Two metrics in-fighting

The Wall Street Journal shows the following chart which pits two metrics against each other:

The primary metric is the change in median yearly salary between the two periods of time. We presume it's primary because of its presence in the chart title, and the blue bars being more readable than the green bubbles. The secondary metric is the median yearly salary in the later period.

That, I believe, was the intended design. When I saw this chart, my eyes went to the numbers inside the green bubbles. Perhaps it's because I didn't read the chart title first, and the horizontal axis wasn't labelled so it wasn't obvious what the blue bars coded.

As with most bubble charts, the data labels exist to cover up the inadequacy of circular areas. The self-sufficiency test - removing the data labels - shows this well:

It's simply impossible to know what values should be in each bubble, or to perceive the relative sizes of those bubbles.

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Reversing the order of the blue bars also helps:

The original order is one of the more annoying features in most visualization packages. Because internally, the categories are numbered 1, 2, 3, ..., and because the convention is to have values run higher as they run up the vertical axis, these packages would place the top-ranked item at the bottom of the chart.

Most people read top to bottom, which means that they read the least important item first, and the most important item last!

In most visualization packages, it takes only 1 click or 1 action to reverse the order of the items. Please do it!

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For change over time, I like using a Bumps chart, otherwise called a slope graph:

Some chart designs bring out more information than others

I forgot where I found this chart but here it is:

The designer realizes the flaw of the design, which is why the number 50 is placed in a red box, and there is another big red box  placed right in our faces telling us that any number above 50 represents growing, while all below 50 shrinking.

The real culprit is the column chart design, which treats zero as the baseline, not 50. Thus, the real solution is to move away from a column chart design.

There are many possibilities. Here's one using the Bumps chart form:

There are several interesting insights buried in that column chart!

First we learn that almost all segments were contracting in both years.

Next, there are some clustering of segments. The Premium Regular and Cider segments were moving in sync. Craft, FMB/SEltzer and Below Premium were similar in 2022; intriguingly, Below Premium diverged from the other two segments.

In fact, Below Premium has distinguished itself as the only segment that experienced an improved index relative to 2022!

 

 

 

 

All about Connecticut

This dataviz project by CT Mirror is excellent. The project walks through key statistics of the state of Connecticut.

Here are a few charts I enjoyed.

The first one shows the industries employing the most CT residents. The left and right arrows are perfect, much better than the usual dot plots.

The industries are sorted by decreasing size from top to bottom, based on employment in 2019. The chosen scale is absolute, showing the number of employees. The relative change is shown next to the arrow heads in percentages.

The inclusion of both absolute and relative scales may be a source of confusion as the lengths of the arrows encode the absolute differences, not the relative differences indicated by the data labels. This type of decision is always difficult for the designer. Selecting one of the two scales may improve clarity but induce loss aversion.

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The next example is a bumps chart showing the growth in residents with at least a bachelor's degree.

This is more like a slopegraph as it appears to draw straight lines between two time points 9 years apart, omitting the intervening years. Each line represents a state. Connecticut's line is shown in red. The message is clear. Connecticut is among the most highly educated out of the 50 states. It maintained this advantage throughout the period.

I'd prefer to use solid lines for the background states, and the axis labels can be sparser.

It's a little odd that pretty much every line has the same slope. I'm suspecting that the numbers came out of a regression model, with varying slopes by state, but the inter-state variance is low.

In the online presentation, one can click on each line to see the values.

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The final example is a two-sided bar chart:

This shows migration in and out of the state. The red bars represent the number of people who moved out, while the green bars represent those who moved into the state. The states are arranged from the most number of in-migrants to the least.

I have clipped the bottom of the chart as it extends to 50 states, and the bottom half is barely visible since the absolute numbers are so small.

I'd suggest showing the top 10 states. Then group the rest of the states by region, and plot them as regions. This change makes the chart more compact, as well as more useful.

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There are many other charts, and I encourage you to visit and support this data journalism.

