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 DataJournalism.com: 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.]

Everything in Texas is big, but not this BIG

Long-time reader John forwarded the following chart via Twitter.

The chart shows the recent explosive growth in deaths due to Covid-19 in Texas. John flagged this graphic as yet another example in which the data are encoded to the lengths of the squares, not their areas.

Fixing this chart just requires fixing the length of one side of the square. I also flipped it to make a conventional column chart.

The final product:

An important qualification lurks in the footnote; it is directly applied to the label of July.

How much visual distortion is created when data are encoded to the lengths and not the areas? The following chart shows what readers see, assuming they correctly perceive the areas of those squares. The value for March is held the same as above while the other months show the death counts implied by the relative areas of the squares.

Owing to squaring, the smaller counts are artificially compressed while the big numbers are massively exaggerated.

What is the price for objectivity

I knew I had to remake this chart.

The simple message of this chart is hidden behind layers of visual complexity. What the analyst wants readers to focus on (as discerned from the text on the right) is the red line, the seven-day moving average of new hospital admissions due to Covid-19 in Texas.

My eyes kept wandering away from the line. It's the sideway data labels on the columns. It's the columns that take up vastly more space than the red line. It's the sideway date labels on the horizontal axis. It's the redundant axis labels for hospitalizations when the entire data set has already been printed. It's the two hanging diamonds, for which the clues are filed away in the legend above.

Here's a version that brings out the message: after Phase 2 re-opening, the number of hospital admissions has been rising steadily.

Dots are used in place of columns, which push these details to the background. The line as well as periods of re-opening are directly labeled, removing the need for a legend.

Here's another visualization:

This chart plots the weekly average new hospital admissions, instead of the seven-day moving average. In the previous chart, the raggedness of moving average isn't transmitting any useful information to the average reader. I believe this weekly average metric is easier to grasp for many readers while retaining the general story.

***

On the original chart by TMC, the author said "the daily hospitalization trend shows an objective view of how COVID-19 impacts hospital systems." Objectivity is an impossible standard for any kind of data analysis or visualization. As seen above, the two metrics for measuring the trend in hospitalizations have pros and cons. Even if one insists on using a moving average, there are choices of averaging methods and window sizes.

Scientists are trained to believe in objectivity. It frequently disappoints when we discover that the rest of the world harbors no such notion. If you observe debates between politicians or businesspeople or social scientists, you rarely hear anyone claim one analysis is more objective - or less subjective - than another. The economist who predicts Dow to reach a new record, the business manager who argues for placing discounted products in the front not the back of the store, the sportscaster who maintains Messi is a better player than Ronaldo: do you ever hear these people describe their methods as objective?

Pursuing objectivity leads to the glorification of data dumps. The scientist proclaims disinterest in holding an opinion about the data. This is self-deception though. We clearly have opinions because when someone else  "misinterprets" the data, we express dismay. What is the point of pretending to hold no opinions when most of the world trades in opinions? By being "objective," we never shape the conversation, and forever play defense.

Designs of two variables: map, dot plot, line chart, table

The New York Times found evidence that the richest segments of New Yorkers, presumably those with second or multiple homes, have exited the Big Apple during the early months of the pandemic. The article (link) is amply assisted by a variety of data graphics.

The first few charts represent different attempts to express the headline message. Their appearance in the same article allows us to assess the relative merits of different chart forms.

First up is the always-popular map.

The advantage of a map is its ease of comprehension. We can immediately see which neighborhoods experienced the greater exoduses. Clearly, Manhattan has cleared out a lot more than outer boroughs.

The limitation of the map is also in view. With the color gradient dedicated to the proportions of residents gone on May 1st, there isn't room to express which neighborhoods are richer. We have to rely on outside knowledge to make the correlation ourselves.

The second attempt is a dot plot.

We may have to take a moment to digest the horizontal axis. It's not time moving left to right but income percentiles. The poorest neighborhoods are to the left and the richest to the right. I'm assuming that these percentiles describe the distribution of median incomes in neighborhoods. Typically, when we see income percentiles, they are based on households, regardless of neighborhoods. (The former are equal-sized segments, unlike the latter.)

