## Bivariate choropleths

##### Apr 03, 2023

A reader submitted a link to Joshua Stephen's post about bivariate choropleths, which is the technical term for the map that FiveThirtyEight printed on abortion bans, discussed here. Joshua advocates greater usage of maps with two-dimensional color scales.

As a reminder, the fundamental building block is expressed in this bivariate color legend:

Counties are classified into one of these nine groups, based on low/middle/high ratings on two dimensions, distance and congestion.

The nine groups are given nine colors, built from superimposing shades of green and pink. All nine colors are printed on the same map.

Without a doubt, using these nine related colors are better than nine arbitrary colors. But is this a good data visualization?

Specifically, is the above map better than the pair of maps below?

The split map is produced by Josh to explain that the bivariate choropleth is just the superposition of two univariate choropleths. I much prefer the split map to the superimposed one.

***

Superimposing the two univariate maps solves one problem: it removes the need to scan back and forth between two maps, looking for the same locations, something that is imprecise. (Unless, the map is interactive, and highlighting one county highlights the same county in the other map.)

For me, that's a small price to pay for quicker translation of color into information.

## The time has arrived for cumulative charts

##### Mar 08, 2021

The dataset behind this chart is highly favorable to the designer, because the signal in the data is so strong. This is a good chart. The key point is shown clearly right at the top, with an informative title. Gridlines are very restrained. I'd draw attention to the horizontal axis. The master stroke here is omitting the week labels, which are likely confusing to all but the people familiar with this dataset.

Scott suggested using a line chart. I agree. And especially if we plot cumulative counts, rather than weekly deaths. Here's a quick sketch of such a chart:

(On second thought, I'd remove the week numbers from the horizontal axis, and just go with the month labels. The Washington Post designer is right in realizing that those week numbers are meaningless to most readers.)

The vaccine trials have brought this cumulative count chart form to the mainstream. For anyone who have seen the vaccine efficacy charts, the interpretation of the panel of line charts should come naturally.

Instead of four plots, I prefer one plot with four superimposed lines. Like this:

## Circular areas offer misleading cues of their underlying data

##### Feb 09, 2021

John M. pointed me on Twitter to this chart about the progress of U.S.'s vaccination campaign:

This looks like a White House production, retweeted by WHO. John is unhappy about this nested bubble format, which I'll come back to later.

Let's zoom in on what matters:

An even bigger problem with this chart is the Q corner in our Trifecta Checkup. What is the question they are trying to address? It would appear to be the proportion of population that has "already received [one or more doses of] vaccine". And the big words tell us the answer is 8 percent.

But is that really the question? Check out the dark blue circle. It is labeled "population that has already received vaccine" and thus we infer this bubble represents 8 percent. Now look at the outer bubble. Its annotation is "new population that received vaccine since January 27, 2021". The only interpretation that makes sense is that 8 percent  is not the most current number. If that is the case, why would the headline highlight an older statistic, and not the most up-to-date one?

Perhaps the real question is how fast is the progress in vaccination. Perhaps it took weeks to get to the dark circle and then days to get beyond. In order to improve this data visualization, we must first decide what the question really is.

***

Now let's get to those nested bubbles. The bubble chart is a format that is not "sufficient," by which I mean the visual by itself does not convey the data without the help of aids such as labels. Try to answer the following questions:

In my view, if your answer to the last question is anything more than 5 seconds, the dataviz has failed. A successful data visualization should not make readers solve puzzles.

The first two questions depict the confusing nature of concentric circle diagrams. The first data point is coded to the inner circle. Where is the second data point? Is it encoded to the outer circle, or just the outer ring?

In either case, human brains are not trained to compare circular areas. For question 1, the outer circle is 70% larger than the smaller circle. For question 2, the ring is 70% of the area of the dark blue circle. If you're thinking those numbers seem unreasonable, I can tell you that was my first reaction too! So I made the following to convince myself that the calculation was correct:

Circular areas offer misleading visual cues, and should be used sparingly.

[P.S. 2/10/2021. In the next post, I sketch out an alternative dataviz for this dataset.]

## Visualizing black unemployment in the U.S.

##### Jun 09, 2020

In a prior post, I explained how the aggregate unemployment rate paints a misleading picture of the employment situation in the United States. Even though the U3 unemployment rate in 2019 has returned to the lowest level we have seen in decades, the aggregate statistic hides some concerning trends. There is an alarming rise in the proportion of people considered "not in labor force" by the Bureau of Labor Statistics - these forgotten people are not counted as "employable": when a worker drops out of the labor force, the unemployment rate ironically improves.

