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.

 

 

Chartjunk as marketing copy

I got some spam marketing message last week. How exciting. They even use a subject line that has absolutely nothing to do with its content, baiting me to open it. And open I did, to some data graphics horrors.

The marketer promises a whole series of charts to prove that art is a great asset class for investment returns.

The very first chart already caught my full attention. It's this one:

It's a simple bar chart, with four values. Looks innocuous.

I'm unable to appreciate the recent trend to align bars in the middle, rather than at their bases. So I converted it to the canonical form:

Do you see the problem?

The second value ($1.7 trillion) is exactly half the size of the first value ($3.4 trillion) and yet the second bar is two-thirds of the length of the first bar. So, the size of the second bar is exaggerated relative to its label – and that’s the bar displaying the market size for “art,” which is what the spammer is pitching.

The bottom pair of values share the same relationship: $0.8 trillion is exactly half of $1.6 trillion. Again, the relative lengths of those two bars are not 50% but slightly over 60%.

Did the designer think that the bar lengths could be customized to whatever s/he desires? This one is hard to crack.

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The sixth chart in the series is a different kind of puzzle:

All three lines have the exact same labels but show different values over time.

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And they have pie charts, of course. Take a look:

Something went wrong here too. I'll leave it to my readers who can certainly figure it out :)

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These charts were probably spammed to at least thousands.

 

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:

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!

 

Graphics that stretch stomachs and make merry

Washington Post has a fun article about the Hot Dog Eating Contest in Coney Island here.

This graphic shows various interesting insights about the annual competition:

Joey Chestnut is the recent king of hot-dog eating. Since the late 2000s, he's dominated the competition. He typically chows down over 60 hot dogs in 10 minutes. This is shown by the yellow line. Even at that high level, Chestnut has shown steady growth over time.

The legend tells us that the chart shows the results of all the other competitors. It's pretty clear that few have been able to even get close to Chestnut all these years. Most contestants were able to swallow 30 hot dogs or fewer.

It doesn't appear that the general standard has increased over time.

In 2011, a separate competition for women started. There is also a female champion (Miki Sudo) who has won almost every competition since she started playing.

One strange feature is the lack of competition in the early years. The footnote informs us that the trend is not real - they simply did not keep records of other competitors in early contests.

The only question I can't answer from this chart is the general standard and number of female competitors. The chart designer chooses not to differentiate between male and female contestants, other than the champions. I can understand that. Adding another dimension to the chart is a double-edged sword.

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There is even more fun. There is a little video illustrating theories about what kind of human bodies can take in that many hot dogs in a short time. Here is a screen shot of it:

 

 

When words speak louder than pictures

I've been staring at this chart from the Wall Street Journal (link) about U.S. workers working remotely:

It's one of those offerings I think on which the designer spent a lot of effort, but ultimately didn't realize that the reader would spend equal if not more effort deciphering.

However, the following paragraph lifted straight from the article says exactly what needs to be said:

Workers overall spent an average of 5 hours and 25 minutes a day working from home in 2022. That is about two hours more than in 2019, the year before Covid-19 sent millions of workers scrambling to set up home oces, and down just 12 minutes from 2021, according to the Labor Department’s American Time Use Survey.

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Why is the chart so hard to read?

It's mostly because the visual is fighting the message. In the Trifecta Checkup (link), this is represented by a disconnect between the Q(uestion) and the V(isual) corners - note the green arrow between these two corners.

The message concentrates on two comparisons: first, the increase in amount of remote work after the pandemic; and second, the mild decrease in 2022 relative to 2021.

On the chart, the elements that grab my attention are (a) the green and orange columns (b) the shading in the bottom part of those green and orange columns (c) the thick black line that runs across the chart (d) the indication on the left side that tells me one unit is an hour.

None of those visual elements directly addresses the comparisons. The first comparison - before and after the pandemic - is found by how much the green column spikes above the thick black line. Our comprehension is retarded by the decision to forego the typical axis labels in favor of chopping columns into one-hour blocks.

The second comparison - between 2022 and 2021 - is found in the white space above the top of the orange column.

So, in reality, the text labels that say exactly what needs to be said are carrying a lot of weight. A slight edit to the pointers helps connect those descriptions to the visual depiction, like this:

I've essentially flipped the tactics used in the various pointers. For the average level of remote work pre-pandemic, I dispense of any pointers while I'm using double-headed arrows to indicate differences across time.

Nevertheless, this modified chart is still too complex.

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Here is a version that aligns the visual to the message:

It's a bit awkward because the 2 hour 48 minutes calculation is the 2021 number minus the average of 2015-19, skipping the 2020 year.

