Using disaggregation in dataviz

This chart appears in a journal article on the use of AI (artificial intelligence) in healthcare (link).

It's a stacked bar chart in which each bar is subdivided into four segments. The authors are interested in the relative frequency of research using AI by disease type. The chart only shows the top 10 disease types.

What is unusual is that the subdivisions are years. So these authors revealed four years of journal articles, and while the overall ranking of the disease types is by the aggregated four-year total counts, each total count has been disaggregated by color so readers can also see the annual counts.

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A slight rearrangement yields the following:

Most readers will only care about the left chart showing the total counts. More invested readers may consider the colored charts that show annual totals. These are arranged so that the annual counts are easily read and compared.

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One annoying aspect of this type of presentation is that in almost all cases, the top 10 types in aggregate will not be the top 10 types by individual year. In some of those years, I expect that the 10 types shown do not include all of the top 10 types for a particular year.

Pie charts and self-sufficiency

This graphic shows up in a recent issue of Princeton alumni magazine, which has a series of pie charts.

The story being depicted is clear: the school has been generously increasing the amount of financial aid given to students since 1998. The proportion receiving any aid went from 43% to 67% so about two out of three students who enrolled in 2023 are getting aid.

The key components of the story are the values in 1998 and 2023, and the growth trend over this period.

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Here is an exercise worth doing. Think about how you figured out the story components.

Is it this?

Or is it this?

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This is what I've been calling a "self-sufficiency test" (link). How much work are the visual elements doing in conveying the graph's message to you? If the visual elements aren't doing much, then the designer hasn't taken advantage of the visual medium.

Expert handling of multiple dimensions of data

I enjoyed reading this Washington Post article about immigration in America. It features a number of graphics. Here's one graphic I particularly like:

This is a small multiples of six maps, showing the spatial distribution of immigrants from different countries. The maps reveal some interesting patterns: Los Angeles is a big favorite of Guatamalans while Houston is preferred by Hondurans. Venezuelans like Salt Lake City and Denver (where there are also some Colombians and Mexicans). The breadth of the spatial distribution surprises me.

The dataset behind this graphic is complex. It's got country of origin, place of settlement, and time of arrival. The maps above collapsed the time dimension, while drawing attention to the other two dimensions.

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They have another set of charts that highlight the time dimension while collapsing the place of settlement dimension. Here's one view of it:

There are various names for this chart form. Stream river is one. I like to call it "inkblot", where the two sides are symmetric around the middle vertical line. The chart shows that "migrants in the U.S. immigration court" system have grown substantially since the end of the Covid-19 pandemic, during which they stopped coming.

I'm not a fan of the inkblot. One reason is visible in the following view, which showcases three Central American countries.

The main message is clear enough. The volume of immigrants from these three countries have been relatively stable over the last decade, with a bulge in the late 2000s. The recent spurt in migrants have come from other places.

But try figuring out what proportion of total immigration is accounted for by these three countries say in 2024. It's a task that is tougher than it should be, and the culprit is that the "other countries" category has been split in half with the two halves separated.

 

The radial is still broken

It's puzzling to me why people like radial charts. Here is a recent set of radial charts that appear in an article in Significance magazine (link to paywall, currently), analyzing NBA basketball data.

This example is not as bad as usual (the color scheme notwithstanding) because the story is quite simple.

The analysts divided the data into three time periods: 1980-94, 1995-15, 2016-23. The NBA seasons were summarized using a battery of 15 metrics arranged in a circle. In the first period, all but 3 of the metrics sat much above the average level (indicated by the inner circle). In the second period, all 15 metrics reduced below the average, and the third period is somewhat of a mirror image of the first, which is the main message.

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The puzzle: why prefer this circular arrangement to a rectangular arrangement?

Here is what the same graph looks like in a rectangular arrangement:

One plausible justification for the circular arrangement is if the metrics can be clustered so that nearby metrics are semantically related.

Nevertheless, the same semantics appear in a rectangular arrangement. For example, P3-P3A are three point scores and attempts while P2-P2A are two-pointers. That is a key trend. They are neighborhoods in this arrangement just as they are in the circular arrangement.

So the real advantage is when the metrics have some kind of periodicity, and the wraparound point matters. Or, that the data are indexed to directions so north, east, south, west are meaningful concepts.

If you've found other use cases, feel free to comment below.

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I can't end this post without returning to the colors. If one can take a negative image of the original chart, one should. Notice that the colors that dominate our attention - the yellow background, and the black lines - have no data in them: yellow being the canvass, and black being the gridlines. The data are found in the white polygons.

The other informative element, as one learns from the caption, is the "blue dashed line" that represents the value zero (i.e. average) in the standardized scale. Because the size of the image was small in the print magazine that I was reading, and they selected a dark blue encroaching on black, I had to squint hard to find the blue line.

