Modern design meets dataviz

This chart was submitted via Twitter (thanks John G.).

Perhaps the designer is inspired by this:

That's the Royal Ontario Museum, one of the beautiful landmarks in Toronto.

***

The chart addresses an interesting question - how much do home buyers over or under-estimate home value?  That said, gathering data to answer this question is challenging. I won't delve into this issue in this post.

Let's ask where readers are looking for data on the chart. It appears that we should use the right edge of each triangle. While the left edge of the red triangle might be useful, the left edges of the other triangles definitely would not contain data.

Note that, like modern architecture, the designer is playing with edges. None of the four right edges is properly vertical - none of the lines cuts the horizontal axis at a right angle. So the data actually reside in the imaginary vertical lines from the apexes to the horizontal baseline.

Where is the horizontal baseline? It's not where it is drawn either. The last number in the series is a negative number and so the real baseline is in the middle of the plot area, where the 0% value is.

The following chart shows (left side) the misleading signals sent to readers and (right side) the proper way to consume the data.

The degree of distortion is quite extreme. Only the fourth value is somewhat accurate, albeit by accident.

The design does not merely perturb the chart; it causes a severe adverse reaction.

 

P.S. [9/19/2022] Added submitter name.

 

 

 

Trying too hard

Today, I return to the life expectancy graphic that Antonio submitted. In a previous post, I looked at the bumps chart. The centerpiece of that graphic is the following complicated bar chart.

Let's start with the dual axes. On the left, age, and on the right, year of birth. I actually like this type of dual axes. The two axes present two versions of the same scale so the dual axes exist without distortion. It just allows the reader to pick which scale they want to use.

It baffles me that the range of each bar runs from 2.5 years to 7.5 years or 7.5 years to 2.5 years, with 5 or 10 years situated in the middle of each bar.

Reading the rest of the chart is like unentangling some balled up wires. The author has created a statistical model that attributes cause of death to male life expectancy in such a way that you can take the difference in life expectancy between two time points, and do a kind of waterfall analysis in which each cause of death either adds to or subtracts from the prior life expectancy, with the sum of these additions and substractions leading to the end-of-period life expectancy.

The model is complicated enough, and the chart doesn't make it any easier.

The bars are rooted at the zero value. The horizontal axis plots addition or substraction to life expectancy, thus zero represents no change during the period. Zero does not mean the cause of death (e.g. cancer) does not contribute to life expectancy; it just means the contribution remains the same.

The changes to life expectancy are shown in units of months. I'd prefer to see units of years because life expectancy is almost always given in years. Using years turn 2.5 months into 0.2 years which is a fraction, but it allows me to see the impact on the reported life expectancy without having to do a month-to-year conversion.

The chart highlights seven causes of death with seven different colors, plus gray for others.

What really does a number on readers is the shading, which adds another layer on top of the hues. Each color comes in one of two shading, referencing two periods of time. The unshaded bar segments concern changes between 2010 and "2019" while the shaded segments concern changes between "2019" and 2020. The two periods are chosen to highlight the impact of COVID-19 (the red-orange color), which did not exist before "2019".

Let's zoom in on one of the rows of data - the 72.5 to 77.5 age group.

COVID-19 (red-orange) has a negative impact on life expectancy and that's the easy one to see. That's because COVID-19's contribution as a cause of death is exactly zero prior to "2019". Thus, the change in life expectancy is a change from zero. This is not how we can interpret any of the other colors.

Next, we look at cancer (blue). Since this bar segment sits on the right side of zero, cancer has contributed positively to change in life expectancy between 2010 and 2020. Practically, that means proportionally fewer people have died from cancer. Since the lengths of these bar segments correspond to the relative value, not absolute value, of life expectancy, longer bars do not necessarily indicate more numerous deaths.

Now the blue segment is actually divided into two parts, the shaded and not shaded. The not-shaded part is for the period "2019" to 2020 in the first year of the COVID-19 pandemic. The shaded part is for the period 2010 to "2019". It is a much wider span but it also contains 9 years of changes versus "1 year" so it's hard to tell if the single-year change is significantly different from the average single-year change of the past 9 years. (I'm using these quotes because I don't know whether they split the year 2019 in the middle since COVID-19 didn't show up till the end of that year.)

