Adjust, and adjust some more

This Financial Times report illustrates the reason why we should adjust data.

The story explores the trend in economic statistics during 14 years of governing by conservatives. One of those metrics is so-called council funding (local governments). The graphic is interactive: as the reader scrolls the page, the chart transforms.

The first chart shows the "raw" data.

The vertical axis shows year-on-year change in funding. It is an index relative to the level in 2010. From this line chart, one concludes that council funding decreased from 2010 to around 2016, then grew; by 2020, funding has recovered to the level of 2010 and then funding expanded rapidly in recent years.

When the reader scrolls down, this chart is replaced by another one:

This chart contains a completely different picture. The line dropped from 2010 to 2016 as before. Then, it went flat, and after 2021, it started raising, even though by 2024, the value is still 10 percent below the level in 2010.

What happened? The data journalist has taken the data from the first chart, and adjusted the values for inflation. Inflation was rampant in recent years, thus, some of the raw growth have been dampened. In economics, adjusting for inflation is also called expressing in "real terms". The adjustment is necessary because the same dollar (hmm, pound) is worth less when there is inflation. Therefore, even though on paper, council funding in 2024 is more than 25 percent higher than in 2010, inflation has gobbled up all of that and more, to the point in which, in real terms, council funding has fallen by 20 percent.

This is one material adjustment!

Wait, they have a third chart:

It's unfortunate they didn't stabilize the vertical scale. Relative to the middle chart, the lowest point in this third chart is about 5 percent lower, while the value in 2024 is about 10 percent lower.

This means, they performed a second adjustment - for population change. It is a simple adjustment of dividing by the population. The numbers look worse probably because population has grown during these years. Thus, even if the amount of funding stayed the same, the money would have to be split amongst more people. The per-capita adjustment makes this point clear.

***

The final story is much different from the initial one. Not only was the magnitude of change different but the direction of change reversed.

Whenever it comes to adjustments, remember that all adjustments are subjective. In fact, choosing not to adjust is also subjective. Not adjusting is usually much worse.

 

 

 

 

The art of making simple things harder

It's no longer a shock when a TV network such as MSNBC plays loose with the scaling of the column heights, as in this recent example:

Hat tip to Mark P. for forwarding the image, and Rachel for the original tweet.

***

What's shocking is that the designer appears to believe that the column heights of a column chart can be determined without reference to the data.

There is not a single relationship that has been retained on this chart. The designer just picks whatever size column is desired.

One obvious distortion is between the Biden and Trump columns. Trump's number is about 1/3 of Biden's (120 vs 40), and yet the red column's height is 70% of the blue's.

Furthermore, amongst the red columns, the heights are also haphazard. Trump's number is almost 3 times larger than Haley's; the ratio of column heights is almost 4 times. Haley's number is just a tad higher than DeSantis and yet Haley's column is twice the height of DeSantis.

***

There is a further, subtle distortion of the column's widths. By curving the chart canvas, certain columns are widened more than others. The diagram above retains the distorted widths and you can see that the Desantis column is wider than that of Haley's.

Here is what the undistorted column chart looks like:

It's easy to make such a chart in Excel or any charting software, so it's mystery why this type of distortion happens. Did the designer open up an empty canvas and start putting up columns of any size?

An elaborate data vessel

I recently came across the following dataviz showing global oil production (link).

This is an ambitious graphic that addresses several questions of composition.

The raw data show the amount of production by country adding up to the global total. The countries are then grouped by region. Further, the graph presents an oil-and-gas specific grouping, as indicated by the legend shown just below the chart title. This grouping is indicated by the color of the circumference of the circle containing the flag of the country.

This chart form is popular in modern online graphics programs. It is like an elaborate data vessel. Because the countries are lined up around the barrel, a space has been created on three sides to admit labels and text annotations. This is a strength of this chart form.