 

Why some dataviz fail

Maxim Lisnic's recent post should delight my readers (link). Thanks Alek for the tip. Maxim argues that charts "deceive" not merely by using visual tricks but by a variety of other non-visual means.

This is also the reasoning behind my Trifecta Checkup framework which looks at a data visualization project holistically. There are lots of charts that are well designed and constructed but fail for other reasons. So I am in agreement with Maxim.

He analyzed "10,000 Twitter posts with data visualizations about COVID-19", and found that 84% are "misleading" while only 11% of the 84% "violate common design guidelines". I presume he created some kind of computer program to evaluate these 10,000 charts, and he compiled some fixed set of guidelines that are regarded as "common" practice.

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Let's review Maxim's examples in the context of the Trifecta Checkup.

The first chart shows Covid cases in the U.S. in July and August of 2021 (presumably the time when the chart was published) compared to a year ago (prior to the vaccination campaign).

Maxim calls this cherry-picking. He's right - and this is a pet peeve of mine, even with all the peer-reviewed scientific research. In my paper on problems with observational studies (link), my coauthors and I call for a new way forward: researchers should put their model calculations up on a website which is updated as new data arrive, so that we can be sure that the conclusions they published apply generally to all periods of time, not just the time window chosen for the publication.

Looking at the pair of line charts, readers can quickly discover its purpose, so it does well on the Q(uestion) corner of the Trifecta. The cherry-picking relates to the link between the Question and the Data, showing that this chart suffers from subpar analysis.

In addition, I find that the chart also misleads visually - the two vertical scales are completely different: the scale on the left chart spans about 60,000 cases while on the right, it's double the amount.

Thus, I'd call this a Type DV chart, offering opportunities to improve in two of the three corners.

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The second chart cited by Maxim plots a time series of all-cause mortality rates (per 100,000 people) from 1999 to 2020 as columns.

The designer does a good job drawing our attention to one part of the data - that the average increase in all-cause mortality rate in 2020 over the previous five years was 15%. I also like the use of a different color for the pandemic year.

Then, the designer lost the plot. Instead of drawing a conclusion based on the highlighted part of the data, s/he pushed a story that the 2020 rate was about the same as the 2003 rate. If that was the main message, then instead of computing a 15% increase relative to the past five years, s/he should have shown how the 2003 and 2020 levels are the same!

On a closer look, there is a dashed teal line on the chart but the red line and text completely dominate our attention.

This chart is also Type DV. The intention of the designer is clear: the question is to put the jump in all-cause mortality rate in a historical context. The problem lies again with subpar analysis. In fact, if we take the two insights from the data, they both show how serious a problem Covid was at the time.

When the rate returned to the level of 2003, we have effectively gave up all the gains made over 17 years in a few months.

Besides, a jump in 15% from year to year is highly significant if we look at all other year-to-year changes shown on the chart.

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The next section concerns a common misuse of charts to suggest causality when the data could only indicate correlation (and where the causal interpretation appears to be dubious). I may write a separate post about this vast topic in the future. Today, I just want to point out that this problem is acute with any Covid-19 research, including official ones.

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I find the fourth section of Maxim's post to be less convincing. In the following example, the tweet includes two charts, one showing proportion of people vaccinated, and the other showing the case rate, in Iceland and Nigeria.

This data visualization is poor even on the V(isual) corner. The first chart includes lots of countries that are irrelevant to the comparison. It includes the unnecessary detail of fully versus partially vaccinated, unnecessary because the two countries selected are at two ends of the scale. The color coding is off sync between the two charts.

Maxim's critique is:

The user fails to account, however, for the fact that Iceland had a much higher testing rate—roughly 200 times as high at the time of posting—making it unreasonable to compare the two countries.

And the section is titled "Issues with Data Validity". It's really not that simple.

First, while the differential testing rate is one factor that should be considered, this factor alone does not account for the entire gap. Second, this issue alone does not disqualify the data. Third, if testing rate differences should be used to invalidate this set of data, then all of the analyses put out by official sources lauding the success of vaccination should also be thrown out since there are vast differences in testing rates across all countries (and also across different time periods for the same country).

One typical workaround for differential testing rate is to look at deaths rather than cases. For the period of time plotted on the case curve, Nigeria's cumulative death per million is about 1/8th that of Iceland. The real problem is again in the Data analysis, and it is about how to interpret this data casually.

This example is yet another Type DV chart. I'd classify it under problems with "Casual Inference". "Data Validity" is definitely a real concern; I just don't find this example convincing.