Next, we look at the yellow-brown color correponding to CVD. The key feature is that this block is split into two parts, one positive, one negative. Prior to "2019", CVD has been contributing positively to life expectancy changes while after "2019", it has contributed negatively. This observation raises some questions: why would CVD behave differently with the arrival of the pandemic? Are there data problems?

***

A small multiples design - splitting the period into two charts - may help here. To make those two charts comparable, I'd suggest annualizing the data so that the 9-year numbers represent the average annual values instead of the cumulative values.

 

 

Speedometer charts: love or hate

Pie chart hate is tired. In this post, I explain my speedometer hate. (Also called gauges,  dials)

Next to pie charts, speedometers are perhaps the second most beloved chart species found on business dashboards. Here is a typical example:

 

For this post, I found one on Reuters about natural gas in Europe. (Thanks to long-time contributor Antonio R. for the tip.)

The reason for my dislike is the inefficiency of this chart form. In classic Tufte-speak, the speedometer chart has a very poor data-to-ink ratio. The entire chart above contains just one datum (73%). Most of the ink are spilled over non-data things.

This single number has a large entourage:

- the curved axis
- ticks on the axis
- labels on the scale
- the dial
- the color segments
- the reference level "EU target"

These are not mere decorations. Taking these elements away makes it harder to understand what's on the chart.

Here is the chart without the curved axis:

Here is the chart without axis labels:

Here is the chart without ticks:

When the tick labels are present, the chart still functions.

Here is the chart without the dial:

The datum is redundantly encoded in the color segments of the "axis".

Here is the chart without the dial or the color segments:

If you find yourself stealing a peek at the chart title below, you're not alone.

All versions except one increases our cognitive load. This means the entourage is largely necessary if one encodes the single number in a speedometer chart.

The problem with the entourage is that readers may resort to reading the text rather than the chart.

***

The following is a minimalist version of the Reuters chart:

I removed the axis labels and the color segments. The number 73% is shown using the dial angle.

The next chart adds back the secondary message about the EU target, as an axis label, and uses color segments to show the 73% number.

Like pie charts, there are limited situations in which speedometer charts are acceptable. But most of the ones we see out there are just not right.

***

One acceptable situation is to illustrate percentages or proportions, which is what the EU gas chart does. Of course, in that situation, one can alo use a pie chart without shame.

For illustrating proportions, I prefer to use a full semicircle, instead of the circular sector of arbitrary angle as Reuters did. The semicircle lends itself to easy marks of 25%, 50%, 75%, etc, eliminating the need to print those tick labels.

***

One use case to avoid is numeric data.

Take the regional sales chart pulled randomly from a Web search above:

These charts are completely useless without the axis labels.

Besides, because the span of the axis isn't 0% to 100%, every tick mark must be labelled with the numeric value. That's a lot of extra ink used to display a single value!

Funnels and scatters

I took a peek at some of the work submitted by Ray Vella's students in his NYU dataviz class recently.

The following chart by Hosanah Bryan caught my eye:

The data concern the GDP gap between rich and poor regions in various countries. In some countries, especially in the U.K., the gap is gigantic. In other countries, like Spain and Sweden, the gap is much smaller.

The above chart uses a funnel metaphor to organize the data, although the funnel does not add more meaning (not that it has to). Between that, the color scheme and the placement of text, it's visually clean and pleasant to look at.

The data being plotted are messy. They are not actual currency values of GDP. Each number is an index, and represents the relative level of the GDP gap in a given year and country. The gap being shown by the colored bars are differences in these indices 15 years apart. (The students were given this dataset to work with.)

So the chart is very hard to understand if one focuses on the underlying data. Nevertheless, the same visual form can hold other datasets which are less complicated.

One can nitpick about the slight misrepresentation of the values due to the slanted edges on both sides of the bars. This is yet another instance of the tradeoff between beauty and precision.

