Junk Charts

Message-first visualization

Sneaky Pete via Twitter sent me the following chart, asking for guidance:

This is a pretty standard dataset, frequently used in industry. It shows a breakdown of a company's profit by business unit, here classified by "state". The profit projection for the next year is measured on both absolute dollar terms and year-on-year growth.

Since those two metrics have completely different scales, in both magnitude and unit, it is common to use dual axes. In the case of the Economist, they don't use dual axes; they usually just print the second data series in its own column.

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I first recommended looking at the scatter plot to see if there are any bivariate patterns. In this case, not much insights are provided via the scatter.

From there, I looked at the data again, and ended up with the following pair of bumps charts (slopegraphs):

A key principle I used is message-first. That is to say, the designer should figure out what message s/he wants to convey via the visualization, and then design the visualization to convey that message.

A second key observation is that the business units are divided into two groups, the two large states (A and F) and the small states (B to E). This is a Pareto principle that very often applies to real-world businesses, i.e. a small number of entities contribute most of the revenues (or profits). It is very likely that these businesses are structured to serve the large and small states differently, and so the separation onto two charts mirrors the internal structure.

Then, within each chart, there is a message. For the large states, it looks like state F is projected to overtake state A next year. That is a big deal because we're talking about the largest unit in the entire company.

For the small states, the standout is state B, decidedly more rosy than the other three small states with similar projected growth rates.

Note also I chose to highlight the actual dollar profits, letting the growth rates be implied in the slopes. Usually, executives are much more concerned about hitting a dollar value than a growth rate target. But that, of course, depends on your management's preference.

 

Finding simple ways to explain complicated data and concepts, using some Pew data

A reader submitted the following chart from Pew Research for discussion.

The reader complained that this chart was difficult to comprehend. What are some of the reasons?

The use of color is superfluous. Each line is a "cohort" of people being tracked over time. Each cohort is given its own color or hue. But the color or hue does not signify much.

The dotted lines. This design element requires a footnote to explain. The reader learns that some of the numbers on the chart are projections because those numbers pertain to time well into the future. The chart was published in 2014, using historical data so any numbers dated 2014 or after (and even some data before 2014) will be projections. The data are in fact encoded in the dots, not the slopes. Look at the cohort that has one solid line segment and one dotted line segment - it's unclear which of those three data points are projections, and which are experienced.

The focus on within-cohort trends. The line segments indicate the desire of the designer to emphasize trends within each cohort. However, it's not clear what the underlying message is. It may be that more and more people are not getting married (i.e. fewer people are getting married). That trend affects each of the three age groups - and it's easier to paint that message by focusing on between-cohort trends.

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Here is a chart that emphasizes the between-cohort trends.

A key decision is to not mix oil and water. The within-cohort analysis is presented in its own chart, next to the between-cohort analysis. It turns out that some of the gap between cohorts can be explained by people deferring marriage to later in life. The steep line on the right indicates that a bigger proportion of people now gets married between 35 and 44 than in previous cohorts.

I experimented a bit with the axes here. Several pie charts are used in lieu of axis labels. I also plotted a dual axis with the proportion of unmarried on the one side, and the corresponding proportion of married on the other side.

Big Macs in Switzerland are amazing, according to my friend

Note for those in or near Zurich: I'm giving a Keynote Speech tomorrow morning at the Swiss Statistics Meeting (link). Here is the abstract:

The best and the worst of data visualization share something in common: these graphics provoke emotions. In this talk, I connect the emotional response of readers of data graphics to the design choices made by their creators. Using a plethora of examples, collected over a dozen years of writing online dataviz criticism, I discuss how some design choices generate negative emotions such as confusion and disbelief while other choices elicit positive feelings including pleasure and eureka. Important design choices include how much data to show; which data to highlight, hide or smudge; what research question to address; whether to introduce imagery, or playfulness; and so on. Examples extend from graphics in print, to online interactive graphics, to visual experiences in society.

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The Big Mac index seems to never want to go away. Here is the latest graphic from the Economist, saying what it says:

The index never made much sense to me. I'm in Switzerland, and everything here is expensive. My friend, who is a U.S. transplant, seems to have adopted McDonald's as his main eating-out venue. Online reviews indicate that the quality of the burger served in Switzerland is much better than the same thing in the States. So, part of the price differential can be explained by quality. The index also confounds several other issues, such as local inflation and exchange rate

Now, on to the data visualization, which is primarily an exercise in rolling one's eyeballs. In order to understand the red and blue line segments, our eyes have to hop over the price bubbles to the top of the page. Then, in order to understand the vertical axis labels, unconventionally placed on the right side, our eyes have to zoom over to the left of the page, and search for the line below the header of the graph. Next, if we want to know about a particular country, our eyes must turn sideways and scan from bottom up.

