Junk Charts

Three estimates, two differences trip up an otherwise good design

Reader Fernando P. was baffled by this chart from the Perception Gap report by More in Common. (link to report)

Overall, this chart is quite good. Its flaws are subtle. There is so much going on, perhaps even the designer found it hard to keep level.

The title is "Democrat's Perception Gap" which actually means the gap between Democrats' perception of Republicans and Republican's self-reported views. We are talking about two estimates of Republican views. Conversely, in Figure 2 (not shown), the "Republican's Perception Gap" describes two estimates of Democrat views.

The gap is visually shown as the gray bar between the red dot and the blue dot. This is labeled perception gap, and its values are printed on the right column, also labeled perception gap.

Perhaps as an after-thought, the designer added the yellow stripes, which is a third estimate of Republican views, this time by Independents. This little addition wreaks havoc. There are now three estimates - and two gaps. There is a new gap, between Independents' perception of Republican views, and Republican's self-reported views. This I-gap is hidden in plain sight. The words "perception gap" obstinately sticks to the D-gap.

***

Here is a slightly modified version of the same chart.

 

The design focuses attention on the two gaps (bars). It also identifies the Republican self-perception as the anchor point from which the gaps are computed.

I have chosen to describe the Republican dot as "self-perception" rather than "actual view," which connotes a form of "truth." Rather than considering the gap as an error of estimation, I like to think of the gap as the difference between two groups of people asked to estimate a common quantity.

Also, one should note that on the last two issues, there is virtual agreement.

***

Aside from the visual, I have doubts about the value of such a study. Only the most divisive issues are being addressed here. Adding a few bipartisan issues would provide controls that can be useful to tease out what is the baseline perception gap.

I wonder whether there is a self-selection in survey response, such that people with extreme views (from each party) will be under-represented. Further, do we believe that all survey respondents will provide truthful answers to sensitive questions that deal with racism, sexism, etc.? For example, if I am a moderate holding racist views, would I really admit to racism in a survey?

 

 

Putting the house in order, two Brexit polls

Reader Steve M. noticed an oversight in the Guardian in the following bar chart (link):

The reporter was discussing an important story that speaks to the need for careful polling design. He was comparing two polls, one by Ipsos Mori, and one by YouGov, that estimates the vote support for each party in the future U.K. general election. The bottom line is that the YouGov poll predicts about double the support for the Brexit Party than the Ipsos-Mori poll.

The stacked bar chart should only be used for data that can be added up. Here, we should be comparing the numbers side by side:

I've always found this standard display inadequate. The story here is the gap in the two bar lengths for the Brexit Party. A secondary story is that the support for the Brexit Party might come from voters breaking from Labour. In other words, we really want the reader to see:

Switching to a dot plot helps bring attention to the gaps:

Now, putting the house in order:

Why do these two polls show such different results? As the reporter explained, the answer is in how the question was asked. The Ipsos-Mori is unprompted, meaning the Brexit Party was not announced to the respondent as one of the choices while the YouGov is prompted.

This last version imposes a direction on the gaps to bring out the secondary message - that the support for Brexit might be coming from voters breaking from Labour.

 

 

The Periodic Table, a challenge in information organization

Reader Chris P. points me to this article about the design of the Periodic Table. I then learned that 2019 is the “International Year of the Periodic Table,” according to the United Nations.

Here is the canonical design of the Periodic Table that science students are familiar with.

(Source: Wikipedia.)

The Periodic Table is an exercise of information organization and display. It's about adding structure to over 100 elements, so as to enhance comprehension and lookup. The canonical tabular design has columns and rows. The columns (Groups) impose a primary classification; the rows (Periods) provide a secondary classification. The elements also follow an aggregate order, which is traced by reading from top left to bottom right. The row structure makes clear the "periodicity" of the elements: the "period" of recurrence is not constant, tending to increase with the heavier elements at the bottom.

As with most complex datasets, these elements defy simple organization, due to a curse of dimensionality. The general goal is to put the similar elements closer together. Similarity can be defined in an infinite number of ways, such as chemical, physical or statistical properties. The canonical design, usually attributed to Russian chemist Mendeleev, attained its status because the community accepted his organizing principles, that is, his definitions of similarity (subsequently modified).

