Ranking data provide context but can also confuse

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

Econ_usaexcept_hispanic

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

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

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

***

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

Econ_usaexcept_thailand

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

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

***

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

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

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

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

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

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

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

***

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

 

 

 

 

 


Stumped by the ATM

The neighborhood bank recently installed brand new ATMs, with tablet monitors and all that jazz. Then, I found myself staring at this screen:

Banknote_picker_us

I wanted to withdraw $100. I ordinarily love this banknote picker because I can get the $5, $10, $20 notes, instead of $50 and $100 that come out the slot when I don't specify my preference.

Something changed this time. I find myself wondering which row represents which note. For my non-U.S. readers, you may not know that all our notes are the same size and color. The screen resolution wasn't great and I had to squint really hard to see the numbers of those banknote images.

I suppose if I grew up here, I might be able to tell the note values from the figureheads. This is an example of a visualization that makes my life harder!

***
I imagine that the software developer might be a foreigner. I imagine the developer might live in Europe. In this case, the developer might have this image in his/her head:

Banknote_picker_euro

Euro banknotes are heavily differentiated - by color, by image, by height and by width. The numeric value also occupies a larger proportion of the area. This makes a lot of sense.

I like designs to be adaptable. Switching data from one country to another should not alter the design. Switching data at different time scales should not affect the design. This banknote picker UI is not adaptable across countries.

***

Once I figured out the note values, I learned another reason why I couldn't tell which row is which note. It's because one note is absent.

Banknote_us_2

Where is the $10 note? That and the twenty are probably the most frequently used. I am also surprised people want $1 notes from an ATM. But I assume the bank knows something I don't.


Same data + same chart form = same story. Maybe.

We love charts that tell stories.

Some people believe that if they situate the data in the right chart form, the stories reveal themselves.

Some people believe for a given dataset, there exists a best chart form that brings out the story.

An implication of these beliefs is that the story is immutable, given the dataset and the chart form.

If you use the Trifecta Checkup, you already know I don't subscribe to those ideas. That's why the Trifecta has three legs, the third is the question - which is related to the message or the story.

***

I came across the following chart by Statista, illustrating the growth in Covid-19 cases from the start of the pandemic to this month. The underlying data are collected by WHO and cover the entire globe. The data are grouped by regions.

Statista_avgnewcases

The story of this chart appears to be that the world moves in lock step, with each region behaving more or less the same.

If you visit the WHO site, they show a similar chart:

WHO_horizontal_casesbyregion

On this chart, the regions at the bottom of the graph (esp. Southeast Asia in purple) clearly do not follow the same time patterns as Americas (orange) or Europe (green).

What we're witnessing is: same data, same chart form, different stories.

This is a feature, not a bug, of the stacked area chart. The story is driven largely by the order in which the pieces are stacked. In the Statista chart, the largest pieces are placed at the bottom while for WHO, the order is exactly reversed.

(There are minor differences which do not affect my argument. The WHO chart omits the "Other" category which accounts for very little. Also, the Statista chart shows the smoothed data using 7-day averaging.)

In this example, the order chosen by WHO preserves the story while the order chosen by Statista wipes it out.

***

What might be the underlying question of someone who makes this graph? Perhaps it is to identify the relative prevalence of Covid-19 in different regions at different stages of the pandemic.

Emphasis on the word "relative". Instead of plotting absolute number of cases, I consider plotting relative number of cases, that is to say, the proportion of cases in each region at given times.

This leads to a stacked area percentage chart.

Junkcharts_redo_statistawho_covidregional

In this side-by-side view, you see that this form is not affected by flipping the order of the regions. Both charts say the same thing: that there were two waves in Europe and the Americas that dwarfed all other regions.

 

 


Dreamy Hawaii

I really enjoyed this visual story by ProPublica and Honolulu Star-Advertiser about the plight of beaches in Hawaii (link).

The story begins with a beautiful invitation:

Propublica_hawaiibeachesfrontimage

This design reminds me of Vimeo's old home page. (It no longer looks like this today but this screenshot came from when I was the data guy there.) In both cases, the images are not static but moving.

Vimeo-homepage

The tour de force of this visual story is an annotated walk along the Lanikai Beach. Here is a snapshot at one of the stops:

Propublica_hawaiibeaches_1368MokuluaDr_small

This shows a particular homeowner who, according to documents, was permitted to rebuild a destroyed seawall even though officials were supposed to disallow reconstruction in order to protect beaches from eroding. The property is marked on the map above. The image inside the box is a gif showing waves smashing the seawall.

As the reader scrolls down, the image window runs through a carousel of gifs of houses along the beach. The images are synchronized to the reader's progress along the shore. The narrative makes stops at specific houses at which point a text box pops up to provide color commentary.

***

The erosion crisis is shown in this pair of maps.

Propublica_hawaiibeaches_oldnewshoreline-sm

There's some fancy work behind the scenes to patch together images, and estimate the boundaries of th beaches.

