Metaphors, maps, and communicating data

There are some data visualization that are obviously bad. But what makes them bad?

Here is an example of such an effort:

Carbon footprint 2021-02-15_0

This visualization of carbon emissions is not successful. There is precious little that a reader can learn from this chart without expensing a lot of effort. It's relatively easy to identify the largest emitters of carbon but since the data are not expressed per-capita, the chart mainly informs us which countries have the largest populations. 

The color of the bubbles informs readers which countries belong to which parts of the world. However, it distorts the location of countries within regions, and regions relative to regions, as the primary constraint is fitting the bubbles inside the shape of a foot.

The visualization gives a very rough estimate of the relative sizes of total emissions. The circles not being perfect circles don't help. 

It's relatively easy to list the top emitters in each region but it's hard to list the top 10 emitters in the world (try!) 

The small emitters stole all of the attention as they account for most of the labels - and they engender a huge web of guiding lines - an unsightly nuisance.

The diagram clings dearly to the "carbon footprint" metaphor. Does this metaphor help readers consume the emissions data? Conversely, does it slow them down?

A more conventional design uses a cartogram, a type of map in which the positioning of countries are roughly preserved while the geographical areas are coded to the data. Here's how it looks:


I can't seem to source this effort. If any reader can find the original source, please comment below.

This cartogram is a rearrangement of the footprint illustration. The map construct eliminates the need to include a color legend which just tells people which country is in which continent. The details of smaller countries are pushed to the bottom. 

In the footprint visualization, I'd even consider getting rid of the legend completely. This means trusting that readers know South Africa is part of Africa, and China is part of Asia.


Imagine: what if this chart comes without a color legend? Do we really need it?


I'd like to try a word cloud visual for this dataset. Something that looks like this (obviously with the right data encoding):


(This map is by Michael Tompsett who sells it here.)


Making graphics last over time

Yesterday, I analyzed the data visualization by the White House showing the progress of U.S. Covid-19 vaccinations. Here is the chart.


John who tweeted this at me, saying "please get a better data viz".

I'm happy to work with them or the CDC on better dataviz. Here's an example of what I do.


Obviously, I'm using made-up data here and this is a sketch. I want to design a chart that can be updated continuously, as data accumulate. That's one of the shortcomings of that bubble format they used.

In earlier months, the chart can be clipped to just the lower left corner.


Reading an infographic about our climate crisis

Let's explore an infographic by SCMP, which draws attention to the alarming temperature recorded at Verkhoyansk in Russia on June 20, 2020. The original work was on the back page of the printed newspaper, referred to in this tweet.

This view of the globe brings out the two key pieces of evidence presented in the infographic: the rise in temperature in unexpected places, and the shrinkage of the Arctic ice.


A notable design decision is to omit the color scale. On inspection, the scale is present - it was sewn into the graphic.


I applaud this decision as it does not take the reader's eyes away from the graphic. Some information is lost as the scale isn't presented in full details but I doubt many readers need those details.

A key takeaway is that the temperature in Verkhoyansk, which is on the edge of the Arctic Circle, was the same as in New Delhi in India on that day. We can see how the red was encroaching upon the Arctic Circle.


Next, the rapid shrinkage of the Arctic ice is presented in two ways. First, a series of maps.

The annotations are pared to the minimum. The presentation is simple enough such that we can visually judge that the amount of ice cover has roughly halved from 1980 to 2009.

A numerical measure of the drop is provided on the side.

Then, a line chart reinforces this message.

The line chart emphasizes change over time while the series of maps reveals change over space.


This chart suggests that the year 2020 may break the record for the smallest ice cover since 1980. The maps of Australia and India provide context to interpret the size of the Arctic ice cover.

I'd suggest reversing the pink and black colors so as to refer back to the blue and pink lines in the globe above.


The final chart shows the average temperature worldwide and in the Arctic, relative to a reference period (1981-2000).