 

 

Aligning V and Q by way of D

In the Trifecta Checkup (link), there is a green arrow between the Q (question) and V (visual) corners, indicating that they should align. This post illustrates what I mean by that.

I saw the following chart in a Washington Post article comparing dairy milk and plant-based "milks".

The article contains a whole series of charts. The one shown here focuses on vitamins.

The red color screams at the reader. At first, it appears to suggest that dairy milk is a standout on all four categories of vitamins. But that's not what the data say.

Let's take a look at the chart form: it's a grid of four plots, each containing one square for each of four types of "milk". The data are encoded in the areas of the squares. The red and green colors represent category labels and do not reflect data values.

Whenever we make bubble plots (the closest relative of these square plots), we have to solve a scale problem. What is the relationship between the scales of the four plots?

I noticed the largest square is the same size across all four plots. So, the size of each square is made relative to the maximum value in each plot, which is assigned a fixed size. In effect, the data encoding scheme is that the areas of the squares show the index values relative to the group maximum of each vitamin category. So, soy milk has 72% as much potassium as dairy milk while oat and almond milks have roughly 45% as much as dairy.

The same encoding scheme is applied also to riboflavin. Oat milk has the most riboflavin, so its square is the largest. Soy milk is 80% of oat, while dairy has 60% of oat.

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Let's step back to the Trifecta Checkup (link). What's the question being asked in this chart? We're interested in the amount of vitamins found in plant-based milk relative to dairy milk. We're less interested in which type of "milk" has the highest amount of a particular vitamin.

Thus, I'd prefer the indexing tied to the amount found in dairy milk, rather than the maximum value in each category. The following set of column charts show this encoding:

I changed the color coding so that blue columns represent higher amounts than dairy while yellow represent lower.

From the column chart, we find that plant-based "milks" contain significantly less potassium and phosphorus than dairy milk while oat and soy "milks" contain more riboflavin than dairy. Almond "milk" has negligible amounts of riboflavin and phosphorus. There is vritually no difference between the four "milk" types in providing vitamin D.

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In the above redo, I strengthen the alignment of the Q and V corners. This is accomplished by making a stop at the D corner: I change how the raw data are transformed into index values. 

Just for comparison, if I only change the indexing strategy but retain the square plot chart form, the revised chart looks like this:

The four squares showing dairy on this version have the same size. Readers can evaluate the relative sizes of the other "milk" types.

Lost in the middle class

Washington Post asks people what it means to be middle class in the U.S. (link; paywall)

The following graphic illustrates one type of definition, purely based on income ranges.

For me, this chart is more taxing to read than it appears.

It can be read column by column. Each column represents a hypotheticial annual income for a family of four. People are asked whether they consider that family lower/working class, middle class or upper class. Be careful as the increments from column to column are not uniform.

Now, what's the question again? We're primarily interested in what incomes constitute middle class.

So, we should be looking at the deep green blocks that hang in the middle of each column. It's not easy to read the proportion of middle blocks in a stacked column chart.

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I tried separating out the three perceived income classes, using a small-multiples design.

One can more directly see what income ranges are most popularly perceived as being in each income class.

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The article also goes into alternative definitions of middle class, using more qualitative metrics, such as "able to pay all bills on time without worry". That's a whole other post.

 

The cult of raw unadjusted data

Long-time reader Aleks came across the following chart on Facebook:

The author attached a message: "Let's look at raw, unadjusted temperature data from remote US thermometers. What story do they tell?"

I suppose this post came from a climate change skeptic, and the story we're expected to take away from the chart is that there is nothing to see here.

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What are we looking at, really?

"Nothing to see" probably refers to the patch of blue squares that cover the entire plot area, as time runs left to right from the 1910s to the present.

But we can't really see what's going on in the middle of the patch. So, "nothing to see" is effectively only about the top-to-bottom range of roughly 29.8 to 82.0. What does that range signify?

The blue patch is subdivided into vertical lines consisting of blue squares. Each line is a year's worth of temperature measurements. Each square is the average temperature on a specific day. The vertical range is the difference between the maximum and minimum daily temperatures in a given year. These are extreme values that say almost nothing about the temperatures in the other ~363 days of the year.

We know quite a bit more about the density of squares along each vertical line. They are broken up roughly by seasons. Those values near the top came from summers while the values near the bottom came from winters. The density is the highest near the middle, where the overplotting is so severe that we can barely see anything.

Within each vertical line, the data are not ordered chronologically. This is a very key observation. From left to right, the data are ordered from earliest to latest but not from top to bottom! Therefore, it is impossible for the human eye to trace the entire trajectory of the daily temperature readings from this chart. At best, you can trace the yearly average temperature – but only extremely roughly by eyeballing where the annual averages are inside the blue patch.

Indeed, there is "nothing to see" on this chart because its design has pulverized the data.

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In Numbersense (link), I wrote "not adjusting the raw data is to knowingly publish bad information. It is analogous to a restaurant's chef knowingly sending out spoilt fish."