This data graphic has the reverse features of the map. It does a great job correlating the drop in proportion of residents at home with the income distribution but it does not convey any spatial information. The message is clear: The residents in the top 10% of New York neighborhoods are much more likely to have left town.

In the following chart, I attempted a different labeling of both axes. It cuts out the need for readers to reverse being home to not being home, and 90th percentile to top 10%.

The third attempt to convey the income--exit relationship is the most successful in my mind. This is a line chart, with time on the horizontal axis.

The addition of lines relegates the dots to the background. The lines show the trend more clearly. If directly translated from the dot plot, this line chart should have 100 lines, one for each percentile. However, the closeness of the top two lines suggests that no meaningful difference in behavior exists between the 20th and 80th percentiles. This can be conveyed to readers through a short note. Instead of displaying all 100 percentiles, the line chart selectively includes only the 99th , 95th, 90th, 80th and 20th percentiles. This is a design choice that adds by subtraction.

Along the time axis, the line chart provides more granularity than either the map or the dot plot. The exit occurred roughly over the last two weeks of March and the first week of April. The start coincided with New York's stay-at-home advisory.

This third chart is a statistical graphic. It does not bring out the raw data but features aggregated and smoothed data designed to reveal a key message.

I encourage you to also study the annotated table later in the article. It shows the power of a well-designed table.

[P.S. 6/4/2020. On the book blog, I have just published a post about the underlying surveillance data for this type of analysis.]

 

 

Consumption patterns during the pandemic

The impact of Covid-19 on the economy is sharp and sudden, which makes for some dramatic data visualization. I enjoy reading the set of charts showing consumer spending in different categories in the U.S., courtesy of Visual Capitalist.

The designer did a nice job cleaning up the data and building a sequential story line. The spending are grouped by categories such as restaurants and travel, and then sub-categories such as fast food and fine dining.

Spending is presented as year-on-year change, smoothed.

Here is the chart for the General Commerce category:

The visual design is clean and efficient. Even too sparse because one has to keep returning to the top to decipher the key events labelled 1, 2, 3, 4. Also, to find out that the percentages express year-on-year change, the reader must scroll to the bottom, and locate a footnote.

As you move down the page, you will surely make a stop at the Food Delivery category, noting that the routine is broken.

I've featured this device - an element of surprise - before. Remember this Quartz chart that depicts drinking around the world (link).

The rule for small multiples is to keep the visual design identical but vary the data from chart to chart. Here, the exceptional data force the vertical axis to extend tremendously.

This chart contains a slight oversight - the red line should be labeled "Takeout" because food delivery is the label for the larger category.

Another surprise is in store for us in the Travel category.

I kept staring at the Cruise line, and how it kept dipping below -100 percent. That seems impossible mathematically - unless these cardholders are receiving more refunds than are making new bookings. Not only must the entire sum of 2019 bookings be wiped out, but the records must also show credits issued to these credit (or debit) cards. It's curious that the same situation did not befall the airlines. I think many readers would have liked to see some text discussing this pattern.

***

Now, let me put on a data analyst's hat, and describe some thoughts that raced through my head as I read these charts.

Data analysis is hard, especially if you want to convey the meaning of the data.

The charts clearly illustrate the trends but what do the data reveal? The designer adds commentary on each chart. But most of these comments count as "story time." They contain speculation on what might be causing the trend but there isn't additional data or analyses to support the storyline. In the General Commerce category, the 50 to 100 percent jump in all subcategories around late March is attributed to people stockpiling "non-perishable food, hand sanitizer, and toilet paper". That might be true but this interpretation isn't supported by credit or debit card data because those companies do not have details about what consumers purchased, only the total amount charged to the cards. It's a lot more work to solidify these conclusions.

A lot of data do not mean complete or unbiased data.

The data platform provided data on 5 million consumers. We don't know if these 5 million consumers are representative of the 300+ million people in the U.S. Some basic demographic or geographic analysis can help establish the validity. Strictly speaking, I think they have data on 5 million card accounts, not unique individuals. Most Americans use more than one credit or debit cards. It's not likely the data vendor have a full picture of an individual's or a family's spending.