 

 

 

Two uses of bumps charts

Long-time reader Antonio R. submitted the following chart, which illustrates analysis from a preprint on the effect of Covid-19 on life expectancy in the U.S. (link)

For this post, I want to discuss the bumps chart on the lower right corner. Bumps charts are great at showing change over time. In this case, the authors are comparing two periods "2010-2019" and "2019-2020". By glancing at the chart, one quickly divides the causes of death into three groups: (a) COVID-19 and CVD, which experienced a big decline (b) respiratory, accidents, others ("rest"), and despair, which experienced increases, and (c) cancer and infectious, which remained the same.

And yet, something doesn't seem right.

What isn't clear is the measured quantity. The chart title says "months gained or lost" but it takes a moment to realize the plotted data are not number of months but ranks of the effects of the causes of deaths on life expectancy.

Observe that the distance between each cause of death is the same. Look at the first rising line (respiratory): the actual values went from 0.8 months down to 0.2.

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While the canonical bumps chart plots ranks, the same chart form can be used to show numeric data. I prefer to use the same term for both charts. In recent years, the bumps chart showing numeric data has been called "slopegraph".

Here is a side-by-side comparison of the two charts:

The one on the left is the same as the original. The one on the right plots the number of months increased or decreased.

The choice of chart form paints very different pictures. There are four blue lines on the left, indicating a relative increase in life expectancy - these causes of death contributed more to life expectancy between the two periods. Three of the four are red lines on the right chart. Cancer was shown as a flat line on the left - because it was the highest ranked item in both periods. The right chart shows that the numeric value for cancer suffered one of the largest drops.

The left chart exaggerates small numeric changes while it condenses large numeric changes.

 

 

Plotting the signal or the noise

Antonio alerted me to the following graphic that appeared in the Economist. This is a playful (?) attempt to draw attention to racism in the game of football (soccer).

The analyst proposed that non-white players have played better in stadiums without fans due to Covid19 in 2020 because they have not been distracted by racist abuse from fans, using Italy's Serie A as the case study.

The chart struggles to bring out this finding. There are many lines that criss-cross. The conclusion is primarily based on the two thick lines - which show the average performance with and without fans of white and non-white players. The blue line (non-white) inched to the right (better performance) while the red line (white) shifted slightly to the left.

If the reader wants to understand the chart fully, there's a lot to take in. All (presumably) players are ranked by the performance score from lowest to highest into ten equally sized tiers (known as "deciles"). They are sorted by the 2019 performance when fans were in the stadiums. Each tier is represented by the average performance score of its members. These are the values shown on the top axis labeled "with fans".

Then, with the tiers fixed, the players are rated in 2020 when stadiums were empty. For each tier, an average 2020 performance score is computed, and compared to the 2019 performance score.

The following chart reveals the structure of the data:

The players are lined up from left to right, from the worst performers to the best. Each decile is one tenth of the players, and is represented by the average score within the tier. The vertical axis is the actual score while the horizontal axis is a relative ranking - so we expect a positive correlation.

The blue line shows the 2019 (with fans) data, which are used to determine tier membership. The gray dotted line is the 2020 (no fans) data - because they don't decide the ranking, it's possible that the average score of a lower tier (e.g. tier 3 for non-whites) is higher than the average score of a higher tier (e.g. tier 4 for non-whites).

What do we learn from the graphic?

It's very hard to know if the blue and gray lines are different by chance or by whether fans were in the stadium. The maximum gap between the lines is not quite 0.2 on the raw score scale, which is roughly a one-decile shift. It'd be interesting to know the variability of the score of a given player across say 5 seasons prior to 2019. I suspect it could be more than 0.2. In any case, the tiny shifts in the averages (around 0.05) can't be distinguished from noise.