It's a fallacy to think that "raw unadjusted" data are the best kind of data. It's actually the opposite. Adjustments are designed to correct biases or other problems in the data. Of course, adjustments can be subverted to introduce biases in the data as well. It is subversive to presume that all adjustments are of the subversive kind.

What kinds of adjustments are of interest in this temperature dataset?

Foremost is the seasonal adjustment. See my old post here. If we want to learn whether temperatures have risen over these decades, we can't do so without separating out the seasons.

The whole dataset can be simplified by drawing the smoothed annual average temperature grouped by season of the year, and when that is done, the trend of rising temperatures is obvious.

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The following chart by the EPA roughly implements the above:

The original can be found here. They made one adjustment which isn't the one I expected.

Note the vertical scale is titled "temperature anomaly". So, they are not plotting the actual recorded average temperatures, but the "anomalies", i.e. the difference between the recorded temperatures and some kind of "expected" temperature. This is a type of data adjustment as well. The purpose is to focus attention on the relative rather than absolute values. Think of this formula: recorded value = expected value + anomaly. The chart shows how many degrees above or below expectation, rather than how many degrees.

For a chart like this, there should be a required footnote that defines what "anomaly" is. Specifically, the reader should know about the model behind the "expectation". Typically, it's a kind of long-term average value.

For me, this adjustment is not necessary. Without the adjustment, the four panels can be combined into one panel with four lines. That's because the data nicely fit into four levels based on seasons.

The further adjustment I'd have liked to see is "smoothing". Each line above has a "smooth" trend, as well as some variability around this trend. The latter is not a big part of the story.

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It's weird to push back on climate change advocacy by attacking data adjustments. The more productive direction, in my view, is to ask whether the observed trend is caused by human activities or part of some long-term up-and-down cycle. That is a very challenging question to answer.

Messing with expectations

A co-worker sent me to the following map, found in Forbes:

It shows the amount of state tax surcharge per gallon of gas in the U.S. And it's got one of the most common issues found in choropleth maps - the color scheme runs opposite to reader expectations.

Typically, if we see a red-green color scale, we would expect red to represent large numbers and green, small numbers. This map reverses the typical setup: California, the state with the heftiest gas tax, is shown green.

I know, I know - if we apply the typical color scheme, California would bleed red, and it's a blue state, damn it.

The solution is to avoid the red color. Just don't use red or blue.

There is no need to use two colors either.

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A few minor fixes. Given that all dollar amounts on the map are shown to two decimal places, the legend labels should also be shown to 2 decimal places, and with dollar signs.

The subtitle should read "Dollars per gallon" instead of "Cents per gallon". Alternatively, keep "Cents per gallon" but convert all data labels into cents.

Some of the states are missing data labels.

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I recast this as a small-multiples by categorizing states into four subgroups.

With this change, one can almost justify using maps because there is sort of a spatial pattern.

 

 

The choice to encode data using colors

NBC News published the following heatmap that shows inflation by product category in the last year or so:

The general story might be that inflation was rampant in airfare and electricity prices about a year ago but these prices have moderated recently, especially in airfare. Gas prices appear to have inflated far less than overall inflation during these months.

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Now, if you're someone who cares about the magnitude of differences, not just the direction, then revisit the above statements, and you'll feel a sense of inadequacy.

When we choose to encode data in colors, we're giving up on showing magnitudes or precision. The color scale shown up top sends the message that the continuous nature of the number line is being displayed but it really isn't.

The largest value of the chart is found on the left side of the airfare row:

The value is about 36% which strangely enough is far larger than the maximum value shown in the legend above. Even if those values align, it is still impossible to guess what values the different colors and shades in the cells map to from the legend.

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The following small-multiples chart shows the underlying values more precisely:

I have transformed the data differently. In these line charts, the data are indexed to the first month (100) so each chart shows the cumulative change in prices from that month to the current month, for each category, compared to the overall.

The two most interesting categories are airfare and gas. Airfare has recently decreased quite drastically relative to September 2022, and thus the line is far below the overall inflation trend. Gas prices moved in reverse: they dropped in the last quarter of 2022 but have steadily risen over 2023, and in the most recent month, is tracking overall inflation.

 

 

Dataviz in camouflage

This subway timetable in Tokyo caught my eye:

It lists the departure times of all trains going toward Shibuya on Saturdays and holidays.

It's a "stem and leaf" plot.

The stem-and-leaf plot is a crude histogram. In this version, the stem is the hour of the day (24-hour clock) and the leaf is the minute (between 0 and 59). The longer the leaf, the higher the frequency of trains.

We can see that there isn't one peak but rather a plateau between hours 9 and 18.

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Contrast this with the weekday schedule in blue:

We can clearly see two rush hours, one peak at hour 8 and a second one at hours 17-18.

Love seeing dataviz in camouflage!