Aligning the visual and the message

Today's post is about work by Diane Barnhart, who is a product manager at Bloomberg, and is taking Ray Vella's infographics class at NYU. The class is given a chart from the Economist, as well as some data on GDP per capita in selected countries at the regional level. The students are asked to produce data visualization that explores the change in income inequality (as indicated by GDP per capita).

Here is Diane's work:

In this chart, the key measure is the GDP per capita of different regions in Germany relative to the national average GDP. Hamburg, for example, has a GDP per capita that was 80% above the national average in 2000 while Leipzig's GDP per capita was 30% below the national average in 2000. (This metric is a bit of a head scratcher, and forms the basis of the Economist chart.)

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Diane made several insightful design choices.

The key insight of this graph is also one of the easiest to see. It's the narrowing of the range of possible values. In 2000, the top value is about 90% while the bottom is under -40%, making a range of 130%. In 2020, the range has narrowed to 90%, with the values falling between 60% and -30%. In other words, the gap between rich and poor regions in Germany has reduced over these two decades.

The chosen chart form makes this message come alive.

Diane divided the regions into three groups, mapped to the black, red and yellow colors of the German flag. Black are for those regions that have GDP per capita above the average; yellow for those regions with GDP per capita over 25% below the average.

Instead of applying color to individual lines that trace the GDP metric over time for each region, she divided the area between the lines into three, and painted them. This necessitates a definition of the boundary line between colored areas over time. I gathered that she classified the regions using the latest GDP data (2020) and then traced the GDP trend lines back in time. Other definitions are also possible.

The two-column data table shown on the right provides further details that aren't found in the data visualization. The table is nicely enhanced with colors. They represent an augmentation of the information in the main chart, not a repetition.

All in all, this is a delightful project, and worthy of a top grade!

Organizing time-stamped data

In a previous post, I looked at the Economist chart about Elon Musk's tweeting compulsion. It's chart that contains lots of data, every tweet included, but one can't tell the number or frequency of tweets.

In today's post, I'll walk through a couple of sketches of other charts. I was able to find a dataset on Github that does not cover the same period of time but it's good enough for illustration purposes.

As discussed previously, I took cues from the Economist chart, in particular that the hours of the day should be divided up into four equal-width periods. One thing Musk is known for is tweeting at any hour of the day.

This is a small-multiples arrangement of column charts. Each column chart represents the tweets that were posted during a six-hour window, across all days in the dataset. A column covers half a year of tweets. We note that there were more tweets in the afternoon hours as he started tweeting more. In the first half of 2022, he sent roughly 750 tweets between 7 pm and midnight.

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In this next sketch, I used a small-multiples of line charts. Each line chart represents tweets posted during a six-hour window, as before. Instead of counting how many tweets, here I "smoothed" the daily tweet count, so that each number is an average daily tweet count, with the average computed based on a rolling time window.

 

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Finally, let's cover a few details only people who make charts would care about. The time of day variable only makes sense if all times are expressed as "local time", i.e. the time at the location where Musk was tweeting from. This knowledge is not necessary to make a chart but it is essential to make the chart interpretable. A statement like Musk tweets a lot around midnight assumes that it was midnight where he was when he sent each tweet.

Since we don't have his travel schedule, we will definitely be wrong. In my charts, I assumed he is in the Pacific time zone, and never tweeted anywhere outside that time zone.

(Food for thought: the server that posts tweets certainly had the record of the time and time zone for each tweet. Typically, databases store these time stamps standardized to one time zone - call it Greenwich Mean Time. If you have all time stamps expressed in GMT, is it now possible to make a statement about midnight tweeting? Does standardizing to one time zone solve this problem?)

In addition, I suspect that there may be problems with the function used to compute those rolling sums and averages, so take the actual numbers on those sketches with a grain of salt. Specifically, it's hard to tell on any of these charts but Musk did not tweet every single day so there are lots of holes in the time series.

Don't show everything

There are many examples where one should not show everything when visualizing data.

