Decluttering charts

Enrico posted about the following chart, addressing the current assault on scientific research funding, and he's worried that poor communications skills are hurting the cause.

He's right. You need half an hour to figure out what's going on here.

Let me write down what I have learned so far.

The designer only cares about eight research areas - all within the IT field - listed across the bottom.

Paired with each named research area are those bolded blue labels that run across the top (but not quite). I think they represent the crowning achievement within each field but I'm just guessing here.

It appears that each field experiences a sequence of development stages. Typically, universities get things going, then industry R&D teams enter the game, and eventually, products appear in the market. The orange, blue and black lines show this progression. The black line morphs into green, and may even expand in thickness - indicating progressive market adoption and growth.

For example, the first field from the left, digital communications, is shown to have begun in 1965 at universities. Then in early 1980s, industry started investing in this area. It was not until the 1990s when products became available, and not until the mid 2000s when the market exceeded $10 billion.

Even now, I haven't resolved all its mysteries. It's not explained the difference between a solid black line and a dotted black line. Further, it appears possible to bypass $1 billion and hit $10 billion right away.

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Next, we must decipher the strange web of gray little arrows.

It appears that the arrows can go from orange to blue, blue to orange, blue to black, orange to black. Under digital communications, I don't see black or green back to blue or orange. However, under computer architecture, I see green to orange; under parallel & distributed systems, I see green to blue. I don't see any black to orange or black to blue, so black is a kind of trapping state (things go in but don't come out). Sometimes, it's better to say which direction is not possible - in this case, I think other than nothing comes out of black, every other direction is possible.

It remains unclear what sort of entity each arrow depicts. Each arrow has a specific start and end time. I'm guessing it has to do with a specific research item. Taking the bottom-most arrow for digital communications, I suppose something begun in academia in 1980 and then attracted industry investment around 1982. An arrow that points backwards from industry to academia indicates that universities pick up new research ideas from industry. Digital communications things tend to have short arrows, suggesting that it takes only a few years to bring a product to market.

To add to this mess, some arrows cross research areas. These are shown as curved arrows, rather than straight arrows. For these curved arrows, the "slope" of the arrow no longer holds any meaning.

The set of gray arrows are trying too hard. They are overstuffed with purposes. On the one hand, the web of arrows - and I'm referring to those between research areas - portray the synergies between different research areas. On the other hand, the arrows within each research area show the development trajectories of anonymized subjects. The arrows going back and forth between the orange and blue bars show the interplay between universities and industry research groups.

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Lastly, we look at those gray text labels at the very top of the page. That's a grab-bag of corporate names (Motorola, Intel, ...) and product names (iPhone, iRobot, ...). Some companies span several research areas. I'm amused and impressed that apparently a linear sequence can be found for the eight research areas such that every single company has investments in only contiguous areas, precluding the need to "leapfrog" certain research areas!

Actually, no, that's wrong. I do notice Nvidia and HP appearing twice. But why is Google not part of digital communications next to iPhone?

Given that no universities are listed, the company and product labels are related to only the blue, black or green lines below. It might be only related to black and/or green. I'm not sure.

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So far, I've expended energy only to tease out the structure of the underlying dataset. I haven't actually learned anything about the data!

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The designer has to make some decisions because the different potential questions that the dataset can address impose conflicting graphical requirements.

If the goal is to surface a general development process that repeats for every research area, then the chart should highlight commonality, rather than difference. By contrast, if one's objective is to illustrate how certain research areas have experiences unique to themselves, one should choose a graphical form that brings out the differences.

If the focus is on larger research areas, then the relevant key dates are really the front ends of each vertical line; nothing else matters. By contrast, if one wants to show individual research items, then many more dates become pertinent.

A linear arrangement of the research areas will not perform if one's goal is to uncover connections between research areas. By contrast, if one attempts to minimize crossovers in a network design, it would be impossible to keep all elements belonging to each research area in close proximity.

A layering approach that involves multiple charts to tell the whole story may be the solution. See for example Gelman's post on ladder of abstraction.

Out of line

This simple chart showing life expectancies in 10 countries raises one's eyebrows.

The first curiosity is the deliberate placement of Pakistan behind India and China. Every nation is sorted from lowest to highest, except for Pakistan. Is the reason politics? I have no idea. If you have an explanation, please leave a comment.

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This graphic is an example of data visualization that does not actually show the data.

The positions of the flags do not in fact encode the data! For example, the Indian flag is closer to the Chinese flag than to the Pakistani flag even though the gap between India and China (7) is more than double the gap between India and Pakistan (3).

Here is what it looks like if the gaps encode the data. With this selection of countries, Pakistan and India are separated from the rest. 

In the original chart, the readers must read the data labels to understand it, and resist intepreting the visual elements.

I removed the flag poles because they have the unintended consequence of establishing a zero level (where the cartoon characters stand) but the positions of the flags don't reflect a start-at-zero posture.

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Returning to our first topic for a second. If the message of the chart is to single out Pakistan, it actually works! If all other countries are sorted by value, with Pakistan inserted out of order, it draws our attention.