***

The next chart by Liz Delessert engages my mind for a different reason.

The scatter plot sets up four quadrants. The top right is "everyone gets richer". The top left, where most of the dots lie, is where "the rich get richer, the poor get poorer".  This chart shows a thoughtfulness about organizing the data, and the story-telling.

The grid setup cues readers toward a particular way of looking at the data.

But power comes with responsibility. Such scatter plots are particularly susceptible to the choice of data, in this case, countries. It is tempting to conclude that there are no countries in which everyone gets poorer. But that statement more likely tells us more about which countries were chosen than the real story.

I like to see the chart applied to other data transformations that are easier. For example, we can start with the % change in GDP computed separately for rich and for poor. Then we can form a ratio of these two percent changes.

 

 

Dataviz is good at comparisons if we make the right comparisons

In an article about gas prices around the world, the Washington Post uses the following bar chart (link):

There are a few wrinkles in this one compared to the most generic bar chart one can produce:

(The numbers on my chart are not the same as Washington Post's. That's because the data vendor charges for data, except for the most recent week. So, my data is from a different week.)

The gas prices are not expressed in dollars but a transformation turns prices into a cost-effectiveness metric: miles per dollar, or more precisely, miles per $40 dollars of gas. The metric has a reverse direction - the higher the price, the lower the miles. The data transformation belongs to the D corner of the Trifecta Checkup framework (link). Depending on how one poses the Q(uestion) of the chart, the shift from dollars to miles can bring the Q and the D in sync.

In the V(isual) corner, the designer embellishes the bars. A car icon is placed at the tip of each bar while the bar itself is turned into a wavy path, symbolizing a dirt path. The driving metaphor is in full play. In fact, the video makes the most out of it. There is no doubt that the embellishment has turned a mere scientific presentation into a form of entertainment.

***

Did the embellishment harm visual clarity? For the most part, no.

The worst it can get is when they compared U.S. and India/South Africa:

The left column shows the original charts from the article. In  both charts, the two cars are so close together that it is impossible to learn the scale of the difference. The amount of difference is a fraction of the width of a car icon.

The right column shows the "self-sufficiency test". Imagine the data labels are not on the chart. What we learn is that if we wanted to know how big of a gap is between the two countries, when reading the charts on the left, we are relying on the data labels, not the visual elements. On the right side, if we really want to learn the gaps, we have to look through the car icons to find the tips of the bars!

This discussion does not necessarily doom the appealing chart. If the message one wants to send with the India/South Afrcia charts is that there is negligible difference between them, then it is not crucial to present the precise differences in prices.

***

The real problem with this dataviz is in the D corner. Comparing countries is hard.

As shown above, by the miles per $40 spend metric, U.S. and India are rated essentially the same. So is the average American and the average Indian suffering equally?

Far from it. The clue comes from the aggregate chart, in which countries are divided into three tiers: high income, upper middle income and lower middle income. The U.S. belongs to the high-income tier while India falls into the lower-middle-income tier.

The cost of living in India is much lower than in the US. Forty dollars is a much bigger chunk of an Indian paycheck than an American one.

To adjust for cost of living, economists use a PPP (purchasing power parity) value. The following chart shows the difference:

The right graph contains cost-of-living adjustments. It shows a completely different picture. Nominally (left chart), the price of gas in about the same in dollar terms between U.S. and India. In terms of cost of living, gas is actually 5 times more expensive in India. Thus, the adjusted miles per $40 gas number is much smaller for India than the unadjusted. (Because PPP is relative to U.S. prices, the U.S. numbers are not affected.)

PPP is not the end-all here. According to the Economic Times (India), only 22 out of 1,000 Indians own cars, compared to 980 out of 1,000 Americans. Think about the implication of using any statistic that averages the entire population!

***

Why is gas more expensive in California than the U.S. average? The talking point I keep hearing is environmental regulations. Gas prices may be higher in Europe for a similar reason. Residents in those places may be willing to pay higher prices because they get satisfaction from playing their part in preserving the planet for future generations.

