## Ask how you can give

##### Aug 12, 2020

A reader and colleague Georgette A was frustrated with the following graphic that appeared in the otherwise commendable article in National Geographic (link). The NatGeo article provides a history lesson on past pandemics that killed millions.

What does the design want to convey to readers?

Our attention is drawn to the larger objects, the red triangle on the left or the green triangle on the right. Regarding the red triangle, we learn that the base is the duration of the pandemic while the height of the black bar represents the total deaths.

An immediate curiosity is why a green triangle is lodged in the middle of the red triangle. Answering this question requires figuring out the horizontal layout. Where we expect axis labels we find an unexpected series of numbers (0, 16, 48, 5, 2, 4, ...). These are durations that measure the widths of the triangular bases.

To solve this puzzle, imagine the chart with the triangles removed, leaving just the black columns. Now replace the durations with index numbers, 1 to 13, corresponding to the time order of the ending years of these epidemics. In other words, there is a time axis hidden behind the chart. [As Ken reminded me on Twitter, I forgot to mention that details of each pandemic are revealed by hovering over each triangle.]

This explains why the green triangle (Antonine Plague) is sitting inside the large red triangle (Plague of Justinian). The latter's duration is 3 times that of the former, and the Antonine Plague ended before the Plague of Justinian. In fact, the Antonine occurred during 165-180 while the Justinian happened during 541-588. The overlap is an invention of the design. To receive what the design gives, we have to think of time as a sequence, not of dates.

***

Now, compare the first and second red triangles. Their black columns both encode 50 million deaths. The Justinian Plague however was spread out over 48 years while the Black Death lasted just 5 years. This suggests that the Black Death was more fearsome than the Justinian Plague. And yet, the graphic presents the opposite imagery.

This is a pretty tough dataset to visualize. Here is a side-by-side bar chart that lets readers first compare deaths, and then compare durations.

In the meantime, I highly recommend the NatGeo article.

## Twitter people UpSet with that Covid symptoms diagram

##### May 01, 2020

Been busy with an exciting project, which I might talk about one day. But I promised some people I'll follow up on Covid symptoms data visualization, so here it is.

After I posted about the Venn diagram used to depict self-reported Covid-19 symptoms by users of the Covid Symptom Tracker app (reported by Nature), Xan and a few others alerted me to Twitter discussion about alternative visualizations that people have made after they suffered the indignity of trying to parse the Venn diagram.

[In the Twitter links below, you almost always have to scroll one message down - saving tweets, linking to tweets, etc. are all stuff I haven't fully figured out.]

Xan’s final comment is especially appropriate: "There's an over-riding Type-Q issue: count charts answer the wrong question".

As dataviz designers, we frequently get locked into the mindset of “what is the best way to present this dataset?” This line of thinking leads to overloaded graphics that attempt to answer every possible question that may arise from the data in one panoptic chart, akin to juggling 10 balls at once.

For complex datasets, it is often helpful to narrow down the list of questions, and provide a series of charts, each addressing one or two questions. I’ll come back to this point. I want to first show some of the nicer visuals that others have produced, which brings out the structure and complexity of this dataset.

The UpSet chart

The primary contender is the “UpSet” chart form, as best exemplified by Bart’s effort

The centerpiece of this chart is the matrix of dots. The horizontal rows of dots represent the presence of specific symptoms such as cough and anosmia (loss of smell and taste). The vertical columns are intuitive, once you get it. They represent combinations of symptoms, and the fill/no-fill of the dots indicates which symptoms are being combined. For example, the first column counts people reporting fatigue plus anosmia (but nothing else).

The UpSet chart clearly communicates the structure of the data. In many survey questions (including this one conducted by the Symptom Tracker app), respondents are allowed to check/tick more than one answer choices. This creates a situation where the number of answers (here, symptoms) per respondent can be zero up to the total number of answer choices.

So far, we have built a structure like we have drawn country outlines on a map. There is no data yet. The data are primarily found in the sidebar histograms (column/bar charts). Reading horizontally to the right side, one learns that the most frequently reported symptom was fatigue, covering 88 percent of the users.* Reading vertically, one learns that the top combination of symptoms was fatigue plus anosmia, covering 16 percent of users.

***

Now come the divisive acts.