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This type of analysis is tough to do. Like other observational studies, there are multiple problems of biases and confounding. Fan attendance was not the only thing that changed between 2019 and 2020. The score used to rank players is a "Fantacalcio algorithmic match-level fantasy-football score." It's odd that real-life players should be judged by their fantasy scores rather than their on-the-field performance.

The causal model appears to assume that every non-white player gets racially abused. At least, the analyst didn't look at the curves above and conclude, post-hoc, that players in the third decile are most affected by racial abuse - which is exactly what has happened with the observational studies I have featured on the book blog recently.

Being a Serie A fan, I happen to know non-white players are a small minority so the error bars are wider, which is another issue to think about. I wonder if this factor by itself explains the shifts in those curves. The curve for white players has a much higher sample size thus season-to-season fluctuations are much smaller (regardless of fans or no fans).

 

 

 

 

Visualizing change over time: case study via Arstechnica

ArsTechnica published the following chart in its article titled "Grim new analyses spotlight just how hard the U.S. is failing in  pandemic" (link).

There are some very good things about this chart, so let me start there.

In a Trifecta Checkup, I'd give the Q corner high marks. The question is clear: how has the U.S. performed relative to other countries? In particular, the chart gives a nuanced answer to this question. The designer realizes that there are phases in the pandemic, so the same question is asked three times: how has the U.S. performed relative to other countries since June, since May, and since the start of the pandemic?

In the D corner, this chart also deserves a high score. It selects a reasonable measure of mortality, which is deaths per population. It simplifies cognition by creating three grades of mortality rates per 100,000. Grade A is below 5 deaths, Grade B, between 5 and 25, and Grade C is above 25. 

A small deduction for not including the source of the data (the article states it's from a JAMA article). If any reader notices problems with the underlying data or calculations, please leave a comment.

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So far so good. And yet, you might feel like I'm over-praising a chart that feels distinctly average. Not terrible, not great.

The reason for our ambivalence is the V corner. This is what I call a Type V chart. The visual design isn't doing justice to the underlying question and data analysis.

The grouped bar chart isn't effective here because the orange bars dominate our vision. It's easy to see how each country performed over the course of the pandemic but it's hard to learn how countries compare to each other in different periods.

How are the countries ordered? It would seem like the orange bars may be the sorting variable but this interpretation fails in the third group of countries.

The designer apparently made the decision to place the U.S. at the bottom (i.e. the worst of the league table). As I will show later, this is justified but the argument cannot be justified by the orange bars alone. The U.S. is worse in both the blue and purple bars but not the orange.

This points out that there is interest in the change in rates (or ranks) over time. And in the following makeover, I used the Bumps chart as the basis, as its chief use is in showing how ranking changes over time.

 

Better clarity can often be gained by subtraction:

Working with multiple dimensions, an example from Germany

An anonymous reader submitted this mirrored bar chart about violent acts by extremists in the 16 German states.

At first glance, this looks like a standard design. On a second look, you might notice what the reader discovered- the chart used two different scales, one for each side. The left side (red) depicting left-wing extremism is artificially compressed relative to the right side (blue). Not sure if this reflects the political bias of the publication - but in any case, this distortion means the only way to consume this chart is to read the numbers.

Even after fixing the scales, this design is challenging for the reader. It's unnatural to compare two years by looking first below then above. It's not simple to compare across states, and even harder to compare left- and right-wing extremism (due to mirroring).

The chart feels busy because the entire dataset is printed on it. I appreciate not including a redundant horizontal axis. (I wonder if the designer first removed the axis, then edited the scale on one side, not realizing the distortion.) Another nice touch, hidden in the legend, is the country totals.

I present two alternatives.

The first is a small-multiples "bumps chart".

Each plot presents the entire picture within a state. You can see the general level of violence, the level of left- and right-wing extremism, and their year-on-year change. States can be compared holistically.

Several German state names are rather long, so I explored a horizontal orientation. In this case, a connected dot plot may be more appropriate.