It's also unclear how much of consumer spending is captured in this dataset. Credit and debit cards are only one form of payment.

Data quality tends to get worse.

One thing that drives data analyst nuts. The spending categories are becoming blurrier. In the last decade or so, big business has come to dominate the American economy. Big business, with bipartisan support, has grown by (a) absorbing little guys, and (b) eliminating boundaries between industry sectors. Around me, there is a Walgreens, several Duane Reades, and a RiteAid. They currently have the same owner, and increasingly offer the same selection. In the meantime, Walmart (big box), CVS (pharmacy), Costco (wholesale), etc. all won regulatory relief to carry groceries, fresh foods, toiletries, etc. So, while CVS or Walgreens is classified as a pharmacy, it's not clear that what proportion of the spending there is for medicines. As big business grows, these categories become less and less meaningful.

Twitter people UpSet with that Covid symptoms diagram

Been busy with an exciting project, which I might talk about one day. But I promised some people I'll follow up on Covid symptoms data visualization, so here it is.

After I posted about the Venn diagram used to depict self-reported Covid-19 symptoms by users of the Covid Symptom Tracker app (reported by Nature), Xan and a few others alerted me to Twitter discussion about alternative visualizations that people have made after they suffered the indignity of trying to parse the Venn diagram.

To avoid triggering post-trauma, for those want to view the Venn diagram, please click here.

[In the Twitter links below, you almost always have to scroll one message down - saving tweets, linking to tweets, etc. are all stuff I haven't fully figured out.]

Start with the Questions

Xan’s final comment is especially appropriate: "There's an over-riding Type-Q issue: count charts answer the wrong question".

As dataviz designers, we frequently get locked into the mindset of “what is the best way to present this dataset?” This line of thinking leads to overloaded graphics that attempt to answer every possible question that may arise from the data in one panoptic chart, akin to juggling 10 balls at once.

For complex datasets, it is often helpful to narrow down the list of questions, and provide a series of charts, each addressing one or two questions. I’ll come back to this point. I want to first show some of the nicer visuals that others have produced, which brings out the structure and complexity of this dataset.

 

The UpSet chart

The primary contender is the “UpSet” chart form, as best exemplified by Bart’s effort

The centerpiece of this chart is the matrix of dots. The horizontal rows of dots represent the presence of specific symptoms such as cough and anosmia (loss of smell and taste). The vertical columns are intuitive, once you get it. They represent combinations of symptoms, and the fill/no-fill of the dots indicates which symptoms are being combined. For example, the first column counts people reporting fatigue plus anosmia (but nothing else).

The UpSet chart clearly communicates the structure of the data. In many survey questions (including this one conducted by the Symptom Tracker app), respondents are allowed to check/tick more than one answer choices. This creates a situation where the number of answers (here, symptoms) per respondent can be zero up to the total number of answer choices.

So far, we have built a structure like we have drawn country outlines on a map. There is no data yet. The data are primarily found in the sidebar histograms (column/bar charts). Reading horizontally to the right side, one learns that the most frequently reported symptom was fatigue, covering 88 percent of the users.* Reading vertically, one learns that the top combination of symptoms was fatigue plus anosmia, covering 16 percent of users.

***

Now come the divisive acts.

Act 1: Bart orders the columns in a particular way that meets his subjective view of how he wants readers to see the data. The columns are sorted from the most frequent combinations to the least. The histogram has a “long tail”, with most of the combinations receiving a small proportion of the total. The top five combinations is where the bulk of the data is – I’d have liked to see all five columns labeled, without decimal places.

This is a choice on the part of the designer. Nils, for example, made two versions of his UpSet charts. The second version arranges the combinations from singles to quintuples.

 

Digression: The Visual in Data Visualization

The two rendering of “UpSet” charts, by Nils and Bart, is a perfect illustration of the Trifecta Checkup framework. Each corner of the Trifecta is an independent dimension, and yet all must sync. With the same data and the same question types, what differentiates the two versions is the visual design.