***

Of interest, there is a list of unsettled issues. According to Wikipedia, the most common arguments concern:

• Hydrogen: typically shown as a member of Group 1 (first column), some argue that it doesn’t belong there since it is a gas not a metal. It is sometimes placed in Group 17 (halogens), where it forms a nice “triad” with fluorine and chlorine. Other designers just float hydrogen up top.
• Helium: typically shown as a member of Group 18 (rightmost column), the  halogens noble gases, it may also be placed in Group 2.
• Mercury: usually found in Group 12, some argue that it is not a metal like cadmium and zinc.
• Group 3: other than the first two elements , there are various voices about how to place the other elements in Group 3. In particular, the pairs of lanthanum / actinium and lutetium / lawrencium are sometimes shown in the main table, sometimes shown in the ‘f-orbital’ sub-table usually placed below the main table.

***

Over the years, there have been numerous attempts to re-design the Periodic table. Some of these are featured in the article that Chris sent me (link).

I checked how these alternative designs deal with those unsettled issues. The short answer is they don't settle the issues.

Wide Table (Janet)

The key change is to remove the separation between the main table and the f-orbital (pink) section shown below, as a "footnote". This change clarifies the periodicity of the elements, especially the elongating periods as one moves down the table. This form is also called "long step".

As a tradeoff, this table requires more space and has an awkward aspect ratio.

In this version of the wide table, the designer chooses to stack lutetium / lawrencium in Group 3 as part of the main table. Other versions place lanthanum / actinium in Group 3 as part of the main table. There are even versions that leave Group 3 with two elements.

Hydrogen, helium and mercury retain their conventional positions.

 

Spiral Design (Hyde)

There are many attempts at spiral designs. Here is one I found on this tumblr:

The spiral leverages the correspondence between periodic and circular. It is visually more pleasing than a tabular arrangement. But there is a tradeoff. Because of the increasing "diameter" from inner to outer rings, the inner elements are visually constrained compared to the outer ones.

In these spiral diagrams, the designer solves the aspect-ratio problem by creating local loops, sometimes called peninsulas. This is analogous to the footnote table solution, and visually distorts the longer periodicity of the heavier elements.

For Hyde's diagram, hydrogen is floated, helium is assigned to Group 2, and mercury stays in Group 12.

 

Racetrack

I also found this design on the same tumblr, but unattributed. It may have come from Life magazine.

It's a variant of the spiral. Instead of peninsulas, the designer squeezes the f-orbital section under Group 3, so this is analogous to the wide table solution.

The circular diagrams convey the sense of periodic return but the wide table displays the magnitudes more clearly.

This designer places hydrogen in group 18 forming a triad with fluorine and chlorine. Helium is in Group 17 and mercury in the usual Group 12 .

 

Cartogram (Sheehan)

This version is different.

The designer chooses a statistical property (abundance) as the primary organizing principle. The key insight is that the lighter elements in the top few rows are generally more abundant - thus more important in a sense. The cartogram reveals a key weakness of the spiral diagrams that draw the reader's attention to the outer (heavier) elements.

Because of the distorted shapes, the cartogram form obscures much of the other data. In terms of the unsettled issues, hydrogen and helium are placed in Groups 1 and 2. Mercury is in Group 12. Group 3 is squeezed inside the main table rather than shown below.

 

Network

The centerpiece of the article Chris sent me is a network graph.

This is a complete redesign, de-emphasizing the periodicity. It's a result of radically changing the definition of similarity between elements. One barrier when introducing entirely new displays is the tendency of readers to expect the familiar.

***

I found the following articles useful when researching this post:

The Conversation

Royal Chemistry Society

 

Wayward legend takes sides in a chart of two sides, plus data woes

Reader Chris P. submitted the following graph, found on Axios:

From a Trifecta Checkup perspective, the chart has a clear question: are consumers getting what they wanted to read in the news they are reading?

Nevertheless, the chart is a visual mess, and the underlying data analytics fail to convince. So, it’s a Type DV chart. (See this overview of the Trifecta Checkup for the taxonomy.)

***

The designer did something tricky with the axis but the trick went off the rails. The underlying data consist of two set of ranks, one for news people consumed and the other for news people wanted covered. With 14 topics included in the study, the two data series contain the same values, 1 to 14. The trick is to collapse both axes onto one. The trouble is that the same value occurs twice, and the reader must differentiate the plot symbols (triangle or circle) to figure out which is which.

It does not help that the lines look like arrows suggesting movement. Without first reading the text, readers may assume that topics change in rank between two periods of time. Some topics moved right, increasing in importance while others shifted left.

The design wisely separated the 14 topics into three logical groups. The blue group comprises news topics for which “want covered” ranking exceeds the “read” ranking. The orange group has the opposite disposition such that the data for “read” sit to the right side of the data for “want covered”. Unfortunately, the legend up top does more harm than good: it literally takes sides!