The sign of a good multi-dimensional visual display is whether readers can easily learn complex relationships. Depending on the question of interest, the reader can mentally elevate parts of this chart. One can compare the set of blue arrows to the set of red arrows, or focus on just blue arrows pointing right, or red arrows pointing left, or all arrows for Berlin, etc.

 

[P.S. Anonymous reader said the original chart came from the Augsburger newspaper. This link in German contains more information.]

When the pie chart is more complex than the data

The trading house, Charles Schwab, included the following graphic in a recent article:

This graphic is more complicated than the story that it illustrates. The author describes a simple scenario in which an investor divides his investments into stocks, bonds and cash. After a stock crash, the value of the portfolio declines.

The graphic is a 3-D pie chart, in which the data are encoded twice, first in the areas of the sectors and then in the heights of the part-cylinders.

As readers, we perceive the relative volumes of the part-cylinders. Volume is the cross-sectional area (i.e. of the base) multipled by the height. Since each component holds the data, the volumes are proportional to the squares of the data.

Here is a different view of the same data:

This "bumps chart" (also called a slopegraph) shows clearly the only thing that drives the change is the drop in stock prices. Because the author assumes no change in bonds or cash, the drop in the entire portfolio is completely accounted for by the decline in stocks. Of course, this scenario seems patently unrealistic - different investment asset classes tend to be correlated.

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A cardinal rule of data visualization is that the visual should be less complex than the data.

Graph literacy, in a sense

Ben Jones tweeted out this chart, which has an unusual feature:

What's unusual is that time runs in both directions. Usually, the rule is that time runs left to right (except, of course, in right-to-left cultures). Here, the purple area chart follows that convention while the yellow area chart inverts it.

On the one hand, this is quite cute. Lines meeting in the middle. Converging. I get it.

On the other hand, every time a designer defies conventions, the reader has to recognize it, and to rationalize it.

In this particular graphic, I'm not convinced. There are four numbers only. The trend on either side looks linear so the story is simple. Why complicate it using unusual visual design?

Here is an entirely conventional bumps-like chart that tells the story:

I've done a couple of things here that might be considered controversial.

First, I completely straightened out the lines. I don't see what additional precision is bringing to the chart.

Second, despite having just four numbers, I added the year 1996 and vertical gridlines indicating decades. A Tufte purist will surely object.

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Related blog post: "The Return on Effort in Data Graphics" (link)

The Bumps come to the NBA, courtesy of 538

The team at 538 did a post-mortem of their in-season forecasts of NBA playoffs, using Bumps charts. These charts have a long history and can be traced back to Cambridge rowing. I featured them in these posts from a long time ago (link 1, link 2). 

Here is the Bumps chart for the NBA West Conference showing all 15 teams, and their ranking by the 538 model throughout the season. 

The highlighted team is the Kings. It's a story of ascent especially in the second half of the season. It's also a story of close but no cigar. It knocked at the door for the last five weeks but failed to grab the last spot. The beauty of the Bumps chart is how easy it is to see this story.

Now, if you'd focus on the dotted line labeled "Makes playoffs," and note that beyond the half-way point (1/31), there are no further crossings. This means that the 538 model by that point has selected the eight playoff teams accurately.

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Now what about NBA East?

This chart highlights the two top teams. This conference is pretty easy to predict at the top. 

What is interesting is the spaghetti around the playoff line. The playoff race was heart-stopping and it wasn't until the last couple of weeks that the teams were settled. 

Also worthy of attention are the bottom-dwellers. Note that the chart is disconnected in the last four rows (ranks 12 to 15). These four teams did not ever leave the cellar, and the model figured out the final rankings around February.

Using a similar analysis, you can see that the model found the top 5 teams by mid December in this Conference, as there are no further crossings beyond that point. 

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Go check out the FiveThirtyEight article for their interpretation of these charts. 

While you're there, read the article about when to leave the stadium if you'd like to leave a baseball game early, work that came out of my collaboration with Pravin and Sriram.