This one is tough. It looks like an area chart but it should be read as a line chart. The darker line is the anomaly of Arctic average temperature while the lighter line is the anomaly of the global average temperature. The two series are synced except for a brief period around 1940. Since 2000, the temperatures have been dramatically rising above that of the reference period.

If this is a stacked area chart, then we'd interpret the two data series as summable, with the sum of the data series signifying something interesting. For example, the market shares of different web browsers sum to the total size of the market.

But the chart above should not be read as a stacked area chart because the outside envelope isn't the sum of the two anomalies. The problem is revealed if we try to articulate what the color shades mean.


On the far right, it seems like the dark shade is paired with the lighter line and represents global positive anomalies while the lighter shade shows Arctic's anomalies in excess of global. This interpretation only works if the Arctic line always sits above the global line. This pattern is broken in the late 1990s.

Around 1999, the Arctic's anomaly is negative while the global anomaly is positive. Here, the global anomaly gets the lighter shade while the Arctic one is blue.

One possible fix is to encode the size of the anomaly into the color of the line. The further away from zero, the darker the red/blue color.



A testing mess: one chart, four numbers, four colors, three titles, wrong units, wrong lengths, wrong data

Twitterstan wanted to vote the following infographic off the island:


(The publisher's website is here but I can't find a direct link to this graphic.)

The mishap is particularly galling given the controversy swirling around this year's A-Level results in the U.K. For U.S. readers, you can think of A-Levels as SAT Subject Tests, which in the U.K. are required of all university applicants, and represent the most important, if not the sole, determinant of admissions decisions. Please see the upcoming post on my book blog for coverage of the brouhaha surrounding the statistical adjustments (to be posted sometime this week, it's here.).

The first issue you may notice about the chart is that the bar lengths have no relationship with the numbers printed on them. Here is a scatter plot correlating the bar lengths and the data.


As you can see, nothing.

Then, you may wonder what the numbers mean. The annotation at the bottom right says "Average number of A level qualifications per student". Wow, the British (in this case, English) education system is a genius factory - with the average student mastering close to three thousand subjects in secondary (high) school!

TES is the cool name for what used to be the Times Educational Supplement. I traced the data back to Ofqual, which is the British regulator for these examinations. This is the Ofqual version of the above chart:


The data match. You may see that the header of the data table reads "Number of students in England getting 3 x A*". This is a completely different metric than number of qualifications - in fact, this metric measures geniuses. "A*" is the U.K. equivalent of "A+". When I studied under the British system, there was no such grade. I guess grade inflation is happening all over the world. What used to be A is now A+, and what used to be B is now A. Scoring three A*s is tops - I wonder if this should say 3 or more because I recall that you can take as many subjects as you desire but most students max out at three (may have been four).

The number of students attaining the highest achievement has increased in the last two years compared to the two years before. We can't interpret these data unless we know if the number of students also grew at similar rates.

The units are students while the units we expect from the TES graphic should be subjects. The cutoff for the data defines top students while the TES graphic should connote minimum qualification, i.e. a passing grade.

Now, the next section of the Ofqual infographic resolves the mystery. Here is the chart:


This dataset has the right units and measurement. There is almost no meaningful shift in the last four years. The average number of qualifications per student is only different at the second decimal place. Replacing the original data with this set removes the confusion.


While I was re-making this chart, I also cleaned out the headers and sub-headers. This is an example of software hegemony: the designer wouldn't have repeated the same information three times on a chart with four numbers if s/he wasn't prompted by software defaults.


The corrected chart violates one of the conventions I described in my tutorial for color difference should reflect data difference.

In the following side-by-side comparison, you see that the use of multiple colors on the left chart signals different data - note especially the top and bottom bars which carry the same number, but our expectation is frustrated.



[P.S. 8/25/2020. Dan V. pointed out another problem with these bar charts: the bars were truncated so that the bar lengths are not proportional to the data. The corrected chart is shown on the right below:


8/26/2020: added link to the related post on my book blog.]

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.


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.

What is a bad chart?