The footnote discloses this not-trivial issue.

When converting from dollars per gallon/liter into miles per $40, we need data on miles per gallon/liter. Americans notoriously drive cars (trucks, SUVs, etc.) that have much lower mileage than those driven by other countries. However, this factor is artificially removed by assuming the same car with 32 mpg on all countries. A quick hop to the BTS website tells us that the average mpg of American cars is a third of that assumption. [See note below.]

Ignoring cross-country comparisons for the time being, the true number for U.S. is not 247 miles per $40 spent on gas as claimed. It is a third of that value: 82 miles per $40 spent.

It's tough to find data on fuel economy of all passenger cars, not just new passenger cars. I found Australia's number, which is 21 mpg. So this brings the miles per $40 number down from about 230 to 115. These are not small adjustments.

Washington Post's analysis paints a simplistic picture that presupposes that price is the only thing people care about. I call this issue xyopia. It's when the analyst frames the problem as factor x explaining outcome y, and when factor x is not the only, and frequently not even the most important, factor affecting y.

More on xyopia.

More discussion of Washington Post graphics.

 

[P.S. 7-25-2022. Reader Cody Curtis pointed out in the comments that the Bureau of Transportation Statistics report was using km/liter as units, not miles per gallon. The 10 km/liter number for average cars is roughly 23 mpg. I'll leave the text as is in the post as the larger point is valid: that there is variation in average fuel economy between nations - partly due to environemental regulation and consumer behavior - and thus, a proper comparison requires adjusting for this factor.]

Funnel is just for fun

This is part 2 of a review of a recent video released by NASA. Part 1 is here.

The NASA video that starts with the spiral chart showing changes in average global temperature takes a long time (about 1 minute) to run through 14 decades of data, and for those who are patient, the chart then undergoes a dramatic transformation.

With a sleight of hand, the chart went from a set of circles to a funnel. Here is a look:

What happens is the reintroduction of a time dimension. Imagine pushing the center of the spiral down into the screen to create a third dimension.

Our question as always is - what does this chart tell readers?

***

The chart seems to say that the variability of temperature has increased over time (based on the width of the funnel). The red/blue color says the temperature is getting hotter especially in the last 20-40 years.

When the reader looks beneath the surface, the chart starts to lose sense.

The width of the funnel is really a diameter of the spiral chart in the given year. But, if you recall, the diameter of the spiral (polar) chart isn't the same between any pairs of months.

In the particular rendering of this video, the width of the funnel is the diameter linking the April and October values.

Remember the polar gridlines behind the spiral:

Notice the hole in the middle. This hole has arbitrary diameter. It can be as big or as small as the designer makes it. Thus, the width of the funnel is as big or as small as the designer wants it. But the first thing that caught our attention is the width of the funnel.

***

The entire section between -1 and + 1 is, in fact, meaningless. In the following chart, I removed the core of the funnel, adding back the -1 degree line. Doing so exposes an incompatibility between the spiral and funnel views. The middle of the polar grid is negative infinity, a black hole.

For a moment, the two sides of the funnel look like they are mirror images. That's not correct, either. Each width of the funnel represents a year, and the extreme values represent April and October values. The line between those two values does not signify anything real.

Let's take a pair of values to see what I mean.

I selected two values for October 2021 and October 1899 such that the first value appears as a line double the length of the second. The underlying values are +0.99C and -0.04C, roughly speaking, +1 and 0, so the first value is definitely not twice the size of the second.

The funnel chart can be interpreted, in an obtuse way, as a pair of dot plots. As shown below, if we take dot plots for Aprils and Octobers of every year, turn the chart around, and then connect the corresponding dots, we arrive at the funnel chart.

***

This NASA effort illustrates a central problem in visual communications: attention (what Andrew Gelman calls "grabbiness") and information integrity. On the one hand, what's the point of an accurate chart when no one is paying attention? On the other hand, what's the point of a grabby chart when anyone who pays attention gets the wrong information? It's not easy to find that happy medium.