Here is a different take on the same data:

I transformed the data as I don't find it compelling to learn that Russian Big Macs are 60% less than American Big Macs. Instead, on my chart, the reader learns that the price paid for a U.S. Big Mac will buy him/her almost 2 and a half Big Macs in Russia.

The arrows pointing left indicate that in most countries, the values of their currencies are declining relative to the dollar from 2017 to 2018 (at least by the Big Mac Index point of view). The only exception is Turkey, where in 2018, one can buy more Big Macs equivalent to the price paid for one U.S. Big Mac. compared to 2017.

The decimal differences are immaterial so I have grouped the countries by half Big Macs.

This example demonstrates yet again, to make good data visualization, one has to describe an interesting question, make appropriate transformations of the data, and then choose the right visual form. I describe this framework as the Trifecta - a guide to it is here.

(P.S. I noticed that Bitly just decided unilaterally to deactivate my customized Bitly link that was configured years and years ago, when it switched design (?). So I had to re-create the custom link. I have never grasped  why "unreliability" is a feature of the offering by most Tech companies.)

Headless people invade London, chart claims

Some 10 days ago, Mike B. on Twitter forwarded me this chart from Time Out:

Mike added: "Wow, decapitations in London have really gone up!"

A closer look at the chart reveals more problems.

The axis labels are in the wrong places. It appears that the second dot represents 1940 and the second-last dot represents 2020. There are 12 dots between those two labels, corresponding to three evenly-spaced labels. This works out to be  6.154 years between each dot, and 20.0 years between labels. The labels actually do not fall on top of the dots but between them! We have to conclude that the axis labels were independently applied onto the chart.

I found another chart of London's population growth from here.

Superimposing the two charts:

The lowest point seemed to be around 1990-ish in the second chart but in the Time Out chart, the reader most likely assumes it occurred around 2000.

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What else? The Time Out chart has no vertical axis, and therefore, the chart fails to deliver any data to the reader: how many people actually live in London? This style - chart with no vertical axis - has been made popular by Google (Google Trends, etc.). 

Further, one should differentiate between historical data and projections. It seems like everything on the right side that exists above the previous peak in 1940 is projected.

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Just for giggles, I made this:

 

 

Lines, gridlines, reference lines, regression lines, the works

This post is part 2 of an appreciation of the chart project by Google Newslab, advised by Alberto Cairo, on the gender and racial diversity of the newsroom. Part 1 can be read here.

In the previous discussion, I left out the following scatter bubble plot.

This plot is available in two versions, one for gender and one for race. The key question being asked is whether the leadership in the newsroom is more or less diverse than the rest of the staff.

The story appears to be a happy one: in many newsrooms, the leadership roughly reflects the staff in terms of gender distribution (even though both parts of the whole compare disfavorably to the gender ratio in the neighborhoods, as we saw in the previous post.)

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Unfortunately, there are a few execution problems with this scatter plot.

First, take a look at the vertical axis labels on the right side. The labels inform the leadership axis. The mid-point showing 50-50 (parity) is emphasized with the gray band. Around the mid-point, the labels seem out of place. Typically, when the chart contains gridlines, we expect the labels to sit right around each gridline, either on top or just below the line. Here the labels occupy the middle of the space between successive gridlines. On closer inspection, the labels are correctly affixed, and the gridlines  drawn where they are supposed to be. The designer chose to show irregularly spaced labels: from the midpoint, it's a 15% jump on either side, then a 10% jump.

I find this decision confounding. It also seems as if two people have worked on these labels, as there exists two patterns: the first is "X% Leaders are Women", and second is "Y% Female." (Actually, the top and bottom labels are also inconsistent, one using "women" and the other "female".)

The horizontal axis? They left out the labels. Without labels, it is not possible to interpret the chart. Inspecting several conveniently placed data points, I figured that the labels on the six vertical gridlines should be 25%, 35%, ..., 65%, 75%, in essence the same scale as the vertical axis.

Here is the same chart with improved axis labels:

Re-labeling serves up a new issue. The key reference line on this chart isn't the horizontal parity line: it is the 45-degree line, showing that the leadership has the same proprotion of females as the rest of the staff. In the following plot (right side), I added in the 45-degree line. Note that it is positioned awkwardly on top of the grid system. The culprit is the incompatible gridlines.