Act 1: Bart orders the columns in a particular way that meets his subjective view of how he wants readers to see the data. The columns are sorted from the most frequent combinations to the least. The histogram has a “long tail”, with most of the combinations receiving a small proportion of the total. The top five combinations is where the bulk of the data is – I’d have liked to see all five columns labeled, without decimal places.

This is a choice on the part of the designer. Nils, for example, made two versions of his UpSet charts. The second version arranges the combinations from singles to quintuples.

Digression: The Visual in Data Visualization

The two rendering of “UpSet” charts, by Nils and Bart, is a perfect illustration of the Trifecta Checkup framework. Each corner of the Trifecta is an independent dimension, and yet all must sync. With the same data and the same question types, what differentiates the two versions is the visual design.

See how many differences you can find, and make your own design choices!

I place the digression here because Act 1 above has to do with the Q corner, and both visual designs can accommodate the sorting decisions. But Act 2 below pertains to the V corner.

Act 2: Bart applies a blue gradient to the matrix of dots that reinforces his subjective view about identifying frequent combinations of symptoms. Nils, by contrast, uses the matrix to show present/absent only.

I’m not sure about Act 2. I think the addition of the color gradient overloads the matrix in the chart. It has the nice effect of focusing the reader’s attention on the top 5 combinations but it also requires the reader to have understood the meaning of columns first. Perhaps applying the gradient to the histogram up top rather than the dots in the matrix can achieve the same goal with less confusion.

Getting Obtuse

For example, some readers (e.g. Robin) expressed confusion.

Robin is alleging something the chart doesn’t do. He pointed out (correctly) that while 16 percent experienced fatigue and anosmia only (without other symptoms), more than 50 percent reported fatigue and anosmia, plus other symptoms. That nugget of information is deeply buried inside Bart’s chart – it’s the sum of each column for which the first two dots are filled in. For example, the second column represents fatigue+anosmia+cough. So Robin wants to aggregate those up.

Robin’s critique arises from the Q(uestion) corner. If the designer wants to highlight specific combinations that occur most frequently in the data, then Bart’s encoding makes perfect sense. On the other hand, if the purpose is to highlight pairs of symptoms that occur most frequently together (disregarding symptoms outside each pair), then the data must be further aggregated. The switch in the Question requires more Data manipulation, which then affects the Visualization. That's the essence of the Trifecta Checkup framework.

Rest assured, the version that addresses Robin’s point will not give an easy answer to Bart’s question. In fact, Xan whipped up a bar chart in response:

This is actually hard to comprehend because Robin’s question is even hard to state. The first bar shows 87 percent of users reported fatigue as a symptom, the same number that appeared on Bart’s version on the right side. Then, the darkened section of the bar indicates the proportion of users who reported only fatigue and nothing else, which appears to be about 10 percent. So 1 out of 9 reported just fatigue while 8 out of 9 who reported fatigue also experienced other symptoms.

Xan’s bar chart can be flipped 90 degrees and replace Bart’s histogram on top of the matrix. But you see, we end up with the same problem as I mentioned up top. By jamming more insights from more questions onto the same chart, we risk dropping the other balls that were already in the air.

So, my advice is always to first winnow down the list of questions you want to address. And don’t be afraid of making a series of charts instead of one panoptic chart.

***

Act 3: Bart decides to leave out labels for the columns.

This is a curious choice given the key storyline we’ve been working with so far (the Top 5 combinations of symptoms). But notice how annoying this problem is. Combinations require long text, which must be written vertically or slanted on this design. Transposing could help but not really. It’s just a limitation of this chart form. For me, reading the filled dots underneath the columns as column labels isn’t a show-stopper.

Histograms vs Bar Charts

It’s worth pointing out that the sidebar “histograms” are not both histograms. I tend to think of histograms as a specific type of bar (column) chart, in which the sum of the bars (columns) can be interpreted as a whole. So all histograms are bar charts but only some bar charts are histograms.

The column chart up top is a histogram. The combinations of symptoms are disjoint, and the total of the combinations should be the total number of answer choices selected by all respondents. The bar chart on the right side however is not a histogram. Each percentage is a proportion to the whole, and adding those percentages yields way above 100%.

I like the annotation on Bart’s chart a lot. They are succinct and they give just the right information to explain how to read the chart.