See how many differences you can find, and make your own design choices!

 

I place the digression here because Act 1 above has to do with the Q corner, and both visual designs can accommodate the sorting decisions. But Act 2 below pertains to the V corner.

Act 2: Bart applies a blue gradient to the matrix of dots that reinforces his subjective view about identifying frequent combinations of symptoms. Nils, by contrast, uses the matrix to show present/absent only.

I’m not sure about Act 2. I think the addition of the color gradient overloads the matrix in the chart. It has the nice effect of focusing the reader’s attention on the top 5 combinations but it also requires the reader to have understood the meaning of columns first. Perhaps applying the gradient to the histogram up top rather than the dots in the matrix can achieve the same goal with less confusion.

 

Getting Obtuse

For example, some readers (e.g. Robin) expressed confusion.

Robin is alleging something the chart doesn’t do. He pointed out (correctly) that while 16 percent experienced fatigue and anosmia only (without other symptoms), more than 50 percent reported fatigue and anosmia, plus other symptoms. That nugget of information is deeply buried inside Bart’s chart – it’s the sum of each column for which the first two dots are filled in. For example, the second column represents fatigue+anosmia+cough. So Robin wants to aggregate those up.

Robin’s critique arises from the Q(uestion) corner. If the designer wants to highlight specific combinations that occur most frequently in the data, then Bart’s encoding makes perfect sense. On the other hand, if the purpose is to highlight pairs of symptoms that occur most frequently together (disregarding symptoms outside each pair), then the data must be further aggregated. The switch in the Question requires more Data manipulation, which then affects the Visualization. That's the essence of the Trifecta Checkup framework.

Rest assured, the version that addresses Robin’s point will not give an easy answer to Bart’s question. In fact, Xan whipped up a bar chart in response:

This is actually hard to comprehend because Robin’s question is even hard to state. The first bar shows 87 percent of users reported fatigue as a symptom, the same number that appeared on Bart’s version on the right side. Then, the darkened section of the bar indicates the proportion of users who reported only fatigue and nothing else, which appears to be about 10 percent. So 1 out of 9 reported just fatigue while 8 out of 9 who reported fatigue also experienced other symptoms.

 

Xan’s bar chart can be flipped 90 degrees and replace Bart’s histogram on top of the matrix. But you see, we end up with the same problem as I mentioned up top. By jamming more insights from more questions onto the same chart, we risk dropping the other balls that were already in the air.

So, my advice is always to first winnow down the list of questions you want to address. And don’t be afraid of making a series of charts instead of one panoptic chart.

***

Act 3: Bart decides to leave out labels for the columns.

This is a curious choice given the key storyline we’ve been working with so far (the Top 5 combinations of symptoms). But notice how annoying this problem is. Combinations require long text, which must be written vertically or slanted on this design. Transposing could help but not really. It’s just a limitation of this chart form. For me, reading the filled dots underneath the columns as column labels isn’t a show-stopper.

 

Histograms vs Bar Charts

It’s worth pointing out that the sidebar “histograms” are not both histograms. I tend to think of histograms as a specific type of bar (column) chart, in which the sum of the bars (columns) can be interpreted as a whole. So all histograms are bar charts but only some bar charts are histograms.

The column chart up top is a histogram. The combinations of symptoms are disjoint, and the total of the combinations should be the total number of answer choices selected by all respondents. The bar chart on the right side however is not a histogram. Each percentage is a proportion to the whole, and adding those percentages yields way above 100%.

I like the annotation on Bart’s chart a lot. They are succinct and they give just the right information to explain how to read the chart.

 

Limitations

I already mentioned the vertical labeling issue for UpSet charts. Here are two other considerations for you.

The majority of the plotting area is dedicated to the matrix of dots. The matrix contains merely labels for data. They are like country boundaries on a map. While it lays out the structure of data very clearly, the designer should ask whether it is essential for the readers to see the entire landscape.

