Variance is a friend of dataviz

Seven years ago, I wrote a post about "invariance" in data visualization, which is something we should avoid (link). Yesterday, Business Insider published the following chart in an article about rising gas prices (link):

Businessinsider_gasprices_prices

The map shows the average prices at the pump in seven regions of the United States. 

This chart is succeeded by the following map:

Businessinsider_gasprices_pricechange

This second map shows the change in average gas prices in the same seven regions.

This design is invariant to the data! While the data change, the visualization looks identical. That's because the data are not encoded to any visual element - they are just printed as labels.

 


Multicultural, multicolor, manufactured outrage

Twitter users were incensed by this chart:

Twitter_worstpiechart

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

Mollywhite_twitter_outrageous

***

An image search reveals this chart form has international appeal.

In Kazakh:

Eurasianbank_piechart_kazakh

In Turkish:

Medirevogrupperformans_piechart_turkey

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

Socialpubli_piechart_spain

In English, from an Indian source:

Panipatinstitute_piechart_india

In Russian:

Russian_piechart

***

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.

Mollywhite_twitter_outrageous_tweet

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

Mollywhite_twitter_outrageous_source

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:

Mollywhite_twitter_outrageous_web3isgoinggreat

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.

Mollywhite_site
]

[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.]


Improving simple bar charts

Here's another bar chart I came across recently. The chart - apparently published by Kaggle - appeared to present challenges data scientists face in industry:

Kaggle

This chart is pretty standard, and inoffensive. But we can still make it better.

Version 1

Redo_kaggle_nodecimals

I removed the decimals from the data labels.

Version 2

Redo_kaggle_noaxislabels

Since every bar is labelled, is anyone looking at the axis labels?

Version 3

Redo_kaggle_nodatalabels

You love axis labels. Then, let's drop the data labels.

Version 4

Redo_kaggle_categories

Ahh, so data scientists struggle with data problems, and people issues. They don't need better tools.


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.

Big-Data-and-the-CMO_chart5-Hurdle-800_30Apr2013Responses 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.)

Redo_CMOsurveyanalytics

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.


Ringing in the data

There is a lot of great stuff at Visual Capitalist.

This circular design isn't one of their best.

Visualcapitalist_GDPDebt2021_1800px_Finalized

***

A self-sufficiency test helps diagnose the problem. Notice that every data point is printed on the diagram. If the data labels were removed, there isn't much one can learn from the chart other than the ranking of countries from most indebted to least. It would be impossible to know the difference in debt levels between any pair of countries.

In other words, the data labels rather than visual elements are doing most of the work. In a good dataviz, we like the visual elements to carry the weight.

***

The concentric rings embed a visual hierarchy: Japan is singled out, then the next tier of countries include Sudan, Greece, Eritrea, Cape Verde, Italy, Suriname, and Barbados; and so on.

What is the clustering algorithm? What determines which countries fall into the same group?

It's implicitly determined by how many countries can fit inside the next ring. The designer carefully computed the number of rings, the widths of the rings, the density of the circles, etc. in such a way that there is no unsightly white space on the outer ring. Score a 10/10 for effort!

So the clustering of countries is not data-driven but constrained by the chart form. This limitation is similar to that found on maps used to illustrate spatial data.

 

 


Speaking to the choir

A friend found the following chart about the "carbon cycle", and sent me an exasperated note, having given up on figuring it out. The chart came from a report, and was reprinted in Ars Technica (link).

Gcp_s09_2021_global_perturbation-800x371

The problem with the chart is that the designer is speaking to the choir. One must know a lot about the carbon cycle already to make sense of everything that's going on.

We see big and small arrows pointing up or down. Each arrow has a number attached to it, plus a range inside brackets. These numbers have no units, and it's not obvious what they are measuring.

The arrows come in a variety of colors. The colors are explained by labels but the labels dexcribe apparently unrelated concepts (e.g. fossil CO2 and land-use change).

Interspersed with the arrows is a singular dot. The dot also has a number attached to it. The number wears a plus sign, which signals it's being treated differently than the quantities with up arrows.

The singular dot is an outcast, ostracized from the community of dots in the bottom part of the chart. These dots have labels but no numbers. They come in different sizes but no scale is provided.