 

The solution, as shown below, is to shift the vertical gridlines by 5% so that the 45-degree line bisects every grid cell it touches.

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Now that we dealt with the purely visual issues, let me get to a statistical issue that's been troubling me. It's about that yellow line. It's supposed to be a regression line that runs through the points.

Does it appear biased downwards to you? It just seems that there are too many dots above and not enough below. The distance of the furthest points above also appears to be larger than that of the distant points below.

How do we know the line is not correct? Notice that the green 45-degree line goes through the point labeled "AVERAGE." That is the "average" newsroom with the average proportion of female staff and the average proportion of leadership staff. Interestingly, the average falls right on the 45-degree line.

In general, the average does not need to hit the 45-degree line. The average, however, does need to hit the regression line! (For a mathematical explanation, see here.)

Note the corresponding chart for racial diversity has it right. The yellow line does pass through the average point here:

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In practice, how do problems seep into dataviz projects? It's the fact that you don't get to the last chart via a clean, streamlined process but that you pass through a cycle of explore-retrench-synthesize, frequently bouncing ideas between several people, and it's challenging to keep consistency!

And let me repeat my original comment about this project - the key learning here is how they took a complex dataset with many variables, broke it down into multiple parts addressing specific problems, and applied the layering principle to make each part of the project digestible.

 

 

The tech world in which everyone is below average

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

What's wrong with this map?

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

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

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

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Here is the second chart.

What's wrong with these lines?

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

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

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

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

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

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

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

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

Here I index all lines to the earliest year.

 

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

 

 

Looking above the waist, dataviz style

I came across this chart on NYU's twitter feed. 

Growth has indeed been impressive; the dataviz less so. Here's the problem with not starting the vertical scale of a column chart at zero:

In a column chart, the heights of the columns should be proportional to the data. Here they are misaligned because an equal amount has been chopped off below 30,000 from all columns. The light purple that I layered on top of the chart presents the correct heights of the columns, assuming that the first column for 2007 indeed properly encoded the data.

The dark purple top of each column represents the "lie factor." It is the amount of exaggeration created by chopping off those legs. The lie factor is of Ed Tufte coinage.

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The designer probably wanted to show the year-to-year trend more starkly. Doubling the number of applications in 10 years is pretty impressive. The solution is not to chop off the legs but to look above the waist. You can't fix the column chart but you can switch to a line chart, as follows:

In a line chart, we are mostly concerned with the changing slope of the line segments going from year to year. The slopes encode the year-on-year growth rates. 

 

A look at how the New York Times readers look at the others

The above chart, when it was unveiled at the end of November last year, got some mileage on my Twitter feed so it got some attention. A reader, Eric N., didn't like it at all, and I think he has a point.

Here are several debatable design decisions.

The chart uses an inverted axis. A tax cut (negative growth) is shown on the right while a tax increase is shown on the left. This type of inversion has gotten others in trouble before, namely, the controversy over the gun deaths chart (link). The green/red color coding is used to signal the polarity although some will argue this is bad for color-blind readers. The annotation below the axis is probably the reason why I wasn't confused in the first place but the other charts further down the page do not repeat the annotation, and that's where the interpretation of -$2,000 as a tax increase is unnatural!

The chart does not aggregate the data. It plots 25,000 households with 25,000 points. Because of the variance of the data, it's hard to judge trends. It's easy enough to see that there are more green dots than red but how many more? 10 percent, 20 percent, 40 percent? It's also hard to answer any specific questions, say, about households with a certain range of incomes. There are various ways to aggregate the data, such as heatmaps, histograms, and so on.

For those used to looking at scientific charts, the x- and y-axes are reversed. By convention, we'd have put the income ranges on the horizontal axis and the tax changes (the "outcome" variable) on the vertical axis.

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The text labels do not describe the data patterns on the chart so much as they offer additional information. To see this, remove the labels as I have done below. Try adding the labels based on what is shown on the chart.

Perhaps it's possible to illustrate those insights with a set of charts.

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While reading this chart, I kept wondering how those 25,000 households were chosen. This is a sample of  households. The methodology is explained in a footnote, which describes the definition of "middle class" but unfortunately, they forgot to tell us how the 25,000 households were chosen from all such middle-class households.

The decision to omit the households with income below $40,000 needs more explanation as it usurps the household-size adjustment. Also, it's not clear that the impact of the tax bill on the households with incomes between $20-40K can be assumed the same as for those above $40K.

Are the 25,000 households is a simple random sample of all "middle class" households or are they chosen in some ways to represent the relative counts? It's also useful to know if they applied the $40K cutoff before or after selecting the 25,000 households. 

