Too many colors on a chart is bad, but why?

The following chart is bad, but how so?

Junkcharts_colors_columnchart

The chart is annoying because of the misuse of colors.

What is the purpose of the multiple colors used in this chart? It's not encoding any data. Colors are used here to differentiate one bar from its two neighbors. Or perhaps to make the chart more "appealing".

The reason why the coloring scheme backfires is that readers may look for meaning in the colors. What's common between Iceland, United States and Germany for them to be assigned green? What about Japan, New Zealand, Spain and France, all of which shown yellow?

The readers' instinct is driven by a set of unspoken rules that govern the production of data visualization. Specifically, the rule here is: color differences reflect data differences. When such a rule is violated, the reader is misled and confused.

***

For more about this rule, other rules related to making bar charts, and other other rules for making data graphics, please read my Long Read article, here.

 


Food coma and self-sufficiency in dataviz

The Hustle wrote a strong analysis of the business of buffets. If you've read my analysis of Groupon's business model in Numbersense (link), you'll find some similarities. A key is to not think of every customer as an average customer; there are segments of customers who behave differently, and creating a proper mix of different types of customers is the management's challenge. I will make further comments on the statistics in a future post on the sister blog.

At Junk Charts, we'll focus on visualizing and communciating data. The article in The Hustle comes with the following dataviz:

Hustle_buffetcost

This dataviz fails my self-sufficiency test. Recall: self-sufficiency is a basic requirement of visualizing data - that the graphical elements should be sufficient to convey the gist of the data. Otherwise, there is no point in augmenting the data with graphical elements.

The self-sufficiency test is to remove the dataset from the dataviz, and ask whether the graphic can stand on its own. So here:

Redo_hustlebuffetcost_selfsufficiency

The entire set of ingredient costs appears on the original graphic. When these numbers are removed, the reader gets the wrong message - that the cost is equally split between these five ingredients.

This chart reminds me of the pizza chart that everyone thought was a pie chart except its designer! I wrote about it here. Food coma is a thing.

The original chart may be regarded as an illustration rather than data visualization. If so, it's just a few steps from becoming a dataviz. Like this:

Redo_hustlebuffetcost

P.S. A preview of what I'll be talking about at the sister blog. The above diagram illustrates the average case - for the average buffet diner. Underneath these costs is an assumption about the relative amounts of each food that is eaten. But eaten by whom?

Also, if you have Numbersense (link), the chapter on measuring the inflation rate is relevant here. Any inflation metric must assume a basket of goods, but then the goods within the basket have to be weighted by the amount of expenditure. It's much harder to get the ratio of expenditures correct compared to getting price data.

 

 


Taking small steps to bring out the message

Happy new year! Good luck and best wishes!

***

We'll start 2020 with something lighter. On a recent flight, I saw a chart in The Economist that shows the proportion of operating income derived from overseas markets by major grocery chains - the headline said that some of these chains are withdrawing from international markets.

Econ_internationalgroceries_sm

The designer used one color for each grocery chain, and two shades within each color. The legend describes the shades as "total" and "of which: overseas". As with all stacked bar charts, it's a bit confusing where to find the data. The "total" is actually the entire bar, not just the darker shaded part. The darker shaded part is better labeled "home market" as shown below:

Redo_econgroceriesintl_1

The designer's instinct to bring out the importance of international markets to each company's income is well placed. A second small edit helps: plot the international income amounts first, so they line up with the vertical zero axis. Like this:

Redo_econgroceriesintl_2

This is essentially the same chart. The order of international and home market is reversed. I also reversed the shading, so that the international share of income is displayed darker. This shading draws the readers' attention to the key message of the chart.

A stacked bar chart of the absolute dollar amounts is not ideal for showing proportions, because each bar is a different length. Sometimes, plotting relative values summing to 100% for each company may work better.

As it stands, the chart above calls attention to a different message: that Walmart dwarfs the other three global chains. Just the international income of Walmart is larger than the total income of Costco.

***

Please comment below or write me directly if you have ideas for this blog as we enter a new decade. What do you want to see more of? less of?


This Excel chart looks standard but gets everything wrong

The following CNBC chart (link) shows the trend of global car sales by region (or so we think).

Cnbc zh global car sales

This type of chart is quite common in finance/business circles, and has the fingerprint of Excel. After examining it, I nominate it for the Hall of Shame.