In the recent issue of Madolyn Smith’s Conversations with Data newsletter hosted by, she discusses “bad charts,” featuring submissions from several dataviz bloggers, including myself.

What is a “bad chart”? Based on this collection of curated "bad charts", it is not easy to nail down “bad-ness”. The common theme is the mismatch between the message intended by the designer and the message received by the reader, a classic error of communication. How such mismatch arises depends on the specific example. I am able to divide the “bad charts” into two groups: charts that are misinterpreted, and charts that are misleading.


Charts that are misinterpreted

The Causes of Death entry, submitted by Alberto Cairo, is a “well-designed” chart that requires “reading the story where it is inserted and the numerous caveats.” So readers may misinterpret the chart if they do not also partake the story at Our World in Data which runs over 1,500 words not including the appendix.


The map of Canada, submitted by Highsoft, highlights in green the provinces where the majority of residents are members of the First Nations. The “bad” is that readers may incorrectly “infer that a sizable part of the Canadian population is First Nations.”


In these two examples, the graphic is considered adequate and yet the reader fails to glean the message intended by the designer.


Charts that are misleading

Two fellow bloggers, Cole Knaflic and Jon Schwabish, offer the advice to start bars at zero (here's my take on this rule). The “bad” is the distortion introduced when encoding the data into the visual elements.

The Color-blindness pictogram, submitted by Severino Ribecca, commits a similar faux pas. To compare the rates among men and women, the pictograms should use the same baseline.


In these examples, readers who correctly read the charts nonetheless leave with the wrong message. (We assume the designer does not intend to distort the data.) The readers misinterpret the data without misinterpreting the graphics.


Using the Trifecta Checkup

In the Trifecta Checkup framework, these problems are second-level problems, represented by the green arrows linking up the three corners. (Click here to learn more about using the Trifecta Checkup.)


The visual design of the Causes of Death chart is not under question, and the intended message of the author is clearly articulated in the text. Our concern is that the reader must go outside the graphic to learn the full message. This suggests a problem related to the syncing between the visual design and the message (the QV edge).

By contrast, in the Color Blindness graphic, the data are not under question, nor is the use of pictograms. Our concern is how the data got turned into figurines. This suggests a problem related to the syncing between the data and the visual (the DV edge).


When you complain about a misleading chart, or a chart being misinterpreted, what do you really mean? Is it a visual design problem? a data problem? Or is it a syncing problem between two components?

The Periodic Table, a challenge in information organization

Reader Chris P. points me to this article about the design of the Periodic Table. I then learned that 2019 is the “International Year of the Periodic Table,” according to the United Nations.

Here is the canonical design of the Periodic Table that science students are familiar with.


(Source: Wikipedia.)

The Periodic Table is an exercise of information organization and display. It's about adding structure to over 100 elements, so as to enhance comprehension and lookup. The canonical tabular design has columns and rows. The columns (Groups) impose a primary classification; the rows (Periods) provide a secondary classification. The elements also follow an aggregate order, which is traced by reading from top left to bottom right. The row structure makes clear the "periodicity" of the elements: the "period" of recurrence is not constant, tending to increase with the heavier elements at the bottom.

As with most complex datasets, these elements defy simple organization, due to a curse of dimensionality. The general goal is to put the similar elements closer together. Similarity can be defined in an infinite number of ways, such as chemical, physical or statistical properties. The canonical design, usually attributed to Russian chemist Mendeleev, attained its status because the community accepted his organizing principles, that is, his definitions of similarity (subsequently modified).


Of interest, there is a list of unsettled issues. According to Wikipedia, the most common arguments concern:

  • Hydrogen: typically shown as a member of Group 1 (first column), some argue that it doesn’t belong there since it is a gas not a metal. It is sometimes placed in Group 17 (halogens), where it forms a nice “triad” with fluorine and chlorine. Other designers just float hydrogen up top.
  • Helium: typically shown as a member of Group 18 (rightmost column), the  halogens noble gases, it may also be placed in Group 2.
  • Mercury: usually found in Group 12, some argue that it is not a metal like cadmium and zinc.
  • Group 3: other than the first two elements , there are various voices about how to place the other elements in Group 3. In particular, the pairs of lanthanum / actinium and lutetium / lawrencium are sometimes shown in the main table, sometimes shown in the ‘f-orbital’ sub-table usually placed below the main table.