Ironically, the media kit of the Times discloses an affluent readership with median household income of almost $190K so it appears that the majority of readers are not represented in the graphic at all!

 

Three pies and a bar: serving visual goodness

If you are not sick of the Washington Post article about friends (not) letting friends join the other party, allow me to write yet another post on, gasp, that pie chart. And sorry to have kept reader Daniel L. waiting, as he pointed out, when submitting this chart to me, that he had tremendous difficulty understanding it:

 

This is not one pie but six pies on a platter. There are two sources of confusion: first, the repeated labels of Republicans and Democrats to refer to different groups of people; and second, the indecision between using two or four categories of "how many".

Let me begin by re-ordering and re-labeling the chart:

From this version, one can pull out the key messages of the analysis. (A) Most voters, regardless of party, have mostly friends from the same party. and (B) Republicans are more likely to have more friends from the other party than Democrats. A third, but really not that interesting, point is that regardless of party, people have about the same likelihood to befriend Independents.

In visualization, less is more is frequently appropriate. So, here is a view of the same chart, using two categories instead of four.

The added advantage is only two required colors, and thus even grayscale can work.

The new arrangement of the pie platter makes it clear that there really isn't that much difference between Republican and Democratic voters along this dimension. Thus, visualizing the aggregate gets us to the same place.

After three servings of pies, the reader might be craving some energy bars. 

One can say that for very simple data like this, pie charts are acceptable. However, the stacked bar is better.

Thanks again Daniel, and it's a pleasure to serve you!

Lop-sided precincts, a visual exploration

In the last post, I discussed one of the charts in the very nice Washington Post feature, delving into polarizing American voters. See the post here. (Thanks again Daniel L.)

Today's post is inspired by the following chart (I am  showing only the top of it - click here to see the entire chart):

The chart plots each state as a separate row, so like most such charts, it is tall. The data analysis behind the chart is fascinating and unusual, although I find the chart harder to grasp than expected. The analyst starts with precinct-level data, and determines which precincts were "lop-sided," defined as having a winning margin of over 50 percent for the winner (either Trump or Clinton). The analyst then sums the voters in those lop-sided precincts, and expresses this as a percent of all voters in the state.

For example, in Alabama, the long red bar indicates that about 48% of the state's voters live in lop-sided precincts that went for Trump. It's important to realize that not all such people voted for Trump - they happened to live in precincts that went heavily for Trump. Interestingly, about 12% of the states voters reside in precincts that went heavily for Clinton. Thus, overall, 60% of Alabama's voters live in lop-sided precincts.

This is more sophisticated than the usual analysis that shows up in journalism.

The bar chart may confuse readers for several reasons:

• The horizontal axis is labeled "50-point plus margin for Trump/Clinton" and has values from 0% to 40-60% range. This description seemingly infers the values being plotted as winning margins. However, the sub-header tells readers that the data values are percentages of total voters in the state.
• The shades of colors are not explained. I believe the dark shade indicates the winning party in each state, so Trump won Alabama and Clinton, California. The addition of this information allows the analysis to become multi-dimensional. It also reveals that the designer wants to address how lop-sided precincts affect the outcome of the election. However, adding shade in this manner effectively turns a two-color composition into a four-color composition, adding to the processing load.
• The chart adopts what Howard Wainer calls the "Alabama first"  ordering. This always messes up the designer's message because the alphabetical order typically does not yield a meaningful correlation.

The bars are facing out from the middle, which is the 0% line. This arrangement is most often used in a population pyramid, and used when the designer feels it important to let readers compare the magnitudes of two segments of a population. I do not feel that the Democrat versus Republican comparison within each state is crucial to this chart, given that most states were not competitive.

What is more interesting to me is the total proportion of voters who live in these lop-sided precincts. The designer agrees on this point, and employs bar stacking to make this point. This yields some amazing insights here: several Democratic strongholds such as Massachusetts surprisingly have few lop-sided precincts.

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Here then is a remake of the chart according to my priorities. Click here for the full chart.

The emphasis is on the total proportion of voters in lop-sided precincts. The states are ordered by that metric from most lop-sided to least. This draws out an unexpected insight: most red states have a relatively high proportion of votesr in lop-sided precincts (~ 30 to 40%) while most blue states - except for the quartet of Maryland, New York, California and Illinois - do not exhibit such demographic concentration.

The gray/grey area offers a counterpoint, that most voters do not live in lop-sided districts.

P.S. I should add that this is one of those chart designs that frustrate standard - I mean, point-and-click - charting software because I am placing the longest bar segments on the left, regardless of color.