***

The chart conveys little information about the underlying data. Each country is given a unique odd shaped polygon, making it impossible to compare sizes. It’s definitely possible to pick out U.S., Russia, Saudi Arabia as the top producers. But in presenting the ranks of the data, this chart form pales in comparison to a straightforward data table, or a bar chart. The less said about presenting values, the better.

Indeed, our self-sufficiency test exposes the inability of these polygons to convey the data. This is precisely why almost all values of the dataset are present on the chart.

***

The dataviz subtly presumes some knowledge on the part of the readers.

The regions are not directly labeled. The readers must know that Saudi Arabia is in the Middle East, U.S. is part of North America, etc. Admittedly this is not a big ask, but it is an ask.

It is also assumed that readers know their flags, especially those of smaller countries. Some of the small polygons have no space left for country names and they are labeled with just flags.

In addition, knowing country acronyms is required for smaller countries as well. For example, in Africa, we find AGO, COG and GAB.

For this chart form the designer treats each country according to the space it has on the chart (except those countries that found themselves on the edges of the barrel). Font sizes, icons, labels, acronyms, data labels, etc. vary.

The readers are assumed to know the significance of OPEC and OPEC+. This grouping is given second fiddle, and can be found via the color of the circumference of the flag icons.

I’d have not assigned a color to the non-OPEC countries, and just use the yellow and blue for OPEC and OPEC+. This is a little edit but makes the search for the edges more efficient.

***

Let’s now return to the perception of composition.

In exactly the same manner as individual countries, the larger regions are represented by polygons that have arbitrary shapes. One can strain to compile the rank order of regions but it’s impossible to compare the relative values of production across regions. Perhaps this explains the presence of another chart at the bottom that addresses this regional comparison.

The situation is worse for the OPEC/OPEC+ grouping. Now, the readers must find all flag icons with edges of a specific color, then mentally piece together these arbitrarily shaped polygons, then realizing that they won’t fit together nicely, and so must now mentally morph the shapes in an area-preserving manner, in order to complete this puzzle.

This is why I said earlier this is an elaborate data vessel. It’s nice to look at but it doesn’t convey information about composition as readers might expect it to.

Partition of Europe

A long-time reader sent me the following map via twitter:

This map tells how the major political groups divide up the European Parliament. I’ll spare you the counting. There are 27 countries, and nine political groups (including the "unaffiliated").

The key chart type is a box of dots. Each country gets its own box. Each box has its own width. What determines the width? If you ask me, it’s the relative span of the countries on the map. For example, the narrow countries like Ireland and Portugal have three dots across while the wider countries like Spain, Germany and Italy have 7, 10 and 8 dots across respectively.

Each dot represents one seat in the Parliament. Each dot has one of 9 possible colors. Each color shows a political lean e.g. the green dots represent Green parties while the maroon dots display “Left” parties.

The end result is a counting game. If we are interested in counts of seats, we have to literally count each dot. If we are interested in proportion of seats, take your poison: either eyeball it or count each color and count the total.

Who does the underlying map serve? Only readers who know the map of Europe. If you don’t know where Hungary or Latvia is, good luck. The physical constraints of the map work against the small-multiples set up of the data. In a small multiples, you want each chart to be identical, except for the country-specific data. The small-multiples structure requires a panel of equal-sized cells. The map does not offer this feature, as many small countries are cramped into Eastern Europe. Also, Europe has a few tiny states e.g. Luxembourg (population 660K)  and Malta (population 520K). To overcome the map, the designer produces boxes of different sizes, substantially loading up the cognitive burden on readers.

The map also dictates where the boxes are situated. The centroids of each country form the scaffolding, with adjustments required when the charts overlap. This restriction ensures a disorderly appearance. By contrast, the regular panel layout of a small multiples facilitates comparisons.

***

Here is something I sketched using a tile map.

First, I have to create a tile map of European countries. Some parts, e.g. western part, are straightforward. The eastern side becomes very congested.

The tile map encodes location in an imprecise sense. Think about the scaffolding of centroids of countries referred to prior. The tile map imposes an order to the madness - we're shifting these centroids so that they line up in a tidier pattern. What we gain in comparability we concede in location precision.

