Junk Charts

This chart advises webpages to add more words

A reader sent me the following chart. In addition to the graphical glitch, I was asked about the study's methodology.

I was able to trace the study back to this page. The study uses a line chart instead of the bar chart with axis not starting at zero. The line shows that web pages ranked higher by Google on the first page tend to have more words, i.e. longer content may help with Google ranking.

On the bar chart, Position 1 is more than 6 times as big as Position 10, if one compares the bar areas. But it's really only 20% larger in the data.

In this case, even the line chart is misleading. If we extend the Google Position to 20, the line would quickly dip below the horizontal axis if the same trend applies.

The line chart includes too much grid, one of Tufte's favorite complaints. The Google position is an integer and yet the chart's gridlines imply that 0.5 rank is possible.

Any chart of this data should supply information about the variance around these average word counts. Would like to see a side-by-side box plot, for example.

Another piece of context is the word counts for results on the second or third pages of Google results. Where are the short pages?

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Turning to methodology, we learn that the research team analyzed 1 million pages of Google search results, and they also "removed outliers from our data (pages that contained fewer than 51 words and more than 9999 words)."

When you read a line like this, you have to ask some questions:

How do they define "outlier"? Why do they choose 51 and 9,999 as the cut-offs?

What proportion of the data was removed at either end of the distribution?

If these proportions are small, then the outliers are not going to affect that average word count by much, and thus there is no point to their removal. If they are large, we'd like to see what impact removing them might have.

In any case, the median is a better number to use here, or just show us the distribution, not just the average number.

It could well be true that Google's algorithm favors longer content, but we need to see more of the data to judge.

 

 

Trump resistance chart: cleaning up order, importance, weight, paneling

Vox featured the following chart when discussing the rise of resistance to President Trump within the GOP.

The chart is composed of mirrored bar charts. On the left side, with thicker pink bars that draw more attention, the design depicts the share of a particular GOP demographic segment that said they'd likely vote for a Trump challenger, according to a Morning Consult poll.

This is the primary metric of interest, and the entire chart is ordered by descending values from African Americans who are most likely (67%) to turn to a challenger to those who strongly support Trump and are the least likely (17%) to turn to someone else.

The right side shows the importance of each demographic, measured by the share of GOP. The relationship between importance and likelihood to defect from Trump is by and large negative but that fact takes a bit of effort to extract from this mirrored bar chart arrangement.

The subgroups are not complete. For example, the only ethnicity featured is African Americans. Age groups are somewhat more complete with under 18 being the only missing category.

The design makes it easy to pick off the most disaffected demographic segments (and the least, from the bottom) but these are disparate segments, possibly overlapping.

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One challenge of this data is differentiating the two series of proportions. In this design, they use visual cues, like the height and width of the bars, colors, stacked vs not, data labels. Visual variety comes to the rescue.

Also note that the designer compensated for the lack of stacking on the left chart by printing data labels.

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When reading this chart, I'm well aware that segments like urban residents, income more than $100K, at least college educated are overlapping, and it's hard to interpret the data the way it's been presented.

I wanted to place the different demographics into their natural groups, such as age, income, urbanicity, etc. Such a structure also surfaces demographic patterns, e.g. men are slightly more disaffected than women (not significant), people earning $100K+ are more unhappy than those earning $50K-.

Further, I'd like to make it easier to understand the importance factor - the share of GOP. Because the original form orders the demographics according to the left side, the proportions on the right side are jumbled.

Here is a draft of what I have in mind:

The widths of the line segments show the importance of each demographic segment. The longest line segments are toward the bottom of the chart (< 40% likely to vote for Trump challenger).

 

The ebb and flow of an effective dataviz showing the rise and fall of GE

A WSJ chart caught my eye the other day – I spotted someone looking at it in a coffee shop, and immediately got a hold of a copy. The chart plots the ebb and flow of GE’s revenues from the 1980s to the present.

What grabbed my attention? The less-used chart form, and the appealing but not too gaudy color scheme.