**

Here, I've put the data onto a scatter plot:

The two sets of ranks are basically uncorrelated, as the regression line is almost flat, with “R-squared” of 0.02.

The analyst tried to "rescue" the data in the following way. Draw the 45-degree line, and color the points above the diagonal blue, and those below the diagonal orange. Color the points on the line gray. Then, write stories about those three subgroups.

Further, the ranking of what was read came from Parse.ly, which appears to be surveillance data (“traffic analytics”) while the ranking of what people want covered came from an Axios/SurveyMonkey poll. As for as I could tell, there was no attempt to establish that the two populations are compatible and comparable.

 

 

 

 

 

Clarifying comparisons in censored cohort data: UK housing affordability

If you're pondering over the following chart for five minutes or more, don't be ashamed. I took longer than that.

The chart accompanied a Financial Times article about inter-generational fairness in the U.K. To cut to the chase, a recently released study found that younger generations are spending substantially higher proportions of their incomes to pay for housing costs. The FT article is here (behind paywall). FT actually slightly modified the original chart, which I pulled from the Home Affront report by the Intergenerational Commission.

One stumbling block is to figure out what is plotted on the horizontal axis. The label "Age" has gone missing. Even though I am familiar with cohort analysis (here, generational analysis), it took effort to understand why the lines are not uniformly growing in lengths. Typically, the older generation is observed for a longer period of time, and thus should have a longer line.

In particular, the orange line, representing people born before 1895 only shows up for a five-year range, from ages 70 to 75. This was confusing because surely these people have lived through ages 20 to 70. I'm assuming the "left censoring" (missing data on the left side) is because of non-existence of old records.

The dataset is also right-censored (missing data on the right side). This occurs with the younger generations (the top three lines) because those cohorts have not yet reached certain ages. The interpretation is further complicated by the range of birth years in each cohort but let me not go there.

TL;DR ... each line represents a generation of Britons, defined by their birth years. The generations are compared by how much of their incomes did they spend on housing costs. The twist is that we control for age, meaning that we compare these generations at the same age (i.e. at each life stage).

***

Here is my version of the same chart:

Here are some of the key edits:

• Vertical blocks are introduced to break up the analysis by life stage. These guide readers to compare the lines vertically i.e. across generations
• The generations are explicitly described as cohorts by birth years
• The labels for the generations are placed next to the lines
• Gridlines are pushed to the back
• The age axis is explicitly labeled
• Age labels are thinned
• A hierarchy on colors
• The line segments with incomplete records are dimmed

The harmful effect of colors can be seen below. This chart is the same as the one above, except for retaining the colors of the original chart:

 

 

Pay levels in the U.S.

The Wall Street Journal published a graphic showing the median pay levels at "most" public companies in the U.S. here.

People who attended my dataviz seminar might recognize the similarity with the graphic showing internet download speeds by different broadband technologies. It's a clean, clear way of showing multiple comparisons on the same chart.

You can see the distribution of pay levels of companies within each industry grouping, and the vertical lines showing the sector medians allow comparison across sectors. The median pay levels are quite similar with the energy sector leaning higher, and consumer sector leaning lower.

The consumer sector is extremely heavy on the low side of the pay range. Companies like Universal, Abercrombie, Skechers, Mattel, Gap, etc. all pay at least half their employees less than $6,000. The data is sourced to MyLogIQ. I have no knowledge of how reliable or valid the data are. It's curious to me that Dunkin Brands showed a median of $110K while Starbucks showed $13K.

***

I like the interactive features.

The window control lets the user zoom in to different parts of the pay range. This is necessary because of the extremely high salaries. The control doubles as a presentation of the overall distribution of median salaries.

The text box can be used to add data labels to specific companies.

***

See previous discussion of WSJ Graphics.

 

Measles babies

Mona Chalabi has made this remarkable graphic to illustrate the effect of the anti-vaccine movement on measles cases in the U.S.: (link)

As a form of agitprop, the graphic seizes upon the fear engendered by the defacing red rash of the disease. And it's very effective in articulating its social message.

***

I wasn't able to find the data except for a specific year or two. So, this post is more inspired by the graphic than a direct response to it.

I think the left-side legend should say "1 case of measles in someone who was not vaccinated" (as opposed to 1 case of measles in aggregate).

The chart encodes the data in the density of the red dots. What does the density of the red dots signify? There are two possibilities: case counts or case rates.

2013 is a year in which I could find data. In 2013, the U.S. saw 187 cases of measles, only 4 of them in someone who was vaccinated. In other words, there are 49 times as many measles cases among the unvaccinated as the vaccinated.