Limitations

I already mentioned the vertical labeling issue for UpSet charts. Here are two other considerations for you.

The majority of the plotting area is dedicated to the matrix of dots. The matrix contains merely labels for data. They are like country boundaries on a map. While it lays out the structure of data very clearly, the designer should ask whether it is essential for the readers to see the entire landscape.

In real-world data, the “long tail” phenomenon we saw earlier is very common. With six featured symptoms, there are 2^6 = 64 possible combinations of symptoms (minus 1 if they filtered out those not reporting symptoms*), almost all of which will be empty. Should the low-frequency columns be removed? This is not as controversial as you think, because implicitly both Bart and Nils already dropped all empty combinations!

Data and Code

Kieran Healy left a comment on the last post, and you can find both the data (thank you!) and some R code for UpSet charts at his blog.

Also, Nils has a Shiny app on Github.

(*) One must be very careful about what “users” are being represented. They form a tiny subset of users of the Symptom Tracker app, just those who have previously taken a diagnostic test and have self-reported at least one symptom. I have separately commented on the analyses of this dataset by the team behind the app. The first post discusses their analytical methods, the second post examines how they pre-processed the data, and a future post will describe the data collection practices. For the purpose of this blog post, I’ll ignore any data issues.

(#) Bart’s chart is conceptual because some of the columns of dots are repeated, and there is one column without fills, which should have been removed by a pre-processing step applied by the research team.

## This exercise plan for your lock-down work-out is inspired by Venn

##### Apr 23, 2020

A twitter follower did not appreciate this chart from Nature showing the collection of flu-like symptoms that people reported they have to an UK tracking app.

It's a super-complicated Venn diagram. I have written about this type of chart before (see here); it appears to be somewhat popular in the medicine/biology field.

A Venn diagram is not a data visualization because it doesn't plot the data.

Notice that the different compartments of the Venn diagram do not have data encoded in the areas.

The chart also fails the self-sufficiency test because if you remove the data from it, you end up with a data container - like a world map showing country boundaries and no data.

If you're new here: if a graphic requires the entire dataset to be printed on it for comprehension, then the visual elements of the graphic are not doing any work. The graphic cannot stand on its own.

When the Venn diagram gets complicated, teeming with many compartments, there will be quite a few empty compartments. If I have to make this chart, I'd be nervous about leaving out a number or two by accident. An empty cell can be truly empty or an oversight.

Another trap is that the total doesn't add up. The numbers on this graphic add to 1,764 whereas the study population in the preprint was 1,702. Interestingly, this diagram doesn't show up in the research paper. Given how they winnowed down the study population from all the app downloads, I'm sure there is an innocent explanation as to why those two numbers don't match.

***

The chart also strains the reader. Take the number 18, right in the middle. What combination of symptoms did these 18 people experience? You have to figure out the layers sitting beneath the number. You see dark blue, light blue, orange. If you blink, you might miss the gray at the bottom. Then you have to flip your eyes up to the legend to map these colors to diarrhoea, shortness of breath, anosmia, and fatigue. Oops, I missed the yellow, which is the cough. To be sure, you look at the remaining categories to see where they stand - I've named all of them except fever. The number 18 lies outside fever so this compartment represents everything except fever.

What's even sadder is there is not much gain from having done it once. Try to interpret the number 50 now. Maybe I'm just slow but it doesn't get better the second or third time around. This graphic not only requires work but painstaking work!

Perhaps a more likely question is how many people who had a loss of smell also had fever. Now it's pretty easy to locate the part of the dark gray oval that overlaps with the orange oval. But now, I have to add all those numbers, 69+17+23+50+17+46 = 222. That's not enough. Next, I must find the total of all the numbers inside the orange oval, which is 222 plus what is inside the orange and outside the dark gray. That turns out to be 829. So among those who had lost smell, the proportion who also had fever is 222/(222+829) = 21 percent.

How many people had three or more symptoms? I'll let you figure this one out!