A long-time reader sent me this chart from the Economist, published around Thanksgiving last year:

It's a scatter plot with each dot representing a single tweet by Elon Musk against a grid of years (on the horizontal axis) and time of day (on the vertical axis).

The easy messages to pick up include:

• the increase in frequency of tweets over the years
• especially, the jump in density after Musk bought Twitter in late 2022 (there is also a less obvious level up around 2018)
• the almost continuous tweeting throughout 24 hours.

By contrast, it's hard if not impossible to learn the following:

• how many tweets did he make on average or in total per year, per day, per hour?
• the density of tweets for any single period of time (i.e., a reference for everything else)
• the growth rate over time, especially the magnitude of the jumps

The paradox: a chart that is data-dense but information-poor.

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The designer added gridlines and axis labels to help structure our reading. Specifically, we're cued to separate the 24 hours into four 6-hour chunks. We're also expected to divide the years into two groups (pre- and post- the Musk acquisition), and secondarily, into one-year intervals.

If we accept this analytical frame, then we can divide time into these boxes, and then compute summary statistics within each box, and present those values.  I'm working on some concepts, will show them next time.

 

Ranking data provide context but can also confuse

This dataviz from the Economist had me spending a lot of time clicking around - which means it is a success.

The graphic presents four measures of wellbeing in society - life expectancy, infant mortality rate, murder rate and prison population. The primary goal is to compare nations across those metrics. The focus is on comparing how certain nations (or subgroups) rank against each other, as indicated by the relative vertical position.

The Economist staff has a particular story to tell about racial division in the US. The dotted bars represent the U.S. average. The colored bars are the averages for Hispanic, white and black Americans. The wider the gap between the colored bars, the more variant is the experiences between American races.

The chart shows that the racial gap of life expectancy is the widest. For prison population, the U.S. and its racial subgroups occupy many of the lowest (i.e. least desirable) ranks, with the smallest gap in ranking.

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The primary element of interactivity is hovering on a bar, which then highlights the four bars corresponding to the particular nation selected. Here is the picture for Thailand:

According to this view of the world, Thailand is a close cousin of the U.S. On each metric, the Thai value clings pretty near the U.S. average and sits within the range by racial groups. I'm surprised to learn that the prison population in Thailand is among the highest in the world.

Unfortunately, this chart form doesn't facilitate comparing Thailand to a country other than the U.S as one can highlight only one country at a time.

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While the main focus of the chart is on relative comparison through ranking, the reader can extract absolute difference by reading the lengths of the bars.

This is a close-up of the bottom of the prison population metric:

The length of each bar displays the numeric data. The red line is an outlier in this dataset. Black Americans suffer an incarceration rate that is almost three times the national average. Even white Americans (blue line) is imprisoned at a rate higher than most countries around the world.

As noted above, the prison population metric exhibits the smallest gap between racial subgroups. This chart is a great example of why ranking data frequently hide important information. The small gap in ranking masks the extraordinary absolute difference in incareration rates between white and black America.

The difference between rank #1 and rank #2 is enormous.

The opposite situation appears for life expectancy. The life expectancy values are bunched up especially at the top of the scale. The absolute difference between Hispanic and black America is 82 - 75 = 7 years, which looks small because the axis starts at zero. On a ranking scale, Hispanic is roughly in the top 15% while black America is just above the median. The relative difference is huge.

For life expectancy, ranking conveys the view that even a 7-year difference is a big deal because the countries are tightly bunched together. For prison population, ranking shows the view that a multiple fold difference is "unimportant" because a 20-0 blowout and a 10-0 blowout are both heavy defeats.

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Whenever you transform numeric data to ranks, remember that you are artificially treating the gap between each value and the next value as a constant, even when the underlying numeric gaps show wide variance.

 

 

 

 

 

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).

 

 

 

 

Reading this chart won't take as long as withdrawing troops from Afghanistan

Art sent me the following Economist chart, noting how hard it is to understand. I took a look, and agreed. It's an example of a visual representation that takes more time to comprehend than the underlying data.

The chart presents responses to 3 questions on a survey. For each question, the choices are Approve, Disapprove, and "Neither" (just picking a word since I haven't seen the actual survey question). The overall approval/disapproval rates are presented, and then broken into two subgroups (Democrats and Republicans).