For the EU tile map, I decided to show the Baltic countries in a row rather than a column; the latter would have been more faithful to the true geography. Malta is shown next to Italy even though it could have been placed below. Similarly, Cyprus in relation to Greece. I also included several key countries that are not part of the EU for context.

Instead of raw seat counts, I'm showing the proportion of seats within each country claimed by each political group. I think this metric is more useful to readers.

The legend is itself a chart that shows the aggregate statistics for all 27 countries.

One bubble is a tragedy, and a bag of bubbles is...

From Kathleen Tyson's twitter account, I came across a graphic showing the destinations of Ukraine's grain exports since 2022 under the auspices of a UN deal. This graphic, made by AFP, uses one of the chart forms that baffle me - the bag of bubbles.

The first trouble with a bag of bubbles is the single bubble. The human brain is just not fit for comparing bubble sizes. The self-sufficiency test is my favorite device for demonstrating this weakness. The following is the European section of the above chart, with the data labels removed.

How much bigger is Spain than the Netherlands? What's the difference between Italy and the Netherlands? The answers don't come easily to mind. (The Netherlands is about 40% the size of Spain, and Italy is about 20% larger than the Netherlands.)

While comparing relative circular areas is a struggle, figuring out the relative ranks is not. Sure, it gets tougher with small differences (Germany vs S. Korea, Belgium vs Portugal) but saying those pairs are tied isn't a tragedy.

***

Another issue with bubble charts is how difficult it is to assess absolute values. A circle on its own has no reference point. The designer needs to add data labels or a legend. Adding data labels is an act of giving up. The data labels become the primary instrument for communicating the data, not the visual construct. Adding one data label is not enough, as the following shows:

Being told that Spain's value is 4.1 does little to help estimate the values for the non-labelled bubbles.

The chart does come with the following legend:

For this legend to work, the sample bubble sizes should span the range of the data. Notice that it's difficult to extrapolate from the size of the 1-million-ton bubble to 2-million, 4-million, etc. The analogy is a column chart in which the vertical axis does not extend through the full range of the dataset.

The designer totally gets this. The chart therefore contains both selected data labels and the partial legend. Every bubble larger than 1 million tons has an explicit data label. That's one solution for the above problem.

Nevertheless, why not use another chart form that avoids these problems altogether?

***

In Tyson's tweet, she showed another chart that pretty much contains the same information, this one from TASS.

This chart uses the flow diagram concept - in an abstract way, as I explained in previous post.

This chart form imposes structure on the data. The relative ranks of the countries within each region are listed from top to bottom. The relative amounts of grains are shown in black columns (and also in the thickness of the flows).

The aggregate value of movements within each region is called out in that middle section. It is impossible to learn this from the bag of bubbles version.

The designer did print the entire dataset onto this chart (except for the smallest countries grouped together as "other"). This decision takes away from the power of the underlying flow chart. Instead of thinking about the proportional representation of each country within its respective region, or the distribution of grains among regions, our eyes hone in on the data labels.

This brings me back to the principle of self-sufficiency: if we expect readers to consume the data labels - which comprise the entire dataset, why not just print a data table? If we decide to visualize, make the visual elements count!

Visual story-telling: do you know or do you think?

One of the most important data questions of all time is: do you know? or do you think?

And one of the easiest traps to fall into is: I think, therefore I know.

***

Visual story-telling can be great but it can also mislead. Deception sometimes happens when readers are nudged to "fill in the blanks" with stuff they think they know, but they don't.

A Twitter reader asked me to look at the map in this Los Angeles Times (paywall) opinion column.

The column promptly announces its premise:

Years of widening economic inequality, compounded by the pandemic and political storm and stress, have given Americans the impression that the country is on the wrong track. Now there’s empirical data to show just how far the country has run off the rails: Life expectancies have been falling.

The writer creates the expectation that he will reveal evidence in the form of data to show that life expectancies have been driven down by economic inequality, pandemic, and politics. Does he succeed?