In that post, I looked at the difference between men and women. This post will examine the racial divide, whites and blacks.

I did not anticipate how many obstacles I'd encounter. It's hard to locate a specific data series, and it's harder to know whether the lack of search results indicates the non-existence of the data, or the incompetence of the search engine. Race-related data tend not to be offered in as much granularity. I was only able to find quarterly data for the racial analysis while I had monthly data for the gender analysis. Also, I only have data from 2000, instead of 1990.

***

As before, I looked at the official unemployment rate first, this time presented by race. Because whites form the majority of the labor force, the overall unemployment rate (not shown) is roughly the same as that for whites, just pulled up slightly toward the line for blacks.

The racial divide is clear as day. Throughout the past two decades, black Americans are much more likely to be unemployed, and worse during recessions.

The above chart determines the color encoding for all the other graphics. Notice that the best employment situations occurred on either end of this period, right before the dotcom bust in 2000, and in 2019 before the Covid-19 pandemic. As explained before, despite the headline unemployment rate being the same in those years, the employment situation was not the same.

***

Here is the scatter plot for white Americans:

Even though both ends of the trajectory are marked with the same shade of blue, indicating almost identical (low) rates of unemployment, we find that the trajectory has failed to return to its starting point after veering off course during the recession of the early 2010s. While the proportion of part-time workers (counted as employed) returned to 17.5% in 2019, as in 2000, about 15 percent more whites are now excluded from the unemployment rate calculation.

The experience of black Americans appears different:

During the first decade, the proportion of black Americans dropping out of the labor force accelerated while among those considered employed, the proportion holding part-time jobs kept increasing. As the U.S. recovered from the Great Recession, we've seen a boomerang pattern. By 2019, the situation was halfway back to 2000. The last available datum for the first quarter of 2020 is before Covid-19; it actually showed a halt of the boomerang.

If the pattern we saw in the prior post holds for the Covid-19 world, we would see a marked spike in the out-of-labor-force statistic, coupled with a drop in part-time employment. It appeared that employers were eliminating part-time workers first.

***

One reader asked about placing both patterns on the same chart. Here is an example of this:

This graphic turns out okay because the two strings of dots fit tightly into the grid while not overlapping. There is a lot going on here; I prefer a multi-step story than throwing everything on the wall.

There is one insight that this chart provides that is not easily observed in two separate plots. Over the two decades, the racial gap has narrowed in these two statistics. Both groups have traveled to the top right corner, which is the worst corner to reside -- where more people are classified as not employable, and more of the employed are part-time workers.

The biggest challenge with making this combined scatter plot is properly controlling the color. I want the color to represent the overall unemployment rate, which is a third data series. I don't want the line for blacks to be all red, and the line for whites to be all blue, just because black Americans face a tough labor market always. The color scheme here facilitates cross-referencing time between the two dot strings.

## NYT hits the trifecta with this market correction chart

##### Dec 12, 2018

Yesterday, in the front page of the Business section, the New York Times published a pair of charts that perfectly captures the story of the ongoing turbulence in the stock market.

Here is the first chart:

Most market observers are very concerned about the S&P entering "correction" territory, which the industry arbitrarily defines as a drop of 10% or more from a peak. This corresponds to the shortest line on the above chart.

The chart promotes a longer-term reflection on the recent turbulence, using two reference points: the index has returned to the level even with that at the start of 2018, and about 16 percent higher since the beginning of 2017.

This is all done tastefully in a clear, understandable graphic.

Then, in a bit of a rhetorical flourish, the bottom of the page makes another point:

When viewed back to a 10-year period, this chart shows that the S&P has exploded by 300% since 2009.

A connection is made between the two charts via the color of the lines, plus the simple, effective annotation "Chart above".

The second chart adds even more context, through vertical bands indicating previous corrections (drops of at least 10%). These moments are connected to the first graphic via the beige color. The extra material conveys the message that the market has survived multiple corrections during this long bull period.

Together, the pair of charts addresses a pressing current issue, and presents a direct, insightful answer in a simple, effective visual design, so it hits the Trifecta!

***

There are a couple of interesting challenges related to connecting plots within a multiple-plot framework.