In real-world data, the “long tail” phenomenon we saw earlier is very common. With six featured symptoms, there are 2^6 = 64 possible combinations of symptoms (minus 1 if they filtered out those not reporting symptoms*), almost all of which will be empty. Should the low-frequency columns be removed? This is not as controversial as you think, because implicitly both Bart and Nils already dropped all empty combinations!

 

Data and Code

Kieran Healy left a comment on the last post, and you can find both the data (thank you!) and some R code for UpSet charts at his blog.

Also, Nils has a Shiny app on Github.

 

(*) One must be very careful about what “users” are being represented. They form a tiny subset of users of the Symptom Tracker app, just those who have previously taken a diagnostic test and have self-reported at least one symptom. I have separately commented on the analyses of this dataset by the team behind the app. The first post discusses their analytical methods, the second post examines how they pre-processed the data, and a future post will describe the data collection practices. For the purpose of this blog post, I’ll ignore any data issues.

(#) Bart’s chart is conceptual because some of the columns of dots are repeated, and there is one column without fills, which should have been removed by a pre-processing step applied by the research team.

How to read this chart about coronavirus risk

In my just-published Long Read article at DataJournalism.com, I touched upon the subject of "How to Read this Chart".

Most data graphics do not come with directions of use because dataviz designers follow certain conventions. We do not need to tell you, for example, that time runs left to right on the horizontal axis (substitute right to left for those living in right-to-left countries). It's when we deviate from the norms that calls for a "How to Read this Chart" box.

***
A discussion over Twitter during the weekend on the following New York Times chart perfectly illustrates this issue. (The article is well worth reading to educate oneself on this red-hot public-health issue. I made some comments on the sister blog about the data a few days ago.)

Reading this chart, I quickly grasp that the horizontal axis is the speed of infection and the vertical axis represents the deadliness. Without being told, I used the axis labels (and some of you might notice the annotations with the arrows on the top right.) But most people will likely miss - at a glance - that the vertical axis utilizes a log scale while the horizontal axis is linear (regular).

The effect of a log scale is to pull the large numbers toward the average while spreading the smaller numbers apart - when compared to a linear scale. So when we look at the top of the coronavirus box, it appears that this virus could be as deadly as SARS.

The height of the pink box is 3.9, while the gap between the top edge of the box and the SARS dot is 6. Yet our eyes tell us the top edge is closer to the SARS dot than it is to the bottom edge!

There is nothing inaccurate about this chart - the log scale introduces such distortion. The designer has to make a choice.

Indeed, there were two camps on Twitter, arguing for and against the log scale.

***

I use log scales a lot in analyzing data, but tend not to use log scales in a graph. It's almost a given that using the log scale requires a "How to Read this Chart" message. And the NY Times crew delivers!

Right below the chart is a paragraph:

To make this even more interesting, the horizontal axis is a hidden "log" scale. That's because infections spread exponentially. Even though the scale is not labeled "log", think as if the large values have been pulled toward the middle.

Here is an over-simplified way to see this. A disease that spreads at a rate of fifteen people at a time is not 3 times worse than one that spreads five at a time. In the former case, the first sick person transmits it to 15, and then each of the 15 transmits the flu to 15 others, thus after two steps, 241 people have been infected (225 + 15 + 1). In latter case, it's 5x5 + 5 + 1 = 31 infections after two steps. So at this point, the number of infected is already 8 times worse, not 3 times. And the gap keeps widening with each step.

P.S. See also my post on the sister blog that digs deeper into the metrics.

 

All these charts lament the high prices charged by U.S. hospitals

A former student asked me about this chart from the New York Times that highlights much higher prices of hospital procedures in the U.S. relative to a comparison group of seven countries.

The dot plot is clearly thought through. It is not a default chart that pops out of software.

Based on its design, we surmise that the designer has the following intentions:

1. The names of the medical procedures are printed to be read, thus the long text is placed horizontally.
   
   
2. The actual price is not as important as the relative price, expressed as an index with the U.S. price at 100%. These reference values are printed in glaring red, unignorable.
   