Over the years, there have been numerous attempts to re-design the Periodic table. Some of these are featured in the article that Chris sent me (link).

I checked how these alternative designs deal with those unsettled issues. The short answer is they don't settle the issues.

Wide Table (Janet)

The key change is to remove the separation between the main table and the f-orbital (pink) section shown below, as a "footnote". This change clarifies the periodicity of the elements, especially the elongating periods as one moves down the table. This form is also called "long step".


As a tradeoff, this table requires more space and has an awkward aspect ratio.

In this version of the wide table, the designer chooses to stack lutetium / lawrencium in Group 3 as part of the main table. Other versions place lanthanum / actinium in Group 3 as part of the main table. There are even versions that leave Group 3 with two elements.

Hydrogen, helium and mercury retain their conventional positions.


Spiral Design (Hyde)

There are many attempts at spiral designs. Here is one I found on this tumblr:


The spiral leverages the correspondence between periodic and circular. It is visually more pleasing than a tabular arrangement. But there is a tradeoff. Because of the increasing "diameter" from inner to outer rings, the inner elements are visually constrained compared to the outer ones.

In these spiral diagrams, the designer solves the aspect-ratio problem by creating local loops, sometimes called peninsulas. This is analogous to the footnote table solution, and visually distorts the longer periodicity of the heavier elements.

For Hyde's diagram, hydrogen is floated, helium is assigned to Group 2, and mercury stays in Group 12.



I also found this design on the same tumblr, but unattributed. It may have come from Life magazine.


It's a variant of the spiral. Instead of peninsulas, the designer squeezes the f-orbital section under Group 3, so this is analogous to the wide table solution.

The circular diagrams convey the sense of periodic return but the wide table displays the magnitudes more clearly.

This designer places hydrogen in group 18 forming a triad with fluorine and chlorine. Helium is in Group 17 and mercury in the usual Group 12 .


Cartogram (Sheehan)

This version is different.


The designer chooses a statistical property (abundance) as the primary organizing principle. The key insight is that the lighter elements in the top few rows are generally more abundant - thus more important in a sense. The cartogram reveals a key weakness of the spiral diagrams that draw the reader's attention to the outer (heavier) elements.

Because of the distorted shapes, the cartogram form obscures much of the other data. In terms of the unsettled issues, hydrogen and helium are placed in Groups 1 and 2. Mercury is in Group 12. Group 3 is squeezed inside the main table rather than shown below.



The centerpiece of the article Chris sent me is a network graph.


This is a complete redesign, de-emphasizing the periodicity. It's a result of radically changing the definition of similarity between elements. One barrier when introducing entirely new displays is the tendency of readers to expect the familiar.


I found the following articles useful when researching this post:

The Conversation

Royal Chemistry Society


GDPR: justice for data visualization

Reader LG found the following chart, tweeted by @EU_Justice.


This chart is a part of a larger infographic, which is found here.

The following points out a few issues with this effort:


The time axis is quite embarrassing. The first six months or so are squeezed into less than half the axis while the distance between Nov and Dec is not the same as that between Dec and Jan. So the slope of each line segment is what the designer wants it to be!

The straight edges of the area chart imply that there were only three data points, with straight lines drawn between each measurement. Sadly, the month labels are not aligned to the data on the line.

Lastly, the dots between May and November intended to facilitate reading this chart backfire. There are 6 dots dividing the May-Nov segment when there should only be five.


The chart looks like this when not distorted:



The French takes back cinema but can you see it?