***

The map portrays average life expectancy (at birth) for some mysterious, presumably very recent, year for every county in the United States. From the color legend, we learn that the bottom-to-top range is about 20 years. There is a clear spatial pattern, with the worst results in the south (excepting south Florida).

The choice of colors is telling. Red and blue on a U.S. map has heavy baggage, as they signify the two main political parties in the country. Given that the author believes politics to be a key driver of health outcomes, the usage of red and blue here is deliberate. Throughout the article, the columnist connects the lower life expectancies in southern states to its politics.

For example, he said "these geographical disparities aren't artifacts of pure geography or demographics; they're the consequences of policy decisions at the state level... Of the 20 states with the worst life expectancies, eight are among the 12 that have not implemented Medicaid expansion under the Affordable Care Act..."

Casual readers may fall into a trap here. There is nothing on the map itself that draws the connection between politics and life expectancies; the idea is evoked purely through the red-blue color scheme. So, as readers, we are filling in the blanks with our own politics.

What could have been done instead? Let's look at the life expectancy map side by side with the map of the U.S. 2020 Presidential election.

Because of how close recent elections have been, we may think the political map has a nice balance of red and blue but it isn't. The Democrats' votes are heavily concentrated in densely-populated cities so most of the Presidential election map is red. When placed next to each other, it's obvious that politics don't explain the variance in life expectancy well. The Midwest is deep red and yet they have above average life expectancies. I have circled out various regions that contradict the claim that Republican politics drove life expectancies down.

It's not sufficient to point to the South, in which Republican votes and life expectancy are indeed inversely correlated. A good theory has to explain most of the country.

***

The columnist also suggests that poverty is the cause of low life expectancy. That too cannot be gleaned from the published map. Again, readers are nudged to use their wild imagination to fill in the blank.

Data come to the rescue. Here is a side-by-side comparison of the map of life expectancies and the map of median incomes.

A similar conundrum. While the story feels right in the South, it fails to explain the northwest, Florida, and various other parts of the country. Take a look again at the circled areas. Lower income brackets are also sometimes associated with high life expectancies.

***

The author supplies a third cause of lower life expectancies: Covid-19 response. Because Covid-19 was the "most obvious and convenient" explanation for the loss of life expectancy during the pandemic, this theory suggests that the red areas on the life expectancy map should correspond to the regions most ravaged by Covid-19.

Let's see the data.

The map on the right shows the number of confirmed cases until June 2021. As before, the correlation holds somewhat in the South but there are notable exceptions, e.g. the Midwest. We also have states with low Covid-19 cases but below-average life expectancy.

***

What caused the decline of life expectancy in the U.S. - which began before the pandemic, and has continued beyond - is highly complex, beyond what a single map or a pair of maps or a few pairs of maps could convey. Showing a red-blue map presents a trap for readers to fall into, in which they start thinking, without knowing.

 

Area chart is not the solution

A reader left a link to a Wiki chart, which is ghastly:

This chart concerns the trend of relative proportions of House representatives in the U.S. Congress by state, and can be found at this Wikipedia entry. The U.S. House is composed of Representatives, and the number of representatives is roughly proportional to each state's population. This scheme actually gives small states disporportional representation, since the lowest number of representatives is 1 while the total number of representatives is fixed at 435.

We can do a quick calculation: 1/435 = 0.23% so any state that has less than 0.23% of the population is over-represented in the House. Alaska, Vermont and Wyoming are all close to that level. The primary way in which small states get larger representation is via the Senate, which sits two senators per state no matter the size. (If you've wondered about Nate Silver's website: 435 Representatives + 100 Senators + 3 for DC = 538 electoral votes for U.S. Presidental elections.)

***

So many things have gone wrong with this chart. There are 50 colors for 50 states. The legend arranges the states by the appropriate metric (good) but in ascending order (bad). This is a stacked area chart, which makes it very hard to figure out the values other than the few at the bottom of the chart.