***

The following map is notable for its simplicity. There are no unnecessary details and labels. We don't need to know the name of every street or a specific restaurant. Removing excess details makes readers focus on the informative parts. 

Propublica_hawaiibeaches_simplemap-sm

Clicking on the dots brings up more details.

***

Enjoy the entire story here.


Convincing charts showing containment measures work

The disorganized nature of U.S.'s response to the coronavirus pandemic has created a sort of natural experiment that allows data journalists to explore important scientific questions, such as the impact of containment measures on cases and hospitalizations. This New York Times article represents the best of such work.

The key finding of the analysis is beautifully captured by this set of scatter plots:

Policies_cases_hosp_static

Each dot is a state. The cases (left plot) and hospitalizations (right plot) are plotted against the severity of containment measures for November. The negative correlation is unmistakable: the more containment measures taken, the lower the counts.

There are a few features worth noting.

The severity index came from a group at Oxford, and is a number between 0 and 100. The journalists decided to leave out the numerical labels, instead simply showing More and Fewer. This significantly reduces processing time. Readers won't be able to understand the index values anyway without reading the manual.

The index values are doubly encoded. They are first encoded by the location on the horizontal axis and redundantly encoded on the blue-red scale. Ordinarily, I do not like redundant encoding because the reader might assume a third dimension exists. In this case, I had no trouble with it.

The easiest way to see the effect is to ignore the muddy middle and focus on the two ends of the severity index. Those states with the fewest measures - South Dakota, North Dakota, Iowa - are the worst in cases and hospitalizations while those states with the most measures - New York, Hawaii - are among the best. This comparison is similar to what is frequently done in scientific studies, e.g. when they say coffee is good for you, they typically compare heavy drinkers (4 or more cups a day) with non-drinkers, ignoring the moderate and light drinkers.

Notably, there is quite a bit of variability for any level of containment measures - roughly 50 cases per 100,000, and 25 hospitalizations per 100,000. This indicates that containment measures are not sufficient to explain the counts. For example, the hospitalization statistic is affected by the stock of hospital beds, which I assume differ by state.

Whenever we use a scatter plot, we run the risk of xyopia. This chart form invites readers to explain an outcome (y-axis values) using one explanatory variable (on x-axis). There is an assumption that all other variables are unimportant, which is usually false.

***

Because of the variability, the horizontal scale has meaningless precision. The next chart cures this by grouping the states into three categories: low, medium and high level of measures.

Cases_over_time_grouped_by_policies

This set of charts extends the time window back to March 1. For the designer, this creates a tricky problem - because states adapt their policies over time. As indicated in the subtitle, the grouping is based on the average severity index since March, rather than just November, as in the scatter plots above.

***

The interplay between policy and health indicators is captured by connected scatter plots, of which the Times article included a few examples. Here is what happened in New York:

NewYork_policies_vs_cases

Up until April, the policies were catching up with the cases. The policies tightened even after the case-per-capita started falling. Then, policies eased a little, and cases started to spike again.

The Note tells us that the containment severity index is time shifted to reflect a two-week lag in effect. So, the case count on May 1 is not paired with the containment severity index of May 1 but of April 15.

***

You can find the full article here.

 

 

 


Why you should expunge the defaults from Excel or (insert your favorite graphing program)

Yesterday, I posted the following chart in the post about Cornell's Covid-19 case rate after re-opening for in-person instruction.

Redo_junkchats_fraziercornellreopeningsuccess2

This is an edited version of the chart used in Peter Frazier's presentation.

Pfrazier_cornellreopeningupdate

The original chart carries with it the burden of Excel defaults.

What did I change and why?

I switched away from the default color scheme, which ignores the relationships between the two lines. In particular, the key comparison on this chart should be the actual case rate versus the nominal case rate. In addition, the three lines at the top are related as they all come from the same underlying mathematical model. I used the same color but different shades.

Also, instead of placing the legend as far away from the data labels as possible, I moved the line labels next to the data labels.

Instead of daily date labels, I moved to weekly labels, and set the month names on a separate level than the day names.

The dots were removed from the top three lines but I'd have retained them, perhaps with some level of transparency, if I spent more time making the edits. I'd definitely keep the last dot to make it clear that the blue lines contain one extra dot.

***

Every graphing program has defaults, typically computed by some algorithm tuned to the average chart. Don't settle for the average chart. Get rid of any default setting that slows down understanding.

 

 


Everything in Texas is big, but not this BIG

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

Covidtracking_texassquare

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.

Redo_texasdeathsquares_process

The final product:

Redo_texasdeaths_columns

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.

Redo_texasdeaths_distortion

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


On data volume, reliability, uncertainty and confidence bands

This chart from the Economist caught my eye because of the unusual use of color-coded hexagonal tiles.

Economist_lifequalitywealth1

The basic design of the chart is easy to grasp: It relates people's "happiness" to national wealth. The thick black line shows that the average citizen of wealthier countries tends to rate their current life situation better.