***

The chart has three major components vying for our attention: (1) the stacked columns, (2) the yellow line, and (3) the big red dashed arrow.

The easiest to interpret is the yellow line, which is labeled "Total" in the legend. It displays the annual growth rate of car sales around the globe. The data consist of annual percentage changes in car sales, so the slope of the yellow line represents a change of change, which is not particularly useful.

The big red arrow is making the point that the projected decline in global car sales in 2019 will return the world to the slowdown of 2008-9 after almost a decade of growth.

The stacked columns appear to provide a breakdown of the global growth rate by region. Looked at carefully, you'll soon learn that the visual form has hopelessly mangled the data.

Cnbc_globalcarsales_2006

What is the growth rate for Chinese car sales in 2006? Is it 2.5%, the top edge of China's part of the column? Between 1.5% and 2.5%, the extant of China's section? The answer is neither. Because of the stacking, China's growth rate is actually the height of the relevant section, that is to say, 1 percent. So the labels on the vertical axis are not directly useful to learning regional growth rates for most sections of the chart.

Can we read the vertical axis as global growth rate? That's not proper either. The different markets are not equal in size so growth rates cannot be aggregated by simple summing - they must be weighted by relative size.

The negative growth rates present another problem. Even if we agree to sum growth rates ignoring relative market sizes, we still can't get directly to the global growth rate. We would have to take the total of the positive rates and subtract the total of the negative rates.  

***

At this point, you may begin to question everything you thought you knew about this chart. Remember the yellow line, which we thought measures the global growth rate. Take a look at the 2006 column again.

The global growth rate is depicted as 2 percent. And yet every region experienced growth rates below 2 percent! No matter how you aggregate the regions, it's not possible for the world average to be larger than the value of each region.

For 2006, the regional growth rates are: China, 1%; Rest of the World, 1%; Western Europe, 0.1%; United States, -0.25%. A simple sum of those four rates yields 2%, which is shown on the yellow line.

But this number must be divided by four. If we give the four regions equal weight, each is worth a quarter of the total. So the overall average is the sum of each growth rate weighted by 1/4, which is 0.5%. [In reality, the weights of each region should be scaled to reflect its market size.]

***

tldr; The stacked column chart with a line overlay not only fails to communicate the contents of the car sales data but it also leads to misinterpretation.

I discussed several serious problems of this chart form: 

  • stacking the columns make it hard to learn the regional data

  • the trend by region takes a super effort to decipher

  • column stacking promotes reading meaning into the height of the column but the total height is meaningless (because of the negative section) while the net height (positive minus negative) also misleads due to presumptive equal weighting

  • the yellow line shows the sum of the regional data, which is four times the global growth rate that it purports to represent

 

***

PS. [12/4/2019: New post up with a different visualization.]


How to read this cost-benefit chart, and why it is so confusing

Long-time reader Antonio R. found today's chart hard to follow, and he isn't alone. It took two of us multiple emails and some Web searching before we think we "got it".

Ar_submit_Fig-3-2-The-policy-cost-curve-525

 

Antonio first encountered the chart in a book review (link) of Hal Harvey et. al, Designing Climate Solutions. It addresses the general topic of costs and benefits of various programs to abate CO2 emissions. The reviewer praised the "wealth of graphics [in the book] which present complex information in visually effective formats." He presented the above chart as evidence, and described its function as:

policy-makers can focus on the areas which make the most difference in emissions, while also being mindful of the cost issues that can be so important in getting political buy-in.

(This description is much more informative than the original chart title, which states "The policy cost curve shows the cost-effectiveness and emission reduction potential of different policies.")

Spend a little time with the chart now before you read the discussion below.

Warning: this is a long read but well worth it.

 

***

 

If your experience is anything like ours, scraps of information flew at you from different parts of the chart, and you had a hard time piecing together a story.

What are the reasons why this data graphic is so confusing?

Everyone recognizes that this is a column chart. For a column chart, we interpret the heights of the columns so we look first at the vertical axis. The axis title informs us that the height represents "cost effectiveness" measured in dollars per million metric tons of CO2. In a cost-benefit sense, that appears to mean the cost to society of obtaining the benefit of reducing CO2 by a given amount.

That's how far I went before hitting the first roadblock.