   
3. Notwithstanding the above point, the actual price is still of secondary importance, and the values are provided as a supplement to the row labels. Getting to the actual prices in the comparison countries requires further effort, and a calculator.
   
   
4. The primary comparison is between the U.S. and the rest of the world (or the group of seven countries included). It is less important to distinguish specific countries in the comparison group, and thus the non-U.S. dots are given pastels that take some effort to differentiate.
   
   
5. Probably due to reader feedback, the font size is subject to a minimum so that some labels are split into two lines to prevent the text from dominating the plotting region.

***

In the Trifecta Checkup view of the world, there is no single best design. The best design depends on the intended message and what’s in the available data.

To illustate this, I will present a few variants of the above design, and discuss how these alternative designs reflect the designer's intentions.

Note that in all my charts, I expressed the relative price in terms of discounts, which is the mirror image of premiums. Instead of saying Country A's price is 80% of the U.S. price, I prefer to say Country A's price is a 20% saving (or discount) off the U.S. price.

First up is the following chart that emphasizes countries instead of hospital procedures:

This chart encourages readers to draw conclusions such as "Hospital prices are 60-80 percent cheaper in Holland relative to the U.S." But it is more taxing to compare the cost of a specific procedure across countries.

The indexing strategy already creates a barrier to understanding relative costs of a specific procedure. For example, the value for angioplasty in Australia is about 55% and in Switzerland, about 75%. The difference 75%-55% is meaningless because both numbers are relative savings from the U.S. baseline. Comparing Australia and Switzerland requires a ratio (0.75/0.55 = 1.36): Australia's prices are 36% above Swiss prices, or alternatively, Swiss prices are a 64% 26% discount off Australia's prices.

The following design takes it even further, excluding details of individual procedures:

For some readers, less is more. It’s even easier to get a rough estimate of how much cheaper prices are in the comparison countries, for now, except for two “outliers”, the chart does not display individual values.

The widths of these bars reveal that in some countries, the amount of savings depends on the specific procedures.

The bar design releases the designer from a horizontal orientation. The country labels are shorter and can be placed at the bottom in a vertical design:

It's not that one design is obviously superior to the others. Each version does some things better. A good designer recognizes the strengths and weaknesses of each design, and selects one to fulfil his/her intentions.

 

P.S. [1/3/20] Corrected a computation, explained in Ken's comment.

Conceptualizing a chart using Trifecta: a practical example

In response to the reader who left a comment asking for ideas for improving the "marginal abatements chart" that was discussed here, I thought it might be helpful to lay out the process I go through when conceptualizing a chart. (Just a reminder, here is the chart we're dealing with.)

First, I'm very concerned about the long program names. I see their proper placement in a horizontal orientation as a hard constraint on the design. I'd reject every design that displays the text vertically, at an angle, or hides it behind some hover effect, or abbreviates or abridges the text.

Second, I strongly suggest re-thinking the "cost-effectiveness" metric on the vertical axis. Flipping the sign of this metric makes a return-on-investment-type metric, which is much more intuitive. Just to reiterate a prior point, it feels odd to be selecting more negative projects before more positive projects.

Third, I'd like to decide what metrics to place on the two axes. There are three main possibilities: a) benefits (that is, the average annual emissions abatement shown on the horizontal axis currently), b) costs, and c) some function that ties together costs and benefits (currently, this design uses cost per unit benefit, and calls it cost effectivness but there are a variety of similar metrics that can be defined).

For each of these metrics, there is a secondary choice. I can use the by-project value or the cumulative value. The cumulative value is dependent on a selection order, in this case, determined by the criterion of selecting from the most cost-effective program to the least (regardless of project size or any other criteria).

This is where I'd bring in the Trifecta Checkup framework (see here for a guide).

The decision of which metrics to use on the axes means I'm operating in the "D" corner. But this decision must be made with respect to the "Q" corner, thus the green arrow between the two. Which two metrics are the most relevant depends on what we want the chart to accomplish. That in turn depends on the audience and what specific question we are addressing for them.