The background is divided into three parts, showing the atmosphere, the land mass, and the ocean. The placement of the arrows and dots suggests each measured quantity concerns one of these three parts. Well... except the dot labeled "surface sediments" that sit on the boundary of the land mass and the ocean.

The three-way classification is only one layer of the chart. A different classification is embedded in the color scheme. The gray, light green, and aquamarine arrows in the sky find their counterparts in the dots of the land mass, and the ocean.

What's more, the boundaries between land and sky, and between land and ocean are also painted with those colors. These boundary segments have been given different colors so that the lengths of these segments seem to contain data but we aren't sure what.

At this point, I noticed thin arrows which appear to depict back and forth flows. There may be two types of such exchanges, one indicated by a cycle, the other by two straight arrows in opposite directions. The cycles have no numbers while each pair of straight thin arrows gets two numbers, always identical.

At the bottom of the chart is a annotation in red: "Budget imbalance = -1.0". Presumably some formula ties the numbers shown above to this -1.0 result. We still don't know the units, and it's unclear if -1.0 is a bad number. A negative number shown in red typically indicates a bad number but how bad is it?

Finally, on the top right corner, I found a legend. It's not obvious at first because the legend symbols (arrows and dots) are shown in gray, a color not used elsewhere on the chart. It appears as if it represents another color category. The legend labels do little for me. What is an "anthropogenic flux"? What does the unit of "GtCO2" stand for? Other jargon includes "carbon cycling" and "stocks". The entire diagram is titled "carbon cycle" while the "carbon cycling" thin arrows are only a small part of the diagram.

The bottom line is I have no idea what this chart is saying to me, other than that the earth is a complex system, and that the designer has tried valiantly to impregnate the diagram with lots of information. If I am well read in environmental science, my experience is likely different.

 

 

 

 

 


Come si dice donut in italiano

One of my Italian readers sent me the following "horror chart". (Last I checked, it's not Halloween.)

Horrorchart

I mean, people are selling these rainbow sunglasses.

Rainbowwunglasses

The dataset behind the chart is the market share of steel production by country in 1992 and in 2014. The presumed story is how steel production has shifted from country to country over those 22 years.

Before anything else, readers must decipher the colors. This takes their eyes off the data and on to the color legend placed on the right column. The order of the color legend is different from that found in the nearest object, the 2014 donut. The following shows how our eyes roll while making sense of the donut chart.

Junkcharts_steeldonuts_eye1

It's easier to read the 1992 donut because of the order but now, our eyes must leapfrog the 2014 donut.

Junkcharts_steeldonuts_eye2

This is another example of a visualization that fails the self-sufficiency test. The entire dataset is actually printed around the two circles. If we delete the data labels, it becomes clear that readers are consuming the data labels, not the visual elements of the chart.

Junkcharts_steeldonuts_sufficiency

The chart is aimed at an Italian audience so they may have a patriotic interest in the data for Italia. What they find is disappointing. Italy apparently completely dropped out of steel production. It produced 3% of the world's steel in 1992 but zero in 2014.

Now I don't know if that is true because while reproducing the chart, I noticed that in the 2014 donut, there is a dark orange color that is not found in the legend. Is that Italy or a mysterious new entrant to steel production?

One alternative is a dot plot. This design accommodates arrows between the dots indicating growth versus decline.

Junkcharts_redo_steeldonuts

 


Pies, bars and self-sufficiency

Andy Cotgreave asked Twitter followers to pick between pie charts and bar charts:

Ac_pie_or_bar

The underlying data are proportions of people who say they won't get the coronavirus vaccine.

I noticed two somewhat unusual features: the use of pies to show single proportions, and the aspect ratio of the bars (taller than typical). Which version is easier to understand?

To answer this question, I like to apply a self-sufficiency test. This test is used to determine whether the readers are using the visual elements of the chart to udnerstand the data, or are they bypassing the visual elements and just reading the data labels? So, let's remove the printed data from the chart and take another look:

Junkcharts_selfsufficiency_pieorbar

For me, these charts are comparable. Each is moderately hard to read. That's because the percentages fall into a narrow range at one end of the range. For both charts, many readers are likely to be looking for the data labels.

Here's a sketch of a design that is self-sufficient.

Junkcharts_selfsufficientdesign

The data do not appear on this chart.