A nice way to plot this data is a tile map with line charts. I found a nice example that my friend Xan put together in 2018:

A tile map is a conceptual representation of the U.S. map in which each state is represented by equal-sized squares. The coordinates of the states are distorted in order to line up the tiles. A tile map is a small-multiples setup in which each square contains a chart of the same design to faciliate inter-state comparisons.

In the above map, Xan also takes advantage of the foregrounding concept. Each chart actually contains all 50 lines for every state, all shown in gray while the line for the specific state is bolded and shown in red.

***

A chart with 50 lines looks very different from one with 50 areas stacked on each other. California, the most populous state, has 12% of the total population so the line chart has 50 lines that will look like spaghetti. Thus, the fore/backgrounding is important to make sure it's readable.

I suspect that the designer chose a stacked area chart because the line chart looked like spaghetti. But that's the wrong solution. While the lines no longer overlap each other, it is a real challenge to figure out the state-level trends - one has to focus on the heights of the areas, rather than the boundary lines.

[P.S. 2/27/2023] As we like to say, a picture is worth a thousand words. Twitter reader with the handle LHZGJG made the tile map I described above. It looks like this:

You can pick out the states with the key changes really fast. California, Texas, Florida on the upswing, and New York, Pennsylvania going down. I like the fact that the state names are spelled out. Little tweaks are possible but this is a great starting point. Thanks LHZGJG! ]

 

Getting simple charts right

Ian K. submitted this chart on Twitter:

The chart comes from a video embedded in this report (link) about Chicago cops leaving their jobs.

Let's start with the basics. This is an example of a simple line chart illustrating a time series of five observations. The vertical axis starts at 10,000 instead of 0. With this choice, the designer wants to focus on the point-to-point change in values, rather than its relation to the initial value.

Every graph has add-ons that assist cognition. On this chart, we have axis labels, gridlines and data labels. Every add-on increases reading time so we should be sparing.

First consider the gridlines. In the following chart, I conduct a self-sufficiency test by removing the data labels from the chart:

You can see that the last three values present no problems. The first two, especially the first value, are hard to read - because the top gridline is missing! The next chart restores the bounding gridline, so you can see the difference that one small detail can make:

***

Next, let's compare the following versions of the chart. The left one contains data labels without gridlines and axis labels. The right one has the gridlines and axis labels but no data labels.

The left chart prints the entire dataset onto the chart. The reader in essence is reading the raw data. That appears to be the intention of the chart designer as the data labels are in large size, placed inside shiny white boxes. The level of the boxes determines the reader's perception as those catch more of our attention than the dots that actually represent the data.

The right chart highlights the dots and the lines between them. The gridlines are way too thick and heavy so as to distract rather than abet. This chart presumes that the reader isn't that interested in the precise numbers as she is in the trend.

***

As Ian pointed out, one of the biggest problems with this chart is the appearance of even time intervals when all except one of the date values are January. This seemingly innocent detail destroys the chart. The line segments of the chart encodes the pre-post change in the staffing numbers. For most of the line segments, the metric is year-on-year change but the last two line segments on the right show something else: a 19-month change, followed by a 5-month change.

I did the following analysis to understand how big of a staffing problem CPD faces.

First I restored the January 2022 time value, while shifting the Aug 2022 value to its rightful place on the time axis. Next, I added the dashed brown line, which represents a linear extension of the trend seen between January 2020-2021, before the sudden dip. We don't know what the true January 2022 value is but the projected value based on past trend is around 12,200. By August, the projected value is around 11,923, about 300 above the actual value of 11,611. By January 2023, the projected value is almost exactly the same as the actual value.

This linear trending analysis is likely too simplistic but it offers a baseline to start thinking about what the story is. The long-term trend is still down but the apparent dip in 2022 may not be meaningful.

 

 

Dual axes: a favorite of tricksters

Twitter readers directed me to this abomination from the St. Louis Fed (link).

This chart is designed to paint the picture that China is this grave threat because it's been ramping up military expenditure so much so that it exceeded U.S. spending since the 2000s.