Multicultural, multicolor, manufactured outrage

Twitter users were incensed by this chart:

It's being slammed as one of the most outrageous charts ever.

***

An image search reveals this chart form has international appeal.

In Kazakh:

In Turkish:

In Arabic, but the image source is a Spanish company:

In English, from an Indian source:

In Russian:

***

Some people are calling this a pie chart.

But it isn't a pie chart since the slices clearly add up to more than one full circle.

It may be a graph template from an infographics website. You see people are applying data labels without changing the sizes or orientation or even colors of the slices. So the chart form is used as a container for data, rather than an encoder.

***

The Twitter user who called this "outrageous" appears to want to protect the designer, as the words have been deliberately snipped from the chart.

Nevertheless, Molly White coughed up the source in a subsequent tweet.

A bit strange, if you stop and think a little. Why would Molly shame the designer 20 hours later after she decided not to?

 

 

According to Molly, the chart appeared on the website of an NFT company. [P.S. See note below]

Here's the top of the page that Molly White linked to:

Notice the author of this page. That's "Molly White",  who is the owner of this NFT company! [See note below: she's the owner of a satire website who was calling out the owner of this company.]

Who's more outrageous?

Someone creating the most outrageous chart in order to get clout from outraged Twitter users and drive traffic to her new NFT venture? Or someone creating the template for the outrageous chart form, spawning an international collection?

 

[P.S. 3/17/2022 The answer is provided by other Twitter users, and the commentors. The people spreading this chart form is more ourageous. I now realized that Molly runs a sarcastic site. When she linked to the "source", she linked to her own website, which I interpreted as the source of the image. The page did contain that image, which added to the confusion. I must also add her work looks valuable, as it assesses some of the wild claims in Web3 land.

]

[P.S. 3/17/2022 Molly also pointed out that her second tweet about the source came around 45 minutes after the first tweet. Twitter showed "20 hours" because it was 20 hours from the time I read the tweet.]

The envelope of one's data

This post is the second post in response to a blog post at StackOverflow (link) in which the author discusses the "harm" of "aggregating away the signal" in your dataset. The first post appears on my book blog earlier this week (link).

One stop in their exploratory data analysis journey was the following chart:

This chart plots all the raw data, all 8,760 values of electricity consumption in California in 2020. Most analysts know this isn't a nice chart, and it's an abuse of ink. This chart is used as a contrast to the 4-week moving average, which was hoisted up as an example of "over-aggregation".

Why is the above chart bad (aside from the waste of ink)? Think about how you consume the information. For me, I notice these features in the following order:

1. I see the upper "envelope" of the data, i.e. the top values at each hour of each day throughout the year. This gives me the seasonal pattern with a peak in the summer months.
2. I see the lower "envelope" of the data
3. I see the "height" of the data, which is, roughly speaking, the range of values within a day
4. If I squint hard enough, I see a darker band within the band, which roughly maps to the most frequently occurring values (this feature becomes more prominent if we select a lighter shade of gray)

The chart may not be as bad as it looks. The "moving average" is sort of visible. The variability of consumption is visible. The primary problem is it draws attention to the outliers, rather than the more common values.

The envelope of any dataset is composed of extreme values, by definition. For most analysis objectives, extreme values are "noise". In the chart above, it's hard to tell how common the maximum values are relative to other possible values but it's the upper envelope that captures my attention - simply because it's the easiest trend to make out.

***

The same problem actually surfaces in the "improved" chart:

As explained in the preceding post, this chart rearranges the data. Instead of a single line, therea are now 52 overlapping lines, one for each week of the year. So each line is much less dense and we can make out the hour of day/day of week pattern.

Notice that the author draws attention to the upper envelope of this chart. They notice the line(s) near the top are from the summer, and this further guides their next analysis.

The reason for focusing on the envelope is the same as in the other chart. Where the lines are dense, it's not easy to make out the pattern.