Fourth, if the purpose of the chart is exploratory - that is to say, we use it to guide decision-makers in choosing a subset of programs, then I would want to introduce an element of interactivity. Imagine an interface that allows the user to move programs in and out of the chart, while the chart updates itself to compute the total costs and total benefits.

This last point ties together the entire Trifacta Checkup framework (link). The Question being exploratory in nature suggests a certain way of organizing and analyzing the Data as well as a Visual form that facilitates interacting with the information.

 

 

How to read this cost-benefit chart, and why it is so confusing

Long-time reader Antonio R. found today's chart hard to follow, and he isn't alone. It took two of us multiple emails and some Web searching before we think we "got it".

 

Antonio first encountered the chart in a book review (link) of Hal Harvey et. al, Designing Climate Solutions. It addresses the general topic of costs and benefits of various programs to abate CO2 emissions. The reviewer praised the "wealth of graphics [in the book] which present complex information in visually effective formats." He presented the above chart as evidence, and described its function as:

policy-makers can focus on the areas which make the most difference in emissions, while also being mindful of the cost issues that can be so important in getting political buy-in.

(This description is much more informative than the original chart title, which states "The policy cost curve shows the cost-effectiveness and emission reduction potential of different policies.")

Spend a little time with the chart now before you read the discussion below.

Warning: this is a long read but well worth it.

 

***

 

If your experience is anything like ours, scraps of information flew at you from different parts of the chart, and you had a hard time piecing together a story.

What are the reasons why this data graphic is so confusing?

Everyone recognizes that this is a column chart. For a column chart, we interpret the heights of the columns so we look first at the vertical axis. The axis title informs us that the height represents "cost effectiveness" measured in dollars per million metric tons of CO2. In a cost-benefit sense, that appears to mean the cost to society of obtaining the benefit of reducing CO2 by a given amount.

That's how far I went before hitting the first roadblock.

For environmental policies, opponents frequently object to the high price of implementation. For example, we can't have higher fuel efficiency in cars because it would raise the price of gasoline too much. Asking about cost-effectiveness makes sense: a cost-benefit trade-off analysis encapsulates the something-for-something principle. What doesn't follow is that the vertical scale sinks far into the negative. The chart depicts the majority of the emissions abatement programs as having negative cost effectiveness.

What does it mean to be negatively cost-effective? Does it mean society saves money (makes a profit) while also reducing CO2 emissions? Wouldn't those policies - more than half of the programs shown - be slam dunks? Who can object to programs that improve the environment at no cost?

I tabled that thought, and proceeded to the horizontal axis.

I noticed that this isn't a standard column chart, in which the width of the columns is fixed and uneventful. Here, the widths of the columns are varying.

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In the meantime, my eyes are distracted by the constellation of text labels. The viewing area of this column chart is occupied - at least 50% - by text. These labels tell me that each column represents a program to reduce CO2 emissions.

The dominance of text labels is a feature of this design. For a conventional column chart, the labels are situated below each column. Since the width does not usually carry any data, we tend to keep the columns narrow - Tufte, ever the minimalist, has even advocated reducing columns to vertical lines. That leaves insufficient room for long labels. Have you noticed that government programs hold long titles? It's tough to capture even the outline of a program with fewer than three big words, e.g. "Renewable Portfolio Standard" (what?).

The design solution here is to let the column labels run horizontally. So the graphical element for each program is a vertical column coupled with a horizontal label that invades the territories of the next few programs. Like this:

The horror of this design constraint is fully realized in the following chart, a similar design produced for the state of Oregon (lifted from the Plan Washington webpage listed as a resource below):

In a re-design, horizontal labeling should be a priority.

 

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Realizing that I've been distracted by the text labels, back to the horizontal axis I went.

This is where I encountered the next roadblock.

The axis title says "Average Annual Emissions Abatement" measured in millions metric tons. The unit matches the second part of the vertical scale, which is comforting. But how does one reconcile the widths of columns with a continuous scale? I was expecting each program to have a projected annual abatement benefit, and those would fall as dots on a line, like this:

Instead, we have line segments sitting on a line, like this:

Think of these bars as the bottom edges of the columns. These line segments can be better compared to each other if structured as a bar chart:

Instead, the design arranges these lines end-to-end.