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The next section, titled "Failure to account for statistical nuance," is a strange one. The example is a chart that the CDC puts out showing the emergence of cases in a specific county, with cases classified by vaccination status. The chart shows that the vast majority of cases were found in people who were fully vaccinated. The person who tweeted concluded that vaccinated people are the "superspreaders". Maxim's objection to this interpretation is that most cases are in the fully vaccinated because most people are fully vaccinated.

I don't think it's right to criticize the original tweeter in this case. If by superspreader, we mean people who are infected and out there spreading the virus to others through contacts, then what the data say is exactly that most such people are fully vaccinated. In fact, one should be very surprised if the opposite were true.

Indeed, this insight has major public health implications. If the vaccine is indeed 90% effective at stopping cases, we should not be seeing that level of cases. And if the vaccine is only moderately effective, then we may not be able to achieve "herd immunity" status, as was the plan originally.

I'd be reluctant to complain about this specific data visualization. It seems that the data allow different interpretations - some of which are contradictory but all of which are needed to draw a measured conclusion.

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The last section on "misrepresentation of scientific results" could use a better example. I certainly agree with the message: that people have confirmation bias. I have been calling this "story-first thinking": people with a set story visualize only the data that support their preconception.

However, the example given is not that. The example shows a tweet that contains a chart from a scientific paper that apparently concludes that hydroxychloroquine helps treat Covid-19. Maxim adds this study was subsequently retracted. If the tweet was sent prior to the retraction, then I don't think we can grumble about someone citing a peer reviewed study published in Lancet.

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Overall, I like Maxim's message. In some cases, I think there are better examples.

 

 

Graph workflow and defaults wreak havoc

For the past week or 10 days, every time I visited one news site, it insisted on showing me an article about precipitation in North Platte. It's baiting me to write a post about this lamentable bar chart (link):

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This chart got problems, and the problems start with the tooling, which dictates a workflow.

I imagine what the chart designer had to deal with.

For a bar chart, the tool requires one data series to be numeric, and the other to be categorical. A four-digit year is a number, which can be treated either as numeric or categorical. In most cases, and by default, numbers are considered numeric. To make this chart, the user asked the tool to treat years as categorical.

Many tools treat categories as distinct entities ("nominal"), mapping each category to a distinct color. So they have 11 colors for 11 years, which is surely excessive.

This happens because the year data is not truly categorical. These eleven years were picked based on the amount of rainfall. There isn't a single year with two values, it's not even possible. The years are just irregularly spaced indices. Nevertheless, the tool misbehaves if the year data are regarded as numeric. (It automatically selects a time-series line chart, because someone's data visualization flowchart says so.) Mis-specification in order to trick the tool has consequences.

The designer's intention is to compare the current year 2023 to the driest years in history. This is obvious from the subtitle in which 2023 is isolated and its purple color is foregrounded.

How unfortunate then that among the 11 colors, this tool grabbed 4 variations of purple! I like to think that the designer wanted to keep 2023 purple, and turn the other bars gray -- but the tool thwarted this effort.

The tool does other offensive things. By default, it makes a legend for categorical data. I like the placement of the legend right beneath the title, a recognition that on most charts, the reader must look at the legend first to comprehend what's on the chart.

Not so in this case. The legend is entirely redundant. Removing the legend does not affect our cognition one bit. That's because the colors encode nothing.

Worse, the legend sows confusion because it presents the same set of years in chronological order while the bars below are sorted by amount of precipitation: thus, the order of colors in the legend differs from that in the bar chart.

I can imagine the frustration of the designer who finds out that the tool offers no option to delete the legend. (I don't know this particular tool but I have encountered tools that are rigid in this manner.)

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Something else went wrong. What's the variable being plotted on the numeric (horizontal) axis?

The answer is inches of rainfall but the answer is actually not found anywhere on the chart. How is it possible that a graphing tool does not indicate the variables being plotted?

I imagine the workflow like this: the tool by default puts an axis label which uses the name of the column that holds the data. That column may have a name that is not reader-friendly, e.g. PRECIP. The designer edits the name to "Rainfall in inches". Being a fan of the Economist graphics style, they move the axis label to the chart title area.

The designer now works the chart title. The title is made to spell out the story, which is that North Platte is experiencing a historically dry year. Instead of mentioning rainfall, the new title emphasizes the lack thereof.

The individual steps of this workflow make a lot of sense. It's great that the title is informative, and tells the story. It's great that the axis label was fixed to describe rainfall in words not database-speak. But the end result is a confusing mess.

The reader must now infer that the values being plotted are inches of rainfall.

Further, the tool also imposes a default sorting of the bars. The bars run from longest to shortest, in this case, the longest bar has the most rainfall. After reading the title, our expectation is to find data on the Top 11 driest years, from the driest of the driest to the least dry of the driest. But what we encounter is the opposite order.