Even the envelope is not as clear as it seems! There is no reason why the highlighted week (August 16 to 23) should have the highest consumption value each hour of each day of the week. It's possible that the line dips into the middle of the range at various points along the line. In the following chart, I highlight two time points in which lines may or may not have crossed:

In an interactive chart, each line can be highlighted to resolve the confusion.

Note that the lower envelope is much harder to decipher, given the density of lines.

***
The author then pursues a hypothesis that there are lines (weeks) with one intra-day peak and there are those with two peaks.

I'd propose that those are not discrete states but continuous. The base pattern can be one with two peaks, a higher peak in the evening, and a lower peak in the morning. Now, if you imagine pushing up the evening peak while holding the lower peak at its height, you'd gradually "erase" the lower peak but it's just receded into the background.

Possibly the underlying driver is the total demand for energy. The higher the demand, the more likely it's concentrated in the evening, which causes the lower peak to recede. The lower the demand, the more likely we see both peaks.

In either case, the prior chart drives the direction of the next analysis.

 

 

 

 

 

Easy breezy bar charts, perhaps

I came across the following bar chart (link), which presents the results of a survey of CMOs (Chief Marketing Officers) on their attitudes toward data analytics.

Responses are tabulated to the question about the most significant hurdle(s) against the increasing use of data and analytics for marketing.

Eleven answers were presented, in addition to the catchall "Other" response. I'm unable to divine the rule used by the designer to sequence the responses.

It's not in order of significance, the most obvious choice. It's not alphabetical, either.

***

I think this indiscretion is partially redeemed by the use of color shades. The darkest blue shade points our eyes to the most significant hurdle - lack of investment in technology (44% of respondents). The second most significant hurdle is "availability of credible tools for measuring effectiveness" (31%), and that too is in dark blue.

Now what? The third most popular answer has 30% of the respondents, but it's shown by the second palest blue! I then realize the colors don't actually convey any information. Five shades of blue were selected, and they are laid out from top to bottom, from palest to darkest, in a sequential, recursive manner.

***

This chart is wild. Notice how the heights of the bars are variable. It seems that some bars have been widened to accommodate wrapped lines of text. These small edits introduce visual distortion so that the areas of these bars no longer are proportional to the data.

I like a pair of design decisions. Not showing decimal places and appending the % sign on each bar label is good. They also extend the horizontal axis to 100%. This shows what proportion of the respondents selected any particular answer - we note that a respondent is allowed to select more than one response.

The following is a more standard way of making a bar chart. (The color shading is not necessary.)

This example proves that the V corner of the Trifecta Checkup is still relevant. After one develops a good question, collects useful data and selects a standard chart form, figuring out how to visually display the information is not as easy breezy as one might think.

Visualizing composite ratings

A twitter reader submitted the following chart from Autoevolution (link):

This is not a successful chart for the simple reason that readers want to look away from it. It's too busy. There is so much going on that one doesn't know where to look.

The underlying dataset is quite common in the marketing world. Through surveys, people are asked to rate some product along a number of dimensions (here, seven). Each dimension has a weight, and combined, the weighted sum becomes a composite ranking (shown here in gray).

Nothing in the chart stands out as particularly offensive even though the overall effect is repelling. Adding the overall rating on top of each column is not the best idea as it distorts the perception of the column heights. But with all these ingredients, the food comes out bland.

***

The key is editing. Find the stories you want to tell, and then deconstruct the chart to showcase them.

I start with a simple way to show the composite ranking, without any fuss:

[Since these are mockups, I have copied all of the data, just the top 11 items.]

Then, I want to know if individual products have particular strengths or weaknesses along specific dimensions. In a ranking like this, one should expect that some component ratings correlate highly with the overall rating while other components deviate from the overall average.

An example of correlated ratings is the Customers dimension.

The general pattern of the red dots clings closely to that of the gray bars. The gray bars are the overall composite ratings (re-scaled to the rating range for the Customers dimension). This dimension does not tell us more than what we know from the composite rating.

By contrast, the Developers Ecosystem dimension provides additional information.

Esri, AzureMaps and Mapbox performed much better on this dimension than on the average dimension. 

***

The following construction puts everything together in one package: