Ask how you can give

A reader and colleague Georgette A was frustrated with the following graphic that appeared in the otherwise commendable article in National Geographic (link). The NatGeo article provides a history lesson on past pandemics that killed millions.

What does the design want to convey to readers?

Our attention is drawn to the larger objects, the red triangle on the left or the green triangle on the right. Regarding the red triangle, we learn that the base is the duration of the pandemic while the height of the black bar represents the total deaths.

An immediate curiosity is why a green triangle is lodged in the middle of the red triangle. Answering this question requires figuring out the horizontal layout. Where we expect axis labels we find an unexpected series of numbers (0, 16, 48, 5, 2, 4, ...). These are durations that measure the widths of the triangular bases.

To solve this puzzle, imagine the chart with the triangles removed, leaving just the black columns. Now replace the durations with index numbers, 1 to 13, corresponding to the time order of the ending years of these epidemics. In other words, there is a time axis hidden behind the chart. [As Ken reminded me on Twitter, I forgot to mention that details of each pandemic are revealed by hovering over each triangle.]

This explains why the green triangle (Antonine Plague) is sitting inside the large red triangle (Plague of Justinian). The latter's duration is 3 times that of the former, and the Antonine Plague ended before the Plague of Justinian. In fact, the Antonine occurred during 165-180 while the Justinian happened during 541-588. The overlap is an invention of the design. To receive what the design gives, we have to think of time as a sequence, not of dates.

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Now, compare the first and second red triangles. Their black columns both encode 50 million deaths. The Justinian Plague however was spread out over 48 years while the Black Death lasted just 5 years. This suggests that the Black Death was more fearsome than the Justinian Plague. And yet, the graphic presents the opposite imagery.

This is a pretty tough dataset to visualize. Here is a side-by-side bar chart that lets readers first compare deaths, and then compare durations.

In the meantime, I highly recommend the NatGeo article.

How many details to include in a chart

This graphic by Bloomberg provides the context for understanding the severity of the Atlantic storm season. (link)

At this point of the season, 2020 appears to be one of the most severe in history.

I was momentarily fascinated by a feature of modern browser-based data visualization: the death of the aspect ratio. When the browser window is stretched sufficiently wide, the chart above is transformed to this look:

The chart designer has lost control of the aspect ratio.

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This Bloomberg chart is an example of the spaghetti-style plots that convey variability by displaying individual units of data (here, storm years). The envelope of the growth curves gives the range of historical counts while the density of curves roughly offers some sense of the most likely counts at different points of the season.

But these spaghetti-style plots are not precise at conveying the variability because the density is hard to gauge. That's where aggregating the individual units helps.

The following chart does not show individual storm years. It shows the counts for the median season at selected points in time, and also a band of variability (for example, you'd include say 90 or 95% of the seasons).

I don't have the raw data so the aggregating is done by eyeballing the spaghetti.

I prefer this presentation even though it does not plot every single data point one has in the dataset.

 

 

Everything in Texas is big, but not this BIG

Long-time reader John forwarded the following chart via Twitter.

The chart shows the recent explosive growth in deaths due to Covid-19 in Texas. John flagged this graphic as yet another example in which the data are encoded to the lengths of the squares, not their areas.

Fixing this chart just requires fixing the length of one side of the square. I also flipped it to make a conventional column chart.

The final product:

An important qualification lurks in the footnote; it is directly applied to the label of July.

How much visual distortion is created when data are encoded to the lengths and not the areas? The following chart shows what readers see, assuming they correctly perceive the areas of those squares. The value for March is held the same as above while the other months show the death counts implied by the relative areas of the squares.

Owing to squaring, the smaller counts are artificially compressed while the big numbers are massively exaggerated.

On data volume, reliability, uncertainty and confidence bands

This chart from the Economist caught my eye because of the unusual use of color-coded hexagonal tiles.

The basic design of the chart is easy to grasp: It relates people's "happiness" to national wealth. The thick black line shows that the average citizen of wealthier countries tends to rate their current life situation better.

For readers alert to graphical details, things can get a little confusing. The horizontal "wealth" axis is shown in log scale, which means that the data on the right side of the chart have been compressed while the data on the left side of the chart have been stretched out. In other words, the curve in linear scale is much flatter than depicted.

One thing you might notice is how poor the fit of the line is at both ends. Singapore and Afghanistan are clearly not explained by the fitted line. (That said, the line is based on many more dots than those eight we can see.) Moreover, because countries are widely spread out on the high end of the wealth axis, the fit is not impressive. Log scales tend to give a false impression of the tightness of fit, as I explained before when discussing coronavirus case curves.

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The hexagonal tiles replace the more typical dot scatter or contour shading. The raw data consist of results from polls conducted in different countries in different years. For each poll, the analyst computes the average life satisfaction score for that country in that year. From national statistics, the analyst pulls out that country's GDP per capita in that year. Thus, each data point is a dot on the canvass. A few data points are shown as black dots. Those are for eight highlighted countries for the year 2018.

The black line is fitted to the underlying dot scatter and summarizes the correlation between average wealth and average life satisfaction. Instead of showing the scatter, this Economist design aggregates nearby dots into hexagons. The deepest red hexagon, sandwiched between Finland and the US, contains about 60-70 dots, according to the color legend.

These details are tough to take in. It's not clear which dots have been collected into that hexagon: are they all Finland or the U.S. in various years, or do they include other countries? Each country is represented by multiple dots, one for each poll year. It's also not clear how much variation there exists within a country across years.

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The hexagonal tiles presumably serve the same role as a dot scatter or contour shading. They convey the amount of data supporting the fitted curve along its trajectory. More data confers more reliability.

For this chart, the hexagonal tiles do not add any value. The deepest red regions are those closest to the black line so nothing is actually lost by showing just the line and not the tiles.

Using the line chart obviates the need for readers to figure out the hexagons, the polls, the aggregation, and the inevitable unanswered questions.

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An alternative concept is to show the "confidence band" or "error bar" around the black line. These bars display the uncertainty of the data. The wider the band, the less certain the analyst is of the estimate. Typically, the band expands near the edges where we have less data.

Here is conceptually what we should see (I don't have the underlying dataset so can't compute the confidence band precisely)

The confidence band picture is the mirror image of the hexagonal tiles. Where the poll density is high, the confidence band narrows, and where poll density is low, the band expands.

A simple way to interpret the confidence band is to find the country's wealth on the horizontal axis, and look at the range of life satisfaction rating for that value of wealth. Now pick any number between the range, and imagine that you've just conducted a survey and computed the average rating. That number you picked is a possible survey result, and thus a valid value. (For those who know some probability, you should pick a number not at random within the range but in accordance with a Bell curve, meaning picking a number closer to the fitted line with much higher probability than a number at either edge.)

Visualizing data involves a series of choices. For this dataset, one such choice is displaying data density or uncertainty or neither.