The chart presents a highly digestible view of the structure of GE’s revenues. We learn about GE’s major divisions, as well as how certain segments split from or merged with others over time. Major acquisitions and divestitures are also depicted; if these events are the main focus, the designer should find ways to make these moments stand out more.

An interesting design decision concerns the sequence of the divisions. One possible order is by increasing or decreasing importance, typically indicated by proportional revenues. This is complicated by the changing nature of the business over the decades. So financial services went from nothing to the largest division by far to almost disappearing.

The sequencing need not be data-driven; it can be design-constrained. The merging and splitting of business units are conveyed via linking arrows. Longer arrows are unsightly, and meshes of arrows are confusing.

On this chart, the long arrow pointing from the orange to the gray around 2004 feels out of place. What if the financial services block is moved to the right of the consumer block? That will significantly shorten the long arrow. It won’t create other entanglements as the media block is completely disjoint and there are no other arrows tying financial services to another division.

 

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To improve readability, the bars are spaced out horizontally. The addition of whitespace distorts the proportionality. So, in 2001, the annotation states that financial services (orange) accounted for “about half of the revenues,” which is directly contradicted by the visual perception – readers find the orange bar to be clearly shorter than the total length of the other bars. This is a serious deficiency of the chart form but this chart conveys the "ebb and flow" very well.

Appreciating population mountains

Tim Harford tweeted about a nice project visualizing of the world's distribution of population, and wondered why he likes it so much. 

That's the question we'd love to answer on this blog! Charts make us emotional - some we love, some we hate. We like to think that designers can control those emotions, via design choices.

I also happen to like the "Population Mountains" project as well. It fits nicely into a geography class.

1. Chart Form

The key feature is to adopt a 3D column chart form, instead of the more conventional choropleth or dot density. The use of columns is particularly effective here because it is natural - cities do tend to expand vertically upwards when ever more people cramp into the same amount of surface area. 

Imagine the same chart form is used to plot the number of swimming pools per square meter. It just doesn't make the same impact. 

2. Color Scale

The designer also made judicious choices on the color scale. The discrete, 5-color scheme is a clear winner over the more conventional, continuous color scale. The designer made a deliberate choice because most software by default uses a continuous color scale for continuous data (population density per square meter).

Also, notice that the color intervals in 5-color scale is not set uniformly because there is a power law in effect - the dense areas are orders of magnitude denser than the sparsely populated areas, and most locations are low-density. 

These decisions have a strong influence on the perception of the information: it affects the heights of the peaks, the contrasts between the highs and lows, etc. It also injects a degree of subjectivity into the data visualization exercise that some find offensive.

3. Background

The background map is stripped of unnecessary details so that the attention is focused on these "population mountains". No unnecessary labels, roads, relief, etc. This demonstrates an acute awareness of foreground/background issues.

4. Insights on the "shape" of the data 

The article makes the following comment:

What stands out is each city’s form, a unique mountain that might be like the steep peaks of lower Manhattan or the sprawling hills of suburban Atlanta. When I first saw a city in 3D, I had a feel for its population size that I had never experienced before.

I'd strike out population size and replace with population density. In theory, the sum of the areas of the columns in any given surface area gives you the "population size" but given the fluctuating heights of these columns, and the different surface areas (sprawls) of different cities, it is an Olympian task to estimate the volumes of the population mountains!

The more salient features of these mountains, most easily felt by readers, are the heights of the peak columns, the sprawl of the cities, and the general form of the mass of columns. The volume of the mountain is one of the tougher things to see. Similarly, the taller 3D columns hide what's behind them, and you'd need to spin and rotate the map to really get a good feel.

Here is the contrast between Paris and London, with comparable population sizes. You can see that the population in Paris (and by extension, France) is much more concentrated than in the U.K. This difference is a surprise to me.

5. Sourcing

Some of the other mountains, especially those in India and China, look a bit odd to me, which leads me to wonder about the source of the data. This project has a very great set of footnotes that not only point to the source of the data but also a discussion of its limitations, including the possibility of inaccuracies in places like India and China. 

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Check out Population Mountains!

 

 

 

 

 

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.

 

No Latin honors for graphic design

This chart appeared on a recent issue of Princeton Alumni Weekly.