## Graphing the extreme

##### Apr 22, 2020

The Covid-19 pandemic has brought about extremes. So many events have never happened before. I doubt The Conference Board has previously seen the collapse of confidence in the economy by CEOs. Here is their graphic showing this extreme event:

To appreciate this effort, you have to see the complexity of the underlying data. There is a CEO Confidence Measure. The measure has three components. Each component is scored on a scale probably from 0 to 100, with 5o as the middle. Then, the components are aggregated into an overall score. The measure is repeatedly estimated over time, and they did two surveys during the Pandemic, pre and post the lockdown in the U.S. And then, there's the rightmost column, which provides another reference point for one of the components of the measure.

One can easily get one's limbs tied up in knots trying to tame this beast.

Of course, the tiny square stands out. CEOs have a super pessimistic outlook for the next 6 months for overall economy. The number 3 on this scale probably means almost every respondent has a negative view.

The grid arrangement does not appear attractive but it is terrifically functional. The grid delivers horizontal and vertical comparisons. Moving vertically, we learn that even at the start of the year, the average sentiment was negative (9 points below 50), then it lost another 10 points, and finally imploded.

Moving horizontally, we can compare related metrics since everything is conveniently expressed in the same scale. While CEOs are depressed about the overall economy, they have slightly more faith about their own industry. And then moving left, we learn that many CEOs expect a V-shaped recovery, a really fast bounceback within 6 months.

As the Conference Board surveys this group again in the near future, I wonder if the optimism still holds.

The Conference Board has an entire set of graphics about the economic crisis of Covid-19 here. For some reason, they don't let me link to a specific chart so I can't directly link to the chart.

## Gazing at petals

##### Jan 21, 2020

Reader Murphy pointed me to the following infographic developed by Altmetric to explain their analytics of citations of journal papers. These metrics are alternative in that they arise from non-academic media sources, such as news outlets, blogs, twitter, and reddit.

The key graphic is the petal diagram with a number in the middle.

I have a hard time thinking of this object as “data visualization”. Data visualization should visualize the data. Here, the connection between the data and the visual design is tenuous.

There are eight petals arranged around the circle. The legend below the diagram maps the color of each petal to a source of data. Red, for example, represents mentions in news outlets, and green represents mentions in videos.

Each petal is the same size, even though the counts given below differ. So, the petals are like a duplicative legend.

The order of the colors around the circle does not align with its order in the table below, for a mysterious reason.

Then comes another puzzle. The bluish-gray petal appears three times in the diagram. This color is mapped to tweets. Does the number of petals represent the much higher counts of tweets compared to other mentions?

To confirm, I pulled up the graphic for a different paper.

Here, each petal has a different color. Eight petals, eight colors. The count of tweets is still much larger than the frequencies of the other sources. So, the rule of construction appears to be one petal for each relevant data source, and if the total number of data sources fall below eight, then let Twitter claim all the unclaimed petals.

A third sample paper confirms this rule:

None of the places we were hoping to find data – size of petals, color of petals, number of petals – actually contain any data. Anything the reader wants to learn can be directly read. The “score” that reflects the aggregate “importance” of the corresponding paper is found at the center of the circle. The legend provides the raw data.

***

Some years ago, one of my NYU students worked on a project relating to paper citations. He eventually presented the work at a conference. I featured it previously.

Notice how the visual design provides context for interpretation – by placing each paper/researcher among its peers, and by using a relative scale (percentiles).

***

I’m ignoring the D corner of the Trifecta Checkup in this post. For any visualization to be meaningful, the data must be meaningful. The type of counting used by Altmetric treats every tweet, every mention, etc. as a tally, making everything worth the same. A mention on CNN counts as much as a mention by a pseudonymous redditor. A pan is the same as a rave. Let’s not forget the fake data menace (link), which  affects all performance metrics.

## Bubble charts, ratios and proportionality

##### Jan 13, 2020

A recent article in the Wall Street Journal about a challenger to the dominant weedkiller, Roundup, contains a nice selection of graphics. (Dicamba is the up-and-comer.)

The change in usage of three brands of weedkillers is rendered as a small-multiples of choropleth maps. This graphic displays geographical and time changes simultaneously.

The staircase chart shows weeds have become resistant to Roundup over time. This is considered a weakness in the Roundup business.

***

In this post, my focus is on the chart at the bottom, which shows complaints about Dicamba by state in 2019. This is a bubble chart, with the bubbles sorted along the horizontal axis by the acreage of farmland by state.

Below left is a more standard version of such a chart, in which the bubbles are allowed to overlap. (I only included the bubbles that were labeled in the original chart).