The first hurdle is reading the scale. Because the section from 75% to 100% has been removed, we are left with labels 0, 25, 50, 75, which do not say percentages unless we've consumed the title and subtitle. The Economist style guide places the units of data in the subtitle instead of on
the axis itself.

Our attention is drawn to the thick lines, which represent the differences between approval and disapproval rates. These differences are signed: it matters whether the proportion approving is higher or lower than the proportion disapproving. This means the data are encoded in the order of the dots plus the length of the line segment between them.

The two bottom rows of the Afghanistan question demonstrates this mental challenge. Our brains have to process the following visual cues:

1) the two lines are about the same lengths

2) the Republican dots are shifted to the right by a little

3) the colors of the dots are flipped

What do they all mean?

A chart runs in trouble when you need a paragraph to explain how to read it.

It's sometimes alright to make complicated data visualization that illustrates complicated concepts. What justifies it is the payoff. I wrote about the concept of return on effort in data visualization here.

The payoff for this chart escaped me. Take the Democratic response to troop withdrawal. About 3/4 of Democrats approve while 15% disapprove. The thick line says 60% more Democrats approve than disapprove.

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Here, I show the full axis, and add a 50% reference line

Small edits but they help visualize "half of", "three quarters of".

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Next, I switch to the more conventional stacked bars.

This format reveals some of the hidden data on the chart - the proportion answering neither approve/disapprove, and neither yes/no.

On the stacked bars visual, the proportions are counted from both ends while in the dot plot above, the proportions are measured from the left end only.

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Read all my posts about Economist charts here

 

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.

This chart shows why the PR agency for the UK government deserves a Covid-19 bonus

The Economist illustrated some interesting consumer research with this chart (link):

The survey by Dalia Research asked people about the satisfaction with their country's response to the coronavirus crisis. The results are reduced to the "Top 2 Boxes", the proportion of people who rated their government response as "very well" or "somewhat well".

This dimension is laid out along the horizontal axis. The chart is a combo dot and bubble chart, arranged in rows by region of the world. Now what does the bubble size indicate?

It took me a while to find the legend as I was expecting it either in the header or the footer of the graphic. A larger bubble depicts a higher cumulative number of deaths up to June 15, 2020.

The key issue is the correlation between a country's death count and the people's evaluation of the government response.

Bivariate correlation is typically shown on a scatter plot. The following chart sets out the scatter plots in a small multiples format with each panel displaying a region of the world.

The death tolls in the Asian countries are low relative to the other regions, and yet the people's ratings vary widely. In particular, the Japanese people are pretty hard on their government.

In Europe, the people of Greece, Netherlands and Germany think highly of their government responses, which have suppressed deaths. The French, Spaniards and Italians are understandably unhappy. The British appears to be the most forgiving of their government, despite suffering a higher death toll than France, Spain or Italy. This speaks well of their PR operation.

Cumulative deaths should be adjusted by population size for a proper comparison across nations. When the same graphic is produced using deaths per million (shown on the right below), the general story is preserved while the pattern is clarified:

The right chart shows deaths per million while the left chart shows total deaths.

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In the original Economist chart, what catches our attention first is the bubble size. Eventually, we notice the horizontal positioning of these bubbles. But the star of this chart ought to be the new survey data. I swapped those variables and obtained the following graphic:

Instead of using bubble size, I switched to using color to illustrate the deaths-per-million metric. If ratings of the pandemic response correlate tightly with deaths per million, then we expect the color of these dots to evolve from blue on the left side to red on the right side.

The peculiar loss of correlation in the U.K. stands out. Their PR firm deserves a bonus!

Taking small steps to bring out the message

Happy new year! Good luck and best wishes!

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We'll start 2020 with something lighter. On a recent flight, I saw a chart in The Economist that shows the proportion of operating income derived from overseas markets by major grocery chains - the headline said that some of these chains are withdrawing from international markets.