I like independent cinema, and here are three French films that come to mind as I write this post: Delicatessen, The Class (Entre les murs), and 8 Women (8 femmes). 

The French people are taking back cinema. Even though they purchased more tickets to U.S. movies than French movies, the gap has been narrowing in the last two decades. How do I know? It's the subject of this infographic


How do I know? That's not easy to say, given how complicated this infographic is. Here is a zoomed-in view of the top of the chart:



You've got the slice of orange, which doubles as the imagery of a film roll. The chart uses five legend items to explain the two layers of data. The solid donut chart presents the mix of ticket sales by country of origin, comparing U.S. movies, French movies, and "others". Then, there are two thin arcs showing the mix of movies by country of origin. 

The donut chart has an usual feature. Typically, the data are coded in the angles at the donut's center. Here, the data are coded twice: once at the center, and again in the width of the ring. This is a self-defeating feature because it draws even more attention to the area of the donut slices except that the areas are highly distorted. If the ratios of the areas are accurate when all three pieces have the same width, then varying those widths causes the ratios to shift from the correct ones!

The best thing about this chart is found in the little blue star, which adds context to the statistics. The 61% number is unusually high, which demands an explanation. The designer tells us it's due to the popularity of The Lion King.


The one donut is for the year 1994. The infographic actually shows an entire time series from 1994 to 2014.

The design is most unusual. The years 1994, 1999, 2004, 2009, 2014 receive special attention. The in-between years are split into two pairs, shrunk, and placed alternately to the right and left of the highlighted years. So your eyes are asked to zig-zag down the page in order to understand the trend. 

To see the change of U.S. movie ticket sales over time, you have to estimate the sizes of the red-orange donut slices from one pie chart to another. 

Here is an alternative visual design that brings out the two messages in this data: that French movie-goers are increasingly preferring French movies, and that U.S. movies no longer account for the majority of ticket sales.


A long-term linear trend exists for both U.S. and French ticket sales. The "outlier" values are highlighted and explained by the blockbuster that drove them.



1. You can register for the free seminar in Lyon here. To register for live streaming, go here.
2. Thanks Carla Paquet at JMP for help translating from French.

The tech world in which everyone is below average

Laura pointed me to an infographic about tech worker salaries in major tech hubs (link).

What's wrong with this map?


The box "Global average" is doubly false. It is not global, and it is not the average!

The only non-American cities included in this survey are Toronto, Paris and London.

The only city with average salary above the "Global average" is San Francisco Bay Area. Since the Bay Area does not outweigh all other cities combined in the number of tech workers, it is impossible to get an average of $135,000.


Here is the second chart.

What's wrong with these lines?


This chart frustrates the reader's expectations. The reader interprets it as a simple line chart, based on three strong hints:

  • time along the horizontal axis
  • data labels show dollar units
  • lines linking time

Each line seems to show the trend of average tech worker salary, in dollar units.

However, that isn't the designer's intention. Let's zoom in on Chicago and Denver:


The number $112,000 (Denver) sits below the number $107,000 (Chicago). It appears that each chart has its own scale. But that's not the case either.

For a small-multiples setup, we expect all charts should use the same scale. Even though the data labels are absolute dollar amounts, the vertical axis is on a relative scale (percent change). To make things even more complicated, the percent change is computed relative to the minimum of the three annual values, no matter which year it occurs.


That's why $106,000 (Chicago) is at the same level as $112,000 (Denver). Those are the minimum values in the respective time series. As shown above, these line charts are easier to understand if the axis is displayed in its true units of percent change.

The choice of using the minimum value as the reference level interferes with comparing one city to the next. For Chicago, the line chart tells us 2015 is about 2 percent above 2016 while 2017 is 6 percent above. For Denver, the line chart tells us that 2016 is about 2 percent above the 2015 and 2017 values. Now what's the message again?

Here I index all lines to the earliest year.


In a Trifecta Checkup analysis (link), I'd be suspicious of the data. Did tech salaries in London really drop by 15-20 percent in the last three years?