To unravel this mystery, we go back to the objective of the chart, as announced by the book reviewer. Here it is again:

policy-makers can focus on the areas which make the most difference in emissions, while also being mindful of the cost issues that can be so important in getting political buy-in.

The primary goal of the chart is a decision-making tool for policy-makers who are evaluating programs. Each program has a cost and also a benefit. The cost is shown on the vertical axis and the benefit is shown on the horizontal. The decision-maker will select some subset of these programs based on the cost-benefit analysis. That subset of programs will have a projected total expected benefit (CO2 abatement) and a projected total cost.

By stacking the line segments end to end on top of the horizontal axis, the chart designer elevates the task of computing the total benefits of a subset of programs, relative to the task of learning the benefits of any individual program. Thus, the horizontal axis is better labeled "Cumulative annual emissions abatement".

 

Look at that axis again. Imagine you are required to learn the specific benefit of program titled "Fuel Economy Standards: Cars & SUVs".  

This is impossible to do without pulling out a ruler and a calculator. What the axis labels do tell us is that if all the programs to the left of Fuel Economy Standards: Cars & SUVs were adopted, the cumulative benefits would be 285 million metric tons of CO2 per year. And if Fuel Economy Standards: Cars & SUVs were also implemented, the cumulative benefits would rise to 375 million metric tons.

***

At long last, we have arrived at a reasonable interpretation of the cost-benefit chart.

Policy-makers are considering throwing their support behind specific programs aimed at abating CO2 emissions. Different organizations have come up with different ways to achieve this goal. This goal may even have specific benchmarks; the government may have committed to an international agreement, for example, to reduce emissions by some set amount by 2030. Each candidate abatement program is evaluated on both cost and benefit dimensions. Benefit is given by the amount of CO2 abated. Cost is measured as a "marginal cost," the amount of dollars required to achieve each million metric ton of abatement.

This "marginal abatement cost curve" aids the decision-making. It lines up the programs from the most cost-effective to the least cost-effective. The decision-maker is presumed to prefer a more cost-effective program than a less cost-effective program. The chart answers the following question: for any given subset of programs (so long as we select them left to right contiguously), we can read off the cumulative amount of CO2 abated.

***

There are still more limitations of the chart design.

• We can't directly read off the cumulative cost of the selected subset of programs because the vertical axis is not cumulative. The cumulative cost turns out to be the total area of all the columns that correspond to the selected programs. (Area is height x width, which is cost per benefit multiplied by benefit, which leaves us with the cost.) Unfortunately, it takes rulers and calculators to compute this total area.
  
  
• We have presumed that policy-makers will make the Go-No-go decision based on cost effectiveness alone. This point of view has already been contradicted. Remember the mystery around negatively cost-effective programs - their existence shows that some programs are stalled even when they reduce emissions in addition to making money!
  
  
• Since many, if not most, programs have negative cost-effectiveness (by the way they measured it), I'd flip the metric over and call it profitability (or return on investment). Doing so removes another barrier to our understanding. With the current cost-effectiveness metric, policy-makers are selecting the "negative" programs before the "positive" programs. It makes more sense to select the "positive" programs before the "negative" ones!

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In a Trifecta Checkup (guide), I rate this chart Type V. The chart has a great purpose, and the design reveals a keen sense of the decision-making process. It's not a data dump for sure. In addition, an impressive amount of data gathering and analysis - and synthesis - went into preparing the two data series required to construct the chart. (Sure, for something so subjective and speculative, the analysis methodology will inevitably be challenged by wonks.) Those two data series are reasonable measures for the stated purpose of the chart.

The chart form, though, has various shortcomings, as shown here.  

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In our email exchange, Antonio and I found the Plan Washington website useful. This is where we learned that this chart is called the marginal abatement cost curve.

Also, the consulting firm McKinsey is responsible for popularizing this chart form. They have published this long report that explains even more of the analysis behind constructing this chart, for those who want further details.