But note that about 90 percent of the population (using 13-17 year olds as a proxy) are vaccinated. The chance of getting measles in the unvaccinated is 0.8 per million, compared to 0.002 per million in the vaccinated - 422 times higher.

The following chart shows the relative appearance of the dot densities. The bottom row which compares the relative chance of getting measles is the more appropriate metric, and it looks much worse.

***

Mona's instagram has many other provocative graphics.

 

Seeking simplicity in complex data: Bloomberg's dataviz on UK gender pay gap

Bloomberg featured a thought-provoking dataviz that illustrates the pay gap by gender in the U.K. The dataset underlying this effort is complex, and the designers did a good job simplifying the data for ease of comprehension.

U.K. companies are required to submit data on salaries and bonuses by gender, and by pay quartiles. The dataset is incomplete, since some companies are slow to report, and the analyst decided not to merge companies that changed names.

Companies are classified into industry groups. Readers who read Chapter 3 of Numbers Rule Your World (link) should ask whether these group differences are meaningful by themselves, without controlling for seniority, job titles, etc. The chapter features one method used by the educational testing industry to take a more nuanced analysis of group differences.

***

The Bloomberg visualization has two sections. In the top section, each company is represented by the percent difference between average female pay and average male pay. Then the companies within a given industry is shown in a histogram. The histograms provide a view of the disparity between companies within a given industry. The black line represents the relative proportion of companies in a given industry that have no gender pay gap but it’s the weight of the histogram on either side of the black line that carries the graphic’s message.

This is the histogram for arts, entertainment and recreation.

The spread within this industry is very wide, especially on the left side of the black line. A large proportion of these companies pay women less on average than men, and how much less is highly variable. There is one extreme positive value: Chelsea FC Foundation that pays the average female about 40% more than the average male.

This is the histogram for the public sector.

It is a much tighter distribution, meaning that the pay gaps vary less from organization to organization (this statement ignores the possibility that there are outliers not visible on this graphic). Again, the vast majority of entities in this sector pay women less than men on average.

***

The second part of the visualization look at the quartile data. The employees of each company are divided into four equal-sized groups, based on their wages. Think of these groups as the Top 25% Earners, the Second 25%, etc. Within each group, the analyst looks at the proportion of women. If gender is independent of pay, then we should expect the proportions of women to be about the same for all four quartiles. (This analysis considers gender to be the only explainer for pay gaps. This is a problem I've called xyopia, that frames a complex multivariate issue as a bivariate problem involving one outcome and one explanatory variable. Chapter 3 of Numbers Rule Your World (link) discusses how statisticians approach this issue.)

On the right is the chart for the public sector. This is a pie chart used as a container. Every pie has four equal-sized slices representing the four quartiles of pay.

The female proportion is encoded in both the size and color of the pie slices. The size encoding is more precise while the color encoding has only 4 levels so it provides a “binned” summary view of the same data.

For the public sector, the lighter-colored slice shows the top 25% earners, and its light color means the proportion of women in the top 25% earners group is between 30 and 50 percent. As we move clockwise around the pie, the slices represent the 2nd, 3rd and bottom 25% earners, and women form 50 to 70 percent of each of those three quartiles.

To read this chart properly, the reader must first do one calculation. Women represent about 60% of the top 25% earners in the public sector. Is that good or bad? This depends on the overall representation of women in the public sector. If the sector employs 75 percent women overall, then the 60 percent does not look good but if it employs 40 percent women, then the same value of 60% tells us that the female employees are disproportionately found in the top 25% earners.

That means the reader must compare each value in the pie chart against the overall proportion of women, which is learned from the average of the four quartiles.

***

In the chart below, I make this relative comparison explicit. The overall proportion of women in each industry is shown using an open dot. Then the graphic displays two bars, one for the Top 25% earners, and one for the Bottom 25% earners. The bars show the gap between those quartiles and the overall female proportion. For the top earners, the size of the red bars shows the degree of under-representation of women while for the bottom earners, the size of the gray bars shows the degree of over-representation of women.

The net sum of the bar lengths is a plausible measure of gender inequality.

The industries are sorted from the ones employing fewer women (at the top) to the ones employing the most women (at the bottom). An alternative is to sort by total bar lengths. In the original Bloomberg chart - the small multiples of pie charts, the industries are sorted by the proportion of women in the bottom 25% pay quartile, from smallest to largest.

In making this dataviz, I elected to ignore the middle 50%. This is not a problem since any quartile above the average must be compensated by a different quartile below the average.

***

The challenge of complex datasets is discovering simple ways to convey the underlying message. This usually requires quite a bit of upfront analytics, data transformation, and lots of sketching.