The designer used one color for each grocery chain, and two shades within each color. The legend describes the shades as "total" and "of which: overseas". As with all stacked bar charts, it's a bit confusing where to find the data. The "total" is actually the entire bar, not just the darker shaded part. The darker shaded part is better labeled "home market" as shown below:

The designer's instinct to bring out the importance of international markets to each company's income is well placed. A second small edit helps: plot the international income amounts first, so they line up with the vertical zero axis. Like this:

This is essentially the same chart. The order of international and home market is reversed. I also reversed the shading, so that the international share of income is displayed darker. This shading draws the readers' attention to the key message of the chart.

A stacked bar chart of the absolute dollar amounts is not ideal for showing proportions, because each bar is a different length. Sometimes, plotting relative values summing to 100% for each company may work better.

As it stands, the chart above calls attention to a different message: that Walmart dwarfs the other three global chains. Just the international income of Walmart is larger than the total income of Costco.

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Please comment below or write me directly if you have ideas for this blog as we enter a new decade. What do you want to see more of? less of?

The rule governing which variable to put on which axis, served a la mode

When making a scatter plot, the two variables should not be placed arbitrarily. There is a rule governing this: the outcome variable should be shown on the vertical axis (also called y-axis), and the explanatory variable on the horizontal (or x-) axis.

This chart from the archives of the Economist has this reversed:

The title of the accompanying article is "Ice Cream and IQ"...

In a Trifecta Checkup (link), it's a Type DV chart. It's preposterous to claim eating ice cream makes one smarter without more careful studies. The chart also carries the xyopia fallacy: by showing just two variables, readers are unwittingly led to explain differences in "IQ" using differences in per-capita ice-cream consumption when lots of other stronger variables will explain any gaps in IQ.

In this post, I put aside my objections to the analysis, and focus on the issue of assigning variables to axes. Notice that this chart reverses the convention: the outcome variable (IQ) is shown on the horizontal, and the explanatory variable (ice cream) is shown on the vertical.

Here is a reconstruction of the above chart, showing only the dots that were labeled with country names. I fitted a straight regression line instead of a curve. (I don't understand why the red line in the original chart bends upwards when the data for Japan, South Korea, Singapore and Hong Kong should be dragging it down.)

Note that the interpretation of the regression line raises eyebrows because the presumed causality is reversed. For each 50 points increase in PISA score (IQ), this line says to expect ice cream consumption to raise by about 1-2 liters per person per year. So higher IQ makes people eat more ice cream.

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If the convention is respected, then the following scatter plot results:

The first thing to note is that the regression analysis is different here from that shown in the previous chart. The blue regression line is not equivalent to the black regression line from the previous chart. You cannot reverse the roles of the x and y variables in a regression analysis, and so neither should you reverse the roles of the x and y variables in a scatter plot.

The blue regression line can be interpreted as having two sections, roughly, for countries consuming more than or less than 6 liters of ice cream per person per year. In the less-ice-cream countries, the correlation between ice cream and IQ is stronger (I don't endorse the causal interpretation of this statement).

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When you make a scatter plot, you have two variables for which you want to analyze their correlation. In most cases, you are exploring a cause-effect relationship.

Higher income households cares more on politics.
Less educated citizens are more likely to not register to vote.
Companies with more diverse workforce has better business performance.

Frequently, the reverse correlation does not admit a causal interpretation:

Caring more about politics does not make one richer.
Not registering to vote does not make one less educated.
Making more profits does not lead to more diversity in hiring.

In each of these examples, it's clear that one variable is the outcome, the other variable is the explanatory factor. Always put the outcome in the vertical axis, and the explanation in the horizontal axis.

The justification is scientific. If you are going to add a regression line (what Excel calls a "trendline"), you must follow this convention, otherwise, your regression analysis will yield the wrong result, with an absurd interpretation!

 

[PS. 11/3/2019: The comments below contain different theories that link the two variables, including theories that treat PISA score ("IQ") as the explanatory variable and ice cream consumption as the outcome. Also, I elaborated that the rule does not dictate which variable is the outcome - the designer effectively signals to the reader which variable is regarded as the outcome by placing it in the vertical axis.]