While the beige color connects the concept of "market correction" in the top and bottom charts, it can also be a source of confusion. The orientation and the visual interpretation of those bands differ. The first chart uses one horizontal band while the chart below shows multiple vertical bands. In the first chart, the horizontal band refers to a definition of correction while in the second chart, the vertical bands indicate experienced corrections.

Is there a solution in which the bands have the same orientation and same meaning?

***

These graphs solve a visual problem concerning the visualization of growth over time. Growth rates are anchored to some starting time. A ten-percent reduction means nothing unless you are told ten-percent of what.

Using different starting times as reference points, one gets different values of growth rates. With highly variable series of data like stock prices, picking starting times even a day apart can lead to vastly different growth rates.

The designer here picked several obvious reference times, and superimposes multiple lines on the same plotting canvass. Instead of having four lines on one chart, we have three lines on one, and four lines on the other. This limits the number of messages per chart, which speeds up cognition.

The first chart depicts this visual challenge well. Look at the start of 2018. This second line appears as if you can just reset the start point to 0, and drag the remaining portion of the line down. The part of the top line (to the right of Jan 2018) looks just like the second line that starts at Jan 2018.

However, a closer look reveals that the shape may be the same but the magnitude isn't. There is a subtle re-scaling in addition to the re-set to zero.

The same thing happens at the starting moment of the third line. You can't just drag the portion of the first or second line down - there is also a needed re-scaling.

## Using a bardot chart for survey data

##### Dec 04, 2017

Aleks J. wasn't amused by the graphs included in Verge's report about user attitudes toward the major Web brands such as Google, Facebook, and Twitter.

Let's use this one as an example:

Survey respondents are asked to rate how much they like or dislike the products and services from each of six companies, on a five-point scale. There is a sixth category for "No opinion/Don't use."

In making this set of charts, the designer uses six different colors for the six categories. This means he/she thinks of these categories as discrete so that the difference between categories carries no meaning. In a bipolar, five-point scale, it is more common to pick two extreme colors and then use shades to indicate the degree of liking or disliking. The middle category can be shown in a neutral color to express the neutrality of opinion.

The color choice baffles me. The two most prominent colors, gray and dark blue, correspond to two minor categories (no opinion and neutral) while the most important category - "greatly like" - is painted the modest yellow, paling away.

Verge sees the popularity of Facebook as the key message, which explains its top position among the six brands. However, readers familar with the stacked bar chart form are likely looking to make sense of the order, and frustrated.

***

In revising this chart, I introduce a second level of grouping: the six categories fit into three color groups: red for dislike, gray for no opinion/neutral, and orange for like. The like and dislike groups are plotted at the left and right ends of the chart while the two less informative categories are lumped toward the middle.

I take great pleasure in dumping the legend box.

***

Now, when a five-point scale is used, many analysts like to analyze the Top 2, or Bottom 2 boxes. The choice of colors in the above chart facilitates this analysis. Adding some subtle dots makes it even better!

Because this chart is a superposition of a stacked bar chart and a dot plot, I am calling this a bardot chart.

Also notice that the brands are re-ordered by Top 2 box popularity.

## Let's not mix these polarized voters as the medians run away from one another

##### Oct 10, 2017

Long-time follower Daniel L. sent in a gem, by the Washington Post. This is a multi-part story about the polarization of American voters, nicely laid out, with superior analyses and some interesting graphics. Click here to see the entire article.

Today's post focuses on the first graphic. This one:

The key messages are written out on the 2017 charts: namely, 95% of Republicans are more conservative than the median Democrat, and 97% of Democrats are more libearl than the median Republicans.

This is a nice statistical way of laying out the polarization. There are a number of additional insights one can draw from the population distributions: for example, in the bottom row, the Democrats have been moving left consistently, and decisively in 2017. By contrast, Republicans moved decisively to the right from 2004 to 2017. I recall reading about polarization in past elections but it is really shocking to see the extreme in 2017.

A really astounding but hidden feature is that the median Democrat and the median Republican were not too far apart in 1994 and 2004 but the gap exploded in 2017.

***

I like to solve a few minor problems on this graphic. It's a bit confusing to have each chart display information on both Republican and Democratic distributions. The reader has to understand that in the top row, the red area represents Republican voters but the blue line shows the median Democrat.