For environmental policies, opponents frequently object to the high price of implementation. For example, we can't have higher fuel efficiency in cars because it would raise the price of gasoline too much. Asking about cost-effectiveness makes sense: a cost-benefit trade-off analysis encapsulates the something-for-something principle. What doesn't follow is that the vertical scale sinks far into the negative. The chart depicts the majority of the emissions abatement programs as having negative cost effectiveness.

What does it mean to be negatively cost-effective? Does it mean society saves money (makes a profit) while also reducing CO2 emissions? Wouldn't those policies - more than half of the programs shown - be slam dunks? Who can object to programs that improve the environment at no cost?

I tabled that thought, and proceeded to the horizontal axis.

I noticed that this isn't a standard column chart, in which the width of the columns is fixed and uneventful. Here, the widths of the columns are varying.

***

In the meantime, my eyes are distracted by the constellation of text labels. The viewing area of this column chart is occupied - at least 50% - by text. These labels tell me that each column represents a program to reduce CO2 emissions.

The dominance of text labels is a feature of this design. For a conventional column chart, the labels are situated below each column. Since the width does not usually carry any data, we tend to keep the columns narrow - Tufte, ever the minimalist, has even advocated reducing columns to vertical lines. That leaves insufficient room for long labels. Have you noticed that government programs hold long titles? It's tough to capture even the outline of a program with fewer than three big words, e.g. "Renewable Portfolio Standard" (what?).

The design solution here is to let the column labels run horizontally. So the graphical element for each program is a vertical column coupled with a horizontal label that invades the territories of the next few programs. Like this:

Redo_fueleconomystandardscars

The horror of this design constraint is fully realized in the following chart, a similar design produced for the state of Oregon (lifted from the Plan Washington webpage listed as a resource below):

Figure 2 oregon greenhouse

In a re-design, horizontal labeling should be a priority.

 

***

Realizing that I've been distracted by the text labels, back to the horizontal axis I went.

This is where I encountered the next roadblock.

The axis title says "Average Annual Emissions Abatement" measured in millions metric tons. The unit matches the second part of the vertical scale, which is comforting. But how does one reconcile the widths of columns with a continuous scale? I was expecting each program to have a projected annual abatement benefit, and those would fall as dots on a line, like this:

Redo_abatement_benefit_dotplot

Instead, we have line segments sitting on a line, like this:

Redo_abatement_benefit_bars_end2end_annuallabel

Think of these bars as the bottom edges of the columns. These line segments can be better compared to each other if structured as a bar chart:

Redo_abatement_benefit_bars

Instead, the design arranges these lines end-to-end.

To unravel this mystery, we go back to the objective of the chart, as announced by the book reviewer. Here it is again:

policy-makers can focus on the areas which make the most difference in emissions, while also being mindful of the cost issues that can be so important in getting political buy-in.

The primary goal of the chart is a decision-making tool for policy-makers who are evaluating programs. Each program has a cost and also a benefit. The cost is shown on the vertical axis and the benefit is shown on the horizontal. The decision-maker will select some subset of these programs based on the cost-benefit analysis. That subset of programs will have a projected total expected benefit (CO2 abatement) and a projected total cost.

By stacking the line segments end to end on top of the horizontal axis, the chart designer elevates the task of computing the total benefits of a subset of programs, relative to the task of learning the benefits of any individual program. Thus, the horizontal axis is better labeled "Cumulative annual emissions abatement".

 

Look at that axis again. Imagine you are required to learn the specific benefit of program titled "Fuel Economy Standards: Cars & SUVs".  

Redo_abatement_benefit_bars_end2end_cumlabel

This is impossible to do without pulling out a ruler and a calculator. What the axis labels do tell us is that if all the programs to the left of Fuel Economy Standards: Cars & SUVs were adopted, the cumulative benefits would be 285 million metric tons of CO2 per year. And if Fuel Economy Standards: Cars & SUVs were also implemented, the cumulative benefits would rise to 375 million metric tons.

***

At long last, we have arrived at a reasonable interpretation of the cost-benefit chart.

Policy-makers are considering throwing their support behind specific programs aimed at abating CO2 emissions. Different organizations have come up with different ways to achieve this goal. This goal may even have specific benchmarks; the government may have committed to an international agreement, for example, to reduce emissions by some set amount by 2030. Each candidate abatement program is evaluated on both cost and benefit dimensions. Benefit is given by the amount of CO2 abated. Cost is measured as a "marginal cost," the amount of dollars required to achieve each million metric ton of abatement.