The WSJ’s twist is to use the vertical spacing to avoid overlapping bubbles. The vertical axis serves a design perogative and does not encode data.

I’m going to stick with the more traditional overlapping bubbles here – I’m getting to a different matter.

***

The question being addressed by this chart is: which states have the most serious Dicamba problem, as revealed by the frequency of complaints? The designer recognizes that the amount of farmland matters. One should expect the more acres, the more complaints.

Let's consider computing directly the number of complaints per million acres.

The resulting chart (shown below right) – while retaining the design – gives a wholly different feeling. Arkansas now owns the largest bubble even though it has the least acreage among the included states. The huge Illinois bubble is still large but is no longer a loner.

Now return to the original design for a moment (the chart on the left). In theory, this should work in the following manner: if complaints grow purely as a function of acreage, then the bubbles should grow proportionally from left to right. The trouble is that proportional areas are not as easily detected as proportional lengths.

The pair of charts below depict made-up data in which all states have 30 complaints for each million acres of farmland. It’s not intuitive that the bubbles on the left chart are growing proportionally.

Now if you look at the right chart, which shows the relative metric of complaints per million acres, it’s impossible not to notice that all bubbles are the same size.

## Tennis greats at the top of their game

##### Sep 12, 2019

The following chart of world No. 1 tennis players looks pretty but the payoff of spending time to understand it isn't high enough. The light colors against the tennis net backdrop don't work as intended. The annotation is well done, and it's always neat to tug a legend inside the text.

The original is found at Tableau Public (link).

The topic of the analysis appears to be the ages at which tennis players attained world #1 ranking. Here are the male players visualized differently:

Some players like Jimmy Connors and Federer have second springs after dominating the game in their late twenties. It's relatively rare for players to get to #1 after 30.

## The Periodic Table, a challenge in information organization

##### Jun 24, 2019

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

## Bar-density and pie-density plots for showing relative proportions

##### Mar 26, 2019

In my last post, I described a bar-density chart to show paired data of proportions with an 80/20-type rule. The following example illustrates that a small proportion of Youtubers generate a large proportion of views.

Other examples of this type of data include:

• the top 10% of families own 75% of U.S. household wealth (link)
• the top 1% of artists earn 77% of recorded music income (link)
• Five percent of AT&T customers consume 46% of the bandwidth (link)

In all these examples, the message of the data is the importance of a small number of people (top earners, superstars, bandwidth hogs). A good visual should call out this message.

The bar-density plot consists of two components:

• the bar chart which shows the distribution of the data (views, wealth, income, bandwidth) among segments of people;
• The embedded Voronoi diagram within each bar that encodes the relative importance of each people segment, as measured by the (inverse) density of the population among these segments - a people segment is more important if each individual accounts for more of the data, or in other words, the density of people within the group is lower.

The bar chart can adopt a more conventional horizontal layout.

Voronoi tessellation

To understand the Voronoi diagram, think of a fixed number (say, 100) of randomly placed points inside a bar. Then, for any point inside the bar area, it has a nearest neighbor among those 100 fixed points. Assign every point on the surface to its nearest neighbor. From this, one can draw a boundary around each of the 100 points to include all its nearest neighbors. The resulting tessellation is the Voronoi diagram. (The following illustration comes from this AMS column.)

The density of points in the respective bars encodes the relative proportions of people within those groups. For my example, I placed 6 points in the red bar, 666 points in the yellow bar, and ~2000 points in the gray bar, which precisely represents the relative proportions of creators in the three segments.

Density is represented statistically

Notice that the density is represented statistically, not empirically. According to the annotation on the original chart, the red bar represents 14,000 super-creators. Correspondingly, there are 4.5 million creators in the gray bar. Any attempt to plot those as individual pieces will result in a much less impactful graphic. If the representation is interpreted statistically, as relative densities within each people segment, the message of relative importance of the units within each group is appropriately conveyed.

A more sophisticated way of deciding how many points to place in the red bar is to be developed. Here, I just used the convenient number of 6.

The color shades are randomly applied to the tessellation pieces, and used to facilitate reading of densities.

