Unlocking the secrets of a marvellous data visualization

The graphics team in my hometown paper SCMP has developed a formidable reputation in data visualization, and I lapped every drop of goodness on this beautiful graphic showing how the coronavirus spread around Hong Kong (in the first wave in April). Marcelo uploaded an image of the printed version to his Twitter. This graphic occupied the entire back page of that day's paper.

An online version of the chart is found here.

The data graphic is a masterclass in organizing data. While it looks complicated, I had no problem unpacking the different layers.

Cases were divided into imported cases (people returning to Hong Kong) and local cases. A small number of cases are considered in-betweens.

The two major classes then occupy one half page each. I first looked at the top half, where my attention is drawn to the thickest flows. The majority of imported cases arrived from the U.K., and most of those were returning students. The U.S. is the next largest source of imported cases. The flows are carefully ordered by continent, with the Americas on the left, followed by Europe, Middle East, Africa, and Asia.

Where there are interesting back stories, the flow blossoms into a flower. An annotation explains the cluster of cases. Each anther represents a case. Eight people caught the virus while touring Bolivia together.

One reads the local cases in the same way. Instead of flowers, think of roots. The biggest cluster by far was a band that played at clubs in three different parts of the city, infecting a total of 72 people.

Everything is understood immediately, without a need to read text or refer to legends. The visual elements carry that kind of power.

***

This data graphic presents a perfect amalgam of art and science. For a flow chart, the data are encoded in the relative thickness of the lines. This leaves two unused dimensions of these lines: the curvature and lengths. The order of the countries and regions take up the horizontal axis, but the vertical axis is free. Unshackled from the data, the designer introduced curves into the lines, varied their lengths, and dispersed their endings around the white space in an artistic manner.

The flowers/roots present another opportunity for creativity. The only data constraint is the number of cases in a cluster. The positions of the dots, and the shape of the lines leading to the dots are part of the playground.

What's more, the data visualization is a powerful reminder of the benefits of testing and contact tracing. The band cluster led to the closure of bars, which helped slow the spread of the coronavirus.