Also, I want to surface two key insights: the huge divide that developed in 2017, and the exploding gap between the two medians.

Here is the revised graphic:

On the left side, each chart focuses on one party, and the trend over the three elections. The reader can cross charts to discover that the median voter in one party is more extreme than essentially all of the voters of the other party. This same conclusion can be drawn from the exploding gap between the median voters in either party, which is explicitly plotted in the lower right chart. The top right chart is a pretty visualization of how polarized the country was in the 2017 election.

## Is this chart rotten?

##### Dec 19, 2016

Some students pointed me to a FiveThirtyEight article about Rotten Tomatoes scores that contain the following chart: (link to original)

This is a chart that makes my head spin. Too much is going on, and all the variables in the plot are tangled with each other. Even after looking at it for a while, I still don't understand how the author looked at the above and drew this conclusion:

"Movies that end up in the top tier miss a step ahead of their release, mediocre movies stumble, and the bottom tiers fall down an elevator shaft."

(Here is the article. It's a great concept but a bit disappointing analysis coming from Nate Silver's site. I have written features for them before so I know they ask good questions. Maybe they should apply the same level of rigor in editing feature writers to editing staff writers.)

## Egregious chart brings back bad memories

##### Nov 19, 2015

My friend Alberto Cairo said it best: if you see bullshit, say "bullshit!"

He was very incensed by this egregious "infographic": (link to his post)

Emily Schuch provided a re-visualization:

The new version provides a much richer story of how Planned Parenthood has shifted priorities over the last few years.

It also exposed what the AUL (American United for Life) organization distorted the story.

The designer extracted only two of the lines, thus readers do not see that the category of services that has really replaced the loss of cancer screening was STI/STD testing and treatment. This is a bit ironic given the other story that has circulated this week - the big jump in STD among Americans (link).

Then, the designer placed the two lines on dual axes, which is a dead giveaway that something awful lies beneath.

Further, this designer dumped the data from intervening years, and drew a straight line from the first to the last year. The straight arrow misleads by pretending that there has been a linear trend, and that it would go on forever.

But the masterstroke is in the treatment of the axes. Let's look at the axes, one at a time:

The horizontal axis: Let me recap. The designer dumped all but the starting and ending years, and drew a straight line between the endpoints. While the data are no longer there, the axis labels are retained. So, our attention is drawn to an area of the chart that is void of data.

The vertical axes: Let me recap. The designer has two series of data with the same units (number of people served) and decided to plot each series on a different scale with dual axes. But readers are not supposed to notice the scales, so they do not show up on the chart.

To summarize, where there are no data, we have a set of functionless labels; where labels are needed to differentiate the scales, we have no axes.

***

This is a tried-and-true tactic employed by propagandists. The egregious chart brings back some bad memories.

Here is a long-ago post on dual axes.

Here is Thomas Friedman's use of the same trick.

## Reimagining the league table

##### Aug 17, 2015

The reason for the infrequent posting is my travel schedule. I spent the past week in Seattle at JSM. This is an annual meeting of statisticians. I presented some work on fantasy football data that I started while writing Numbersense.

For my talk, I wanted to present the ubiquitous league table in a more useful way. The league table is a table of results and relevant statistics, at the team level, in a given sports league, usually ordered by the current winning percentage. Here is an example of ESPN's presentation of the NFL end-of-season league table from 2014.

If you want to know weekly results, you have to scroll to each team's section, and look at this format:

For the graph that I envisioned for the talk,  I wanted to show the correlation between Points Scored and winning/losing. Needless to say, the existing format is not satisfactory. This format is especially poor if I want my readers to be able to compare across teams.

***

The graph that I ended up using is this one:

The teams are sorted by winning percentage. One thing should be pretty clear... the raw Points Scored are only weakly associated with winning percentage. Especially in the middle of the Points distribution, other factors are at play determining if the team wins or loses.

The overlapping dots present a bit of a challenge. I went through a few other drafts before settling on this.

The same chart but with colored dots, and a legend:

Only one line of dots per team instead of two, and also requiring a legend:

Jittering is a popular solution to separating co-located dots but the effect isn't very pleasing to my eye:

Small multiples is another frequently prescribed solution. Here I separated the Wins and Losses in side-by-side panels. The legend can be removed.

As usual, sketching is one of the most important skills in data visualization; and you'd want to have a tool that makes sketching painless and quick.