***

In this section, I provide R code for those who want to explore this some more. This is code used for prototyping, and you're welcome to improve them. The general strategy is as follows:

• Set the rectangular area (bar) in which the Voronoi diagram is to be embedded. The length of the bar is set to the proportion of views, appropriately scaled. The code utilizes the dirichlet function within the spatstat package to generate the fixed points; this requires setting up the owin parameter to represent a rectangle.
• Set the number of points (n) to be embedded in the bar, determined by the relative proportion of creators, appropriately scaled. Generate a data frame containing the x-y coordinates of n randomly placed points, within the rectangle defined above.
• Use the ppp function to generate the Voronoi data
• Set up a colormap for plotting the Voronoi diagram
• Plot the Voronoi diagram; assign shades at random to the pieces (in a production code, these random numbers should be set as marks in the ppp but it's easier to play around with the shades if placed here)

The code generates separate charts for each bar segment. A post-processing step is currently required to align the bars to attain equal height. I haven't figured out whether the multiplot option helps here.

library(spatstat)

# enter the scaled proportions of creators and views
# the Youtube example has three creator segments

# number of randomly generated points should be proportional to proportion of creators. Multiply nc by a scaling factor if desired

nc = c(3, 33, 965)*2

# bar widths should be proportional to proportion of views
# total width should be set based on the width of your page

wide = c(378, 276, 346)/2

# set bar height, to attain a particular aspect ratio
bar_h = 50

# define function to generate points
# defines rectangular window

makepoints = function (n, wide, height) {
df <- data.frame(x = runif(n,0,wide),y = runif(n,0,height))
W <- owin( c(0, wide), c(0,height) ) # rectangular window
pp1 <- as.ppp( df, W )
y <- dirichlet(pp1)
# y\$marks <- sample(0:wide, n, replace=T) # marks are for colors
return (y)
}

y_red = makepoints(nc[1], wide[1], bar_h) # height of each bar fixed
y_yel = makepoints(nc[2], wide[2], bar_h)
y_gry = makepoints(nc[3], wide[3], bar_h)

# setting colors (4 shades per bar, one color per bar)

cr_red = colourmap(c("lightsalmon","lightsalmon2", "lightsalmon4", "brown"), breaks=round(seq(0, wide[1],length.out=5)))

cr_yel = colourmap(c("burlywood1", "burlywood2", "burlywood3", "burlywood4"), breaks=round(seq(0, wide[2],length.out=5)))

cr_gry = colourmap(c("gray80", "gray60", "gray40", "gray20"), breaks=round(seq(0, wide[3],length.out=5)))

# plotting

par(mar=c(0,0,0,0))

# add png to save image to png

# remove values= if colors set in ppp

plot.tess(y_red, main="", border="pink3", do.col=T, values = sample(0:wide[1], nc[1], replace=T), col=cr_red, xlim=c(0, wide[1]), ylim=c(0,bar_h), ribbon=F)

plot.tess(y_yel, main="", border="darkgoldenrod4", do.col=T, values=sample(0:wide[2], nc[2], replace=T), col=cr_yel, xlim=c(0, wide[2]), ylim=c(0,bar_h), ribbon=F)

plot.tess(y_gry, main="", border="darkgray", do.col=T, values=sample(0:wide[3], nc[3], replace=T), col=cr_gry, xlim=c(0, wide[3]), ylim=c(0,bar_h), ribbon=F)

# because of random points, the tessellation looks different each time
# post-processing: make each bar the same height when aligned side by side

***

A cousin of the bar-density plot is the pie-density plot. Since I'm using only three creator segments, which each account for about 30-40% of the total views, it is natural to use a pie chart. In this case, we embed the Voronoi diagrams into the pie sectors.

If the distribution were more even, that is to say, the creators are more or less equally important, the pie-density plot looks like this:

***

Something that is more like 80/20

The original chart shows the top 0.3 percent generating almost 40 percent of the views. A more typical insight is top X percent generates 80 percent of the data. For the YouTube data, X is 11 percent. What does the pie-density chart look like if  top 11 percent <-> 80 percent, middle 33 percent <-> 11 percent, bottom 56 percent <-> 8 percent?

Roughly speaking, the second segment includes 3 times the people as the largest, and the third has 5 times as the largest.

P.S.

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

2) The first post on bar-density charts is here.

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

##### Mar 25, 2019

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.