If you read the sister blog, you'll be aware that at most universities in the United States, every student is above average! At Princeton,  47% of the graduating class earned "Latin" honors. The median student just missed graduating with honors so the honors graduate is just above average! The 47% number is actually lower than at some other peer schools - at one point, Harvard was giving 90% of its graduates Latin honors.

Side note: In researching this post, I also learned that in the Senior Survey for Harvard's Class of 2018, two-thirds of the respondents (response rate was about 50%) reported GPA to be 3.71 or above, and half reported 3.80 or above, which means their grade average is higher than A-.  Since Harvard does not give out A+, half of the graduates received As in almost every course they took, assuming no non-response bias.

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Back to the chart. It's a simple chart but it's not getting a Latin honor.

Most readers of the magazine will not care about the decimal point. Just write 18.9% as 19%. Or even 20%.

The sequencing of the honor levels is backwards. Summa should be on top.

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Warning: the remainder of this post is written for graphics die-hards. I go through a bunch of different charts, exploring some fine points.

People often complain that bar charts are boring. A trendy alternative when it comes to count or percentage data is the "pictogram."

Here are two versions of the pictogram. On the left, each percent point is shown as a dot. Then imagine each dot turned into a square, then remove all padding and lines, and you get the chart on the right, which is basically an area chart.

The area chart is actually worse than the original column chart. It's now much harder to judge the areas of irregularly-shaped pieces. You'd have to add data labels to assist the reader.

The 100 dots is appealing because the reader can count out the number of each type of honors. But I don't like visual designs that turn readers into bean-counters.

So I experimented with ways to simplify the counting. If counting is easier, then making comparisons is also easier.

Start with this observation: When asked to count a large number of objects, we group by 10s and 5s.

So, on the left chart below, I made connectors to form groups of 5 or 10 dots. I wonder if I should use different line widths to differentiate groups of five and groups of ten. But the human brain is very powerful: even when I use the same connector style, it's easy to see which is a 5 and which is a 10.

On the left chart, the organizing principles are to keep each connector to its own row, and within each category, to start with 10-group, then 5-group, then singletons. The anti-principle is to allow same-color dots to be separated. The reader should be able to figure out Summa = 10+3, Magna = 10+5+1, Cum Laude = 10+5+4.

The right chart is even more experimental. The anti-principle is to allow bending of the connectors. I also give up on using both 5- and 10-groups. By only using 5-groups, readers can rely on their instinct that anything connected (whether straight or bent) is a 5-group. This is powerful. It relieves the effort of counting while permitting the dots to be packed more tightly by respective color.

Further, I exploited symmetry to further reduce the counting effort. Symmetry is powerful as it removes duplicate effort. In the above chart, once the reader figured out how to read Magna, reading Cum Laude is simplified because the two categories share two straight connectors, and two bent connectors that are mirror images, so it's clear that Cum Laude is more than Magna by exactly three dots (percentage points).

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Of course, if the message you want to convey is that roughly half the graduates earn honors, and those honors are split almost even by thirds, then the column chart is sufficient. If you do want to use a pictogram, spend some time thinking about how you can reduce the effort of the counting!

 

 

 

 

 

Two views of earthquake occurrence in the Bay Area

This article has a nice description of earthquake occurrence in the San Francisco Bay Area. A few quantities are of interest: when the next quake occurs, the size of the quake, the epicenter of the quake, etc. The data graphic included in the article fails the self-sufficiency test: the only way to read this chart is to read out the entire data set - in other words, the graphical details have no utility.

The article points out the clustering of earthquakes. In particular, there is a 68-year "quiet period" between 1911 and 1979, during which no quakes over 6.0 in size occurred. The author appears to have classified quakes into three groups: "Largest" which are those at 6.5 or over; "Smaller but damaging" which are those between 6.0 and 6.5; and those below 6.0 (not shown).

For a more standard and more effective visualization of this dataset, see this post on a related chart (about avian flu outbreaks). The post discusses a bubble chart versus a column chart. I prefer the column chart.

This chart focuses on the timing of rare events. The time between events is not as easy to see. 