Sadly, this is not what the data are suggesting at all! This story is constructed by manipulating the dual axes. Someone has already fixed it. Here's the same data plotted with a single axis:

(There are two set of axis labels but they have the same scale and both start at zero, so there is only one axis.)

Certainly, China has been ramping up military spending. Nevertheless, China's current level of spending is about one-third of America's. Also, imagine the cumulative spending excess over the 30 years shown on the chart.

Note also, the growth line of U.S. military spending in this period is actually similarly steep as China's.

***

Apparently, the St. Louis Fed is intent on misleading its readers. Even though on Twitter, they acknowledged people's feedback, they decided not to alter the chart.

If you click through to the article, you'll find the same flawed chart as before so I'm not sure how they "listened". I went to Wayback Machine to check the first version of this page, and I notice no difference.

***

If one must make a dual axes chart, it is the responsibility of the chart designer to make it clear to readers that different lines on the chart use different axes. In this case, since the only line that uses the right hand side axis is the U.S. line, which is blue, they should have colored the right hand axis blue. Doing that does not solve the visualization problem; it merely reduces the chance of not noticing the dual axes.

***

I have written about dual axes a lot in the past. Here's a McKinsey chart from 2006 that offends.

A graphical compass

A Twitter user pointed me to this article from Washington Post, ruminating about the correlation between gas prices and measures of political sentiment (such as Biden's approval rating or right-track-wrong-track). As common in this genre, the analyst proclaims that he has found something "counter intuitive".

The declarative statement strikes me as odd. In the first two paragraphs, he said the data showed "as gas prices fell, American optimism rose. As prices rose, optimism fell... This seems counterintuitive."

I'm struggling to see what's counterintuitive. Aren't the data suggesting people like lower prices? Is that not what we think people like?

The centerpiece of the article concerns the correlation between metrics. "If two numbers move in concert, they can be depicted literally moving in concert. One goes up, the other moves either up or down consistently." That's a confused statement and he qualifies it by typing "That sort of thing."

He's reacting to the following scatter plot with lines. The Twitter user presumably found it hard to understand. Count me in.

Why is this chart difficult to grasp?

The biggest puzzle is: what differentiates those two lines? The red and the gray lines are not labelled. One would have to consult the article to learn that the gray line represents the "raw" data at weekly intervals. The red line is aggregated data at monthly intervals. In other words, each red dot is an average of 4 or 5 weekly data points. The red line is just a smoothed version of the gray line. Smoothed lines show the time trend better.

The next missing piece is the direction of time, which can only be inferred by reading the month labels on the red line. But the chart without the direction of time is like a map without a compass. Take this segment for example:

If time is running up to down, then approval ratings are increasing over time while gas prices are decreasing. If time is running down to up, then approval ratings are decreasing over time while gas prices are increasing. Exactly the opposite!

The labels on the red line are not sufficient. It's possible that time runs in the opposite direction on the gray line! We only exclude that possibility if we know that the red line is a smoothed version of the gray line.

This type of chart benefits from having a compass. Here's one:

It's useful for readers to know that the southeast direction is "good" (higher approval ratings, lower gas prices) while the northwest direction is "bad". Going back to the original chart, one can see that the metrics went in the "bad" direction at the start of the year and has reverted to a "good" direction since.

***

What does this chart really say? The author remarked that "correlation is not causation". "Just because Biden’s approval rose as prices dropped doesn’t mean prices caused the drop."

Here's an alternative: People have general sentiments. When they feel good, they respond more positively to polls, as in they rate everything more positively. The approval ratings are at least partially driven by this general sentiment. The same author apparently has another article saying that the right-track-wrong-track sentiment also moved in tandem with gas prices.

One issue with this type of scatter plot is that it always cues readers to make an incorrect assumption: that the outcome variables (approval rating) is solely - or predominantly - driven by the one factor being visualized (gas prices). This visual choice completely biases the reader's perception.

P.S. [11-11-22] The source of the submission was incorrectly attributed.