 

 

An exercise in decluttering

My friend Xan found the following chart by Pew hard to understand. Why is the chart so taxing to look at? 

It's packing too much.

I first notice the shaded areas. Shading usually signifies "look here". On this chart, the shading is highlighting the least important part of the data. Since the top line shows applicants and the bottom line admitted students, the shaded gap displays the rejections.

The numbers printed on the chart are growth rates but they confusingly do not sync with the slopes of the lines because the vertical axis plots absolute numbers, not rates. 

The vertical axis presents the total number of applicants, and the total number of admitted students, in each "bucket" of colleges, grouped by their admission rate in 2017. On the right, I drew in two lines, both growth rates of 100%, from 500K to 1 million, and from 1 to 2 million. The slopes are not the same even though the rates of growth are.

Therefore, the growth rates printed on the chart must be read as extraneous data unrelated to other parts of the chart. Attempts to connect those rates to the slopes of the corresponding lines are frustrated.

Another lurking factor is the unequal sizes of the buckets of colleges. There are fewer than 10 colleges in the most selective bucket, and over 300 colleges in the largest bucket. We are unable to interpret properly the total number of applicants (or admissions). The quantity of applications in a bucket depends not just on the popularity of the colleges but also the number of colleges in each bucket.

The solution isn't to resize the buckets but to select a more appropriate metric: the number of applicants per enrolled student. The most selective colleges are attracting about 20 applicants per enrolled student while the least selective colleges (those that accept almost everyone) are getting 4 applicants per enrolled student, in 2017.

As the following chart shows, the number of applicants has doubled across the board in 15 years. This raises an intriguing question: why would a college that accepts pretty much all applicants need more applicants than enrolled students?

Depending on whether you are a school administrator or a student, a virtuous (or vicious) cycle has been realized. For the top four most selective groups of colleges, they have been able to progressively attract more applicants. Since class size did not expand appreciably, more applicants result in ever-lower admit rate. Lower admit rate reduces the chance of getting admitted, which causes prospective students to apply to even more colleges, which further suppresses admit rate. 

 

 

 

Visualizing the 80/20 rule, with the bar-density plot

Through Twitter, Danny H. submitted the following chart that shows a tiny 0.3 percent of Youtube creators generate almost 40 percent of all viewing on the platform. He asks for ideas about how to present lop-sided data that follow the "80/20" rule.

In the classic 80/20 rule, 20 percent of the units account for 80 percent of the data. The percentages vary, so long as the first number is small relative to the second. In the Youtube example, 0.3 percent is compared to 40 percent. The underlying reason for such lop-sidedness is the differential importance of the units. The top units are much more important than the bottom units, as measured by their contribution to the data.

I sense a bit of "loss aversion" on this chart (explained here). The designer color-coded the views data into blue, brown and gray but didn't have it in him/her to throw out the sub-categories, which slows down cognition and adds hardly to our understanding.

I like the chart title that explains what it is about.

Turning to the D corner of the Trifecta Checkup for a moment, I suspect that this chart only counts videos that have at least one play. (Zero-play videos do not show up in a play log.) For a site like Youtube, a large proportion of uploaded videos have no views and thus, many creators also have no views.

***

My initial reaction on Twitter is to use a mirrored bar chart, like this:

I ended up spending quite a bit of time exploring other concepts. In particular, I like to find an integrated way to present this information. Most charts, such as the mirrored bar chart, a Bumps chart (slopegraph), and Lorenz chart, keep the two series of percentages separate.

Also, the biggest bar (the gray bar showing 97% of all creators) highlights the least important Youtubers while the top creators ("super-creators") are cramped inside a slither of a bar, which is invisible in the original chart.

What I came up with is a bar-density plot, where I use density to encode the importance of creators, and bar lengths to encode the distribution of views.

Each bar is divided into pieces, with the number of pieces proportional to the number of creators in each segment. This has the happy result that the super-creators are represented by large (red) pieces while the least important creators by little (gray) pieces.

The embedded tessellation shows the structure of the data: the bottom third of the views are generated by a huge number of creators, producing a few views each - resulting in a high density. The top 38% of the views correspond to a small number of super-creators - appropriately shown by a bar of low density.

For those interested in technicalities, I embed a Voronoi diagram inside each bar, with randomly placed points. (There will be a companion post later this week with some more details, and R code.)

Here is what the bar-density plot looks like when the distribution is essentially uniform:

The density inside each bar is roughly the same, indicating that the creators are roughly equally important.

 

P.S.

1) The next post on the bar-density plot, with some experimental R code, will be available here.

2) Check out my first Linkedin "article" on this topic.