***

My first reaction to Andy's tweet turned out to be a misreading of the charts. I thought he was disaggregating the pie chart, like we can unstack a stacked bar chart.

Junkcharts_probabilities_proportions

Looking at the data more carefully, I realize that the "proportions" are not part to the whole. Or rather, the whole isn't "all races" or "all education levels". The whole is all respondents of a particular type.

 

 


Circular areas offer misleading cues of their underlying data

John M. pointed me on Twitter to this chart about the progress of U.S.'s vaccination campaign:

Whgov_proportiongettingvaccinated

This looks like a White House production, retweeted by WHO. John is unhappy about this nested bubble format, which I'll come back to later.

Let's zoom in on what matters:

Whgov_proportiongettingvaccinated_clip

An even bigger problem with this chart is the Q corner in our Trifecta Checkup. What is the question they are trying to address? It would appear to be the proportion of population that has "already received [one or more doses of] vaccine". And the big words tell us the answer is 8 percent.

_junkcharts_trifectacheckupBut is that really the question? Check out the dark blue circle. It is labeled "population that has already received vaccine" and thus we infer this bubble represents 8 percent. Now look at the outer bubble. Its annotation is "new population that received vaccine since January 27, 2021". The only interpretation that makes sense is that 8 percent  is not the most current number. If that is the case, why would the headline highlight an older statistic, and not the most up-to-date one?

Perhaps the real question is how fast is the progress in vaccination. Perhaps it took weeks to get to the dark circle and then days to get beyond. In order to improve this data visualization, we must first decide what the question really is.

***

Now let's get to those nested bubbles. The bubble chart is a format that is not "sufficient," by which I mean the visual by itself does not convey the data without the help of aids such as labels. Try to answer the following questions:

Junkcharts_whgov_vaccineprogress_bubblequiz

In my view, if your answer to the last question is anything more than 5 seconds, the dataviz has failed. A successful data visualization should not make readers solve puzzles.

The first two questions depict the confusing nature of concentric circle diagrams. The first data point is coded to the inner circle. Where is the second data point? Is it encoded to the outer circle, or just the outer ring?

In either case, human brains are not trained to compare circular areas. For question 1, the outer circle is 70% larger than the smaller circle. For question 2, the ring is 70% of the area of the dark blue circle. If you're thinking those numbers seem unreasonable, I can tell you that was my first reaction too! So I made the following to convince myself that the calculation was correct:

Junkcharts_whgov_vaccineprogress_bubblequiz_2

Circular areas offer misleading visual cues, and should be used sparingly.

[P.S. 2/10/2021. In the next post, I sketch out an alternative dataviz for this dataset.]


Atypical time order and bubble labeling

This chart appeared in a Charles Schwab magazine in Summer, 2019.

Schwab_volatility2018

This bubble chart does not print any data labels. The bubbles take our attention but the designer realizes that the actual values of the volatility are not intuitive numbers. The same is true of any standard deviation numbers. If you're told SD of a data series is 3, it doesn't tell you much by itself.

I first transformed this chart into the equivalent column chart:

Junkcharts_redo_schwabvolatility_columnrank

Two problems surface on the axes.

For the time axis, the years are jumbled. Readers experience vertigo, as we try to figure out how to read the chart. Our expectation that time moves left to right is thwarted. This ordering also requires every single year label to be present.

For the vertical axis, I could have left out the numbers completely. They are not really meaningful. These represent the areas of the bubbles but only relative to how I measured them.

***

In the next version, I sorted time in the conventional manner. Following Tufte's classic advice, only the tops of the columns are plotted.

Junkcharts_redo_schwabvolatility_hashyear

What you see is that this ordering is much easier to comprehend. Figuring out that 2018 is an average year in terms of volatility is not any harder than in the original. In fact, we can reproduce the order of the previous chart just by letting our eyes sweep top to bottom.

To make it even easier to read the vertical axis, I converted the numbers into an index, with the average volatility as 100 (assigned to 0% on the chart) .

Junkcharts_redo_schwabvolatility_hashyearrelative

Now, you can see that 2018 is roughly at the average while 2008 is 400% above the average level. (How should we interpret this statement? That's a question I pose to my statistics students. It's not intuitive how one should interpret the statement that the standard deviation is 5 times higher.)