What if we want to focus on the "quiet years" between earthquakes? Here is a visualization that addresses the question: when will the next one hit us?

 

 

Two good charts can use better titles

NPR has this chart, which I like:

It's a small multiples of bumps charts. Nice, clear labels. No unnecessary things like axis labels. Intuitive organization by Major Factor, Minor Factor, and Not a Factor.

Above all, the data convey a strong, surprising, message - despite many high-profile gun violence incidents this year, some Democratic voters are actually much less likely to see guns as a "major factor" in deciding their vote!

Of course, the overall importance of gun policy is down but the story of the chart is really about the collapse on the Democratic side, in a matter of two months.

The one missing thing about this chart is a nice, informative title: In two months, gun policy went from a major to a minor issue for some Democratic voters.

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 I am impressed by this Financial Times effort:

The key here is the analysis. Most lazy analyses compare millennials to other generations but at current ages but this analyst looked at each generation at the same age range of 18 to 33 (i.e. controlling for age).

Again, the data convey a strong message - millennials have significantly higher un(der)employment than previous generations at their age range. Similar to the NPR chart above, the overall story is not nearly as interesting as the specific story - it is the pink area ("not in labour force") that is driving this trend.

Specifically, millennial unemployment rate is high because the proportion of people classified as "not in labour force" has doubled in 2014, compared to all previous generations depicted here. I really like this chart because it lays waste to a prevailing theory spread around by reputable economists - that somehow after the Great Recession, demographics trends are causing the explosion in people classified as "not in labor force". These people are nobodies when it comes to computing the unemployment rate. They literally do not count! There is simply no reason why someone just graduated from college should not be in the labour force by choice. (Dean Baker has a discussion of the theory that people not wanting to work is a long term trend.)

The legend would be better placed to the right of the columns, rather than the top.

Again, this chart benefits from a stronger headline: BLS Finds Millennials are twice as likely as previous generations to have dropped out of the labour force.

 

 

 

 

Discoloring the chart to re-discover its plot

Today's chart comes from Pew Research Center, and the big question is why the colors?

The data show the age distributions of people who believe different religions. It's a stacked bar chart, in which the ages have been grouped into the young (under 15), the old (60 plus) and everyone else. Five religions are afforded their own bars while "folk" religions are grouped as one, and so have "other" religions. There is even a bar for the unaffiliated. "World" presumably is the aggregate of all the other bars, weighted by the popularity of each religion group.

So far so good. But what is it that demands 9 colors, and 27 total shades? In other words, one shade for every data point on this chart.

Here is a more restrained view:

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Let's follow the designer's various decisions. The choice of those age groups indicates that the story is really happening at the "margins": Muslims and Hindus have higher proportions of younger followers while Jews and Buddhists have higher concentrations of older followers.

Therein lies the problem. Because of the lengths, their central locations, and the tints, the middle section of each bar is the most eye-catching: the reader is glancing at the wrong part of the chart.

So, let me fix this by re-ordering the three panels:

Is there really a need to draw those gray bars? The middle age group (grab-all) only exists to assure readers that everyone who's supposed to be included has been included. Why plot it?

The above chart says "trust me, what isn't drawn here constitutes the remaining population, and the whole adds to 100%."

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Another issue of these charts, exacerbated by inflexible software defaults, is the forced choice of imbuing one variable with a super status above the others. In the Pew chart, the rows are ordered by decreasing proportion of the young age group, except for the "everyone" group pinned as the bottom row. Therefore, the green bars (old age group) are not in a particular order, its pattern much harder to comprehend.

In the final version, I break the need to keep bars of the same religion on the same row:

Five colors are used. Three of them are used to cluster similar religions: Muslims and Hindus (in blue) have higher proportions of the young compared to the world average (gray) while the religions painted in green have higher proportions of the old. Christians (in orange) are unusual in that the proportions are higher than average in both young and old age groups. Everyone and unaffiliated are given separate colors.

The colors here serve two purposes: connecting the two panels, and revealing the cluster structure.

 

 

 

 

Graphical evidence that Bernie got shafted

Note that I am placing this post under Light Entertainment.