For readers alert to graphical details, things can get a little confusing. The horizontal "wealth" axis is shown in log scale, which means that the data on the right side of the chart have been compressed while the data on the left side of the chart have been stretched out. In other words, the curve in linear scale is much flatter than depicted.

Redo_economistlifesatisfaction_linear

One thing you might notice is how poor the fit of the line is at both ends. Singapore and Afghanistan are clearly not explained by the fitted line. (That said, the line is based on many more dots than those eight we can see.) Moreover, because countries are widely spread out on the high end of the wealth axis, the fit is not impressive. Log scales tend to give a false impression of the tightness of fit, as I explained before when discussing coronavirus case curves.

***

The hexagonal tiles replace the more typical dot scatter or contour shading. The raw data consist of results from polls conducted in different countries in different years. For each poll, the analyst computes the average life satisfaction score for that country in that year. From national statistics, the analyst pulls out that country's GDP per capita in that year. Thus, each data point is a dot on the canvass. A few data points are shown as black dots. Those are for eight highlighted countries for the year 2018.

The black line is fitted to the underlying dot scatter and summarizes the correlation between average wealth and average life satisfaction. Instead of showing the scatter, this Economist design aggregates nearby dots into hexagons. The deepest red hexagon, sandwiched between Finland and the US, contains about 60-70 dots, according to the color legend.

These details are tough to take in. It's not clear which dots have been collected into that hexagon: are they all Finland or the U.S. in various years, or do they include other countries? Each country is represented by multiple dots, one for each poll year. It's also not clear how much variation there exists within a country across years.

***

The hexagonal tiles presumably serve the same role as a dot scatter or contour shading. They convey the amount of data supporting the fitted curve along its trajectory. More data confers more reliability.

For this chart, the hexagonal tiles do not add any value. The deepest red regions are those closest to the black line so nothing is actually lost by showing just the line and not the tiles.

Redo_economistlifesatisfaction_nohex

Using the line chart obviates the need for readers to figure out the hexagons, the polls, the aggregation, and the inevitable unanswered questions.

***

An alternative concept is to show the "confidence band" or "error bar" around the black line. These bars display the uncertainty of the data. The wider the band, the less certain the analyst is of the estimate. Typically, the band expands near the edges where we have less data.

Here is conceptually what we should see (I don't have the underlying dataset so can't compute the confidence band precisely)

Redo_economistlifesatisfaction_confband

The confidence band picture is the mirror image of the hexagonal tiles. Where the poll density is high, the confidence band narrows, and where poll density is low, the band expands.

A simple way to interpret the confidence band is to find the country's wealth on the horizontal axis, and look at the range of life satisfaction rating for that value of wealth. Now pick any number between the range, and imagine that you've just conducted a survey and computed the average rating. That number you picked is a possible survey result, and thus a valid value. (For those who know some probability, you should pick a number not at random within the range but in accordance with a Bell curve, meaning picking a number closer to the fitted line with much higher probability than a number at either edge.)

Visualizing data involves a series of choices. For this dataset, one such choice is displaying data density or uncertainty or neither.


Working with multiple dimensions, an example from Germany

An anonymous reader submitted this mirrored bar chart about violent acts by extremists in the 16 German states.

Germanextremists_bars

At first glance, this looks like a standard design. On a second look, you might notice what the reader discovered- the chart used two different scales, one for each side. The left side (red) depicting left-wing extremism is artificially compressed relative to the right side (blue). Not sure if this reflects the political bias of the publication - but in any case, this distortion means the only way to consume this chart is to read the numbers.

Even after fixing the scales, this design is challenging for the reader. It's unnatural to compare two years by looking first below then above. It's not simple to compare across states, and even harder to compare left- and right-wing extremism (due to mirroring).

The chart feels busy because the entire dataset is printed on it. I appreciate not including a redundant horizontal axis. (I wonder if the designer first removed the axis, then edited the scale on one side, not realizing the distortion.) Another nice touch, hidden in the legend, is the country totals.

I present two alternatives.

The first is a small-multiples "bumps chart".

Redo_junkcharts_germanextremists_sidebysidelines

Each plot presents the entire picture within a state. You can see the general level of violence, the level of left- and right-wing extremism, and their year-on-year change. States can be compared holistically.

Several German state names are rather long, so I explored a horizontal orientation. In this case, a connected dot plot may be more appropriate.

Redo_junkcharts_germanextremists_dots

The sign of a good multi-dimensional visual display is whether readers can easily learn complex relationships. Depending on the question of interest, the reader can mentally elevate parts of this chart. One can compare the set of blue arrows to the set of red arrows, or focus on just blue arrows pointing right, or red arrows pointing left, or all arrows for Berlin, etc.

 

[P.S. Anonymous reader said the original chart came from the Augsburger newspaper. This link in German contains more information.]


Presented without comment

Weekend assignment - which of these tells the story better?

Ourworldindata_cases_log

Or:

Ourworldindata_cases_linear

The cop-out answer is to say both. If you must pick one, which one?

***

When designing a data visualization as a living product (not static), you'd want a design that adapts as the data change.