Most graphics software behaves like this as they are plotting the ranks of the categories with the driest being rank 1, counting up. Because the vertical axis moves upwards from zero, the top-ranked item ends up at the bottom of the chart.

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Moving now from the V corner to the D corner of the Trifecta checkup (link), I can't end this post without pointing out that the comparisons shown on the chart don't work. It's the first few months of 2023 versus the full years of the others.

The fix is to plot the same number of months for all years. This can be done in two ways: find the partial year data for the historical years, or project the 2023 data for the full year.

(If the rainy season is already over, then the chart will look exactly the same at the end of 2023 as it is now. Then, I'd just add a note to explain this.)

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Here is a version of the chart after doing away with unhelpful default settings:

Deconstructing graphics as an analysis tool in dataviz

One of the useful exercises I like to do with charts is to "deconstruct" them. (This amounts to a deeper version of the self-sufficiency test.)

Here is a chart stripped down to just the main visual elements.

The game is to guess what is the structure of the data given these visual elements.

I guessed the following:

• The data has a top-level split into two groups
• Within each group, the data is further split into 3 parts, corresponding to the 3 columns
• With each part, there are a variable number of subparts, each of which is given a unique color
• The color legend suggests that each group's data are split into 7 subparts, so I'm guessing that the 7 subparts are aggregated into 3 parts
• The core chart form is a stacked column chart with absolute values so relative proportions within each column (part) is important
• Comparing across columns is not supported because each column has its own total value
• Comparing same-color blocks across the two groups is meaningful. It's easier to compare their absolute values but harder to compare the relative values (proportions of total)

If I knew that the two groups are time periods, I'd also guess that the group on the left is the earlier time period, and the one on the right is the later time period. In addition to the usual left-to-right convention for time series, the columns are getting taller going left to right. Many things (not all, obviously) grow over time.

The color choice is a bit confusing because if the subparts are what I think they are, then it makes more sense to use one color and different shades within each column.

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The above guesses are a mixed bag. What one learns from the exercise is what cues readers are receiving from the visual structure.

Here is the same chart with key contextual information added back:

Now I see that the chart concerns revenues of a business over two years.

My guess on the direction of time was wrong. The more recent year is placed on the left, counter to convention. This entity therefore suffered a loss of revenues from 2017-8 to 2018-9.

The entity receives substantial government funding. In 2017-8, it has 1 dollar of government funds for every 2 dollars of revenues. In 2018-9, it's roughly 2 dollars of government funds per every 3 dollars of revenues. Thus, the ratio of government funding to revenues has increased.

On closer inspection, the 7 colors do not represent 7 components of this entity's funding. The categories listed in the color legend overlap.

It's rather confusing but I missed one very important feature of the chart in my first assessment: the three columns within each year group are nested. The second column breaks down revenues into 3 parts while the third column subdivides advertising revenues into two parts.

What we've found is that this design does not offer any visual cues to help readers understand how the three columns within a year-group relates to each other. Adding guiding lines or changing the color scheme helps.

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Next, I add back the data labels:

The system of labeling can be described as: label everything that is not further broken down into parts on the chart.

Because of the nested structure, this means two of the column segments, which are the sums of subparts, are not labeled. This creates a very strange appearance: usually, the largest parts are split into subparts, so such a labeling system means the largest parts/subparts are not labeled while the smaller, less influential, subparts are labeled!

You may notice another oddity. The pink segment is well above $1 billion but it is roughly the size of the third column, which represents $250 million. Thus, these columns are not drawn to scale. What happened? Keep reading.

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Here is the whole chart:

A twitter follower sent me this chart. Elon Musk has been feuding with the Canadian broadcaster CBC.

Notice the scale of the vertical axis. It has a discontinuity between $700 million and $1.7 billion. In other words, the two pink sections are artificially shortened. The erased section contains $1 billion (!) Notice that the erased section is larger than the visible section.

The focus of Musk's feud with CBC is on what proportion of the company's funds come from the government. On this chart, the only way to figure that out is to copy out the data and divide. It's roughly 1.2/1.7 = 70% approx.

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The exercise of deconstructing graphics helps us understand what parts are doing what, and it also reveals what cues certain parts send to readers.

In better dataviz, every part of the chart is doing something useful, it's free of redundant parts that take up processing time for no reason, and the cues to readers move them towards the intended message, not away from it.

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A couple of additional comments:

I'm not sure why old data was cited because in the most recent accounting report, the proportion of government funding was around 65%.

Source of funding is not a useful measure of pro- or anti-government bias, especially in a democracy where different parties lead the government at different times. There are plenty of mouthpiece media that do not apparently receive government funding.

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!