In a conventional layout, Pakistan is shoved to the left side in the bottom corner. See below:

 

 

The line-angle illusion

In a recent presentation, Prof. Matthias Schonlau explains his "hammock plot." I wrote about it here. During the talk, he used the hammock plot to illustrate an optical illusion found in plots requiring users to compare angular lines, known as the line-angle illusion. (Others prefer the name "sine" illusion.)

Here is a simple demonstration of the line-angle illusion, extracted from this paper.

Think of the two sine curves as time series, and we're comparing the differences between them. This requires us to assess trend in the vertical distances between the two lines. Weirdly, we perceive the vertical lines on the above chart to have varying lengths, even though they have equal lengths.

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The link here contains an example of how the line-angle illusion can lead to misreading of trends on line charts:

Is there a bigger difference in revenue at Time 1 than Time 2? Many of us will think so but on careful judgment, I think all of us can agree that the difference at Time 2 is in fact larger.

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Much of the interest in a hammock plot lies in the links between the vertical blocks, and this is where the line-angle illustion can distort our perception. Studies have shown that humans tend to read not the vertical gaps but the angular gaps. Again, this issue is illustrated in the first mentioned paper:

Matthias explained that their implementation of the hammock plot uses a strategy to counteract this line-angle illusion.

I take this to mean they distort the data in such a way that after readers apply the line-angle illusion, the resulting view would convey correctly the correct trend. A kind of double negative strategy. The paper linked above offers one such counter-illusion strategy.

I imagine this is a bit controversial as we are introducing deliberate distortion to counteract an expected perceptual illusion.

I'm not aware of any software that offers built-in functions that perform this type of illusion-busting adjustments. Do you know any?

 

P.S. [5-30-2025] Andrew Gelman has some comments on this topic on his blog. He said:

But to get closer to what Kaiser is asking: the analogy I’ve given is, suppose you’re building a wooden chair but using boards that are warped. In this case, the right thing to do is to incorporate the warp into the design, i.e. cut some pieces shorter than others and at different angles, etc., so that they fit together as is, rather than trying to go all rectilinear and then glue/nail everything together. The trouble with the latter strategy is that the wood will exert pressure on the joints and eventually the chair will break or distort itself in some way.

Hammock plots

Prof. Matthias Schonlau gave a presentation about "hammock plots" in New York recently.

Here is an example of a hammock plot that shows the progression of different rounds of voting during the 1903 papal conclave. (These are taken at the event and thus a little askew.)

The chart shows how Cardinal Sarto beat the early favorite Rampolla during later rounds of voting. The chart traces the movement of votes from one round to the next. The Vatican destroys voting records, and apparently, records were unexpectedly retained for this particular conclave.

The dataset has several features that brings out the strengths of such a plot.

There is a fixed number of votes, and a fixed number of candidates. At each stage, the votes are distributed across the subset of candidates. From stage to stage, the support levels for candidate shift. The chart brings out the evolution of the vote.

From the "marginals", i.e. the stacked columns shown at each time point, we learn the relative strengths of the candidates, as they evolve from vote to vote.

The links between the column blocks display the evolution of support from one vote to the next. We can see which candidate received more votes, as well as where the additional votes came from (or, to whom some voters have drifted).

The data are neatly arranged in successive stages, resulting in discrete time steps.

Because the total number of votes are fixed, the relative sizes of the marginals are nicely constrained.

The chart is made much more readable because of binning. Only the top three candidates are shown individually with all the others combined into a single category. This chart would have been quite a mess if it showed, say, 10 candidates.

How precisely we can show the intra-stage movement depends on how the data records were kept. If we have the votes for each person in each round, then it should be simple to execute the above! If we only have the marginals (the vote distribution by candidate) at each round, then we are forced to make some assumptions about which voters switched their votes. We'd likely have to rule out unlikely scenarios, such as that in which all of the previous voters for candidate X switched to someone other candidates while another set of voters switched their votes to candidate X.

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Matthias also showed examples of hammock plots applied to different types of datasets.

The following chart displays data from course evaluations. Unlike the conclave example, the variables tied to questions on the survey are neither ordered nor sequential. Therefore, there is no natural sorting available for the vertical axes.

Time is a highly useful organizing element for this type of charts. Without such an organizing element, the designer manually customizes an order.

The vertical axes correspond to specific questions on the course evaluation. Students are aggregated into groups based on the "profile" of grades given for the whole set of questions. It's quite easy to see that opinions are most aligned on the "workload" question while most of the scores are skewed high.

Missing values are handled by plotting them as a new category at the bottom of each vertical axis.

This example is similar to the conclave example in that each survey response is categorical, one of five values (plus missing). Matthias also showed examples of hammock plots in which some or all of the variables are numeric data.

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Some of you will see some resemblance of the hammock plot with various similar charts, such as the profile chart, the alluvial chart, the parallel coordinates chart, and Sankey diagrams. Matthias discussed all those as well.

Matthias has a book out called "Applied Statistical Learning" (link).

Also, there is a Python package for the hammock plot on github.