This "marginal abatement cost curve" aids the decision-making. It lines up the programs from the most cost-effective to the least cost-effective. The decision-maker is presumed to prefer a more cost-effective program than a less cost-effective program. The chart answers the following question: for any given subset of programs (so long as we select them left to right contiguously), we can read off the cumulative amount of CO2 abated.

***

There are still more limitations of the chart design.

  • We can't directly read off the cumulative cost of the selected subset of programs because the vertical axis is not cumulative. The cumulative cost turns out to be the total area of all the columns that correspond to the selected programs. (Area is height x width, which is cost per benefit multiplied by benefit, which leaves us with the cost.) Unfortunately, it takes rulers and calculators to compute this total area.

  • We have presumed that policy-makers will make the Go-No-go decision based on cost effectiveness alone. This point of view has already been contradicted. Remember the mystery around negatively cost-effective programs - their existence shows that some programs are stalled even when they reduce emissions in addition to making money!

  • Since many, if not most, programs have negative cost-effectiveness (by the way they measured it), I'd flip the metric over and call it profitability (or return on investment). Doing so removes another barrier to our understanding. With the current cost-effectiveness metric, policy-makers are selecting the "negative" programs before the "positive" programs. It makes more sense to select the "positive" programs before the "negative" ones!

***

In a Trifecta Checkup (guide), I rate this chart Type V. The chart has a great purpose, and the design reveals a keen sense of the decision-making process. It's not a data dump for sure. In addition, an impressive amount of data gathering and analysis - and synthesis - went into preparing the two data series required to construct the chart. (Sure, for something so subjective and speculative, the analysis methodology will inevitably be challenged by wonks.) Those two data series are reasonable measures for the stated purpose of the chart.

The chart form, though, has various shortcomings, as shown here.  

***

In our email exchange, Antonio and I found the Plan Washington website useful. This is where we learned that this chart is called the marginal abatement cost curve.

Also, the consulting firm McKinsey is responsible for popularizing this chart form. They have published this long report that explains even more of the analysis behind constructing this chart, for those who want further details.


Marketers want millennials to know they're millennials

When I posted about the lack of a standard definition of "millennials", Dean Eckles tweeted about the arbitrary division of age into generational categories. His view is further reinforced by the following chart, courtesy of PewResearch by way of MarketingCharts.com.

PewResearch-Generational-Identification-Sept2015

Pew asked people what generation they belong to. The amount of people who fail to place themselves in the right category is remarkable. One way to interpret this finding is that these are marketing categories created by the marketing profession. We learned in my other post that even people who use the term millennial do not have a consensus definition of it. Perhaps the 8 percent of "millennials" who identify as "boomers" are handing in a protest vote!

The chart is best read row by row - the use of stacked bar charts provides a clue. Forty percent of millennials identified as millennials, which leaves sixty percent identifying as some other generation (with about 5 percent indicating "other" responses). 

While this chart is not pretty, and may confuse some readers, it actually shows a healthy degree of analytical thinking. Arranging for the row-first interpretation is a good start. The designer also realizes the importance of the diagonal entries - what proportion of each generation self-identify as a member of that generation. Dotted borders are deployed to draw eyes to the diagonal.

***

The design doesn't do full justice for the analytical intelligence. Despite the use of the bar chart form, readers may be tempted to read column by column due to the color scheme. The chart doesn't have an easy column-by-column interpretation.

It's not obvious which axis has the true category and which, the self-identified category. The designer adds a hint in the sub-title to counteract this problem.

Finally, the dotted borders are no match for the differential colors. So a key message of the chart is buried.

Here is a revised chart, using a grouped bar chart format:

Redo_junkcharts_millennial_id

***

In a Trifecta checkup (link), the original chart is a Type V chart. It addresses a popular, pertinent question, and it shows mature analytical thinking but the visual design does not do full justice to the data story.

 

 


Who is a millennial? An example of handling uncertainty

I found this fascinating chart from CNBC, which attempts to nail down the definition of a millennial.

Millennials2-01

It turns out everyone defines "millennials" differently. They found 23 different definitions. Some media outlets apply different definitions in different items.

I appreciate this effort a lot. The design is thoughtful. In making this chart, the designer added the following guides:

  • The text draws attention to the definition with the shortest range of birth years, and the one with the largest range.
  • The dashed gray gridlines help with reading the endpoints of each bar.
  • The yellow band illustrates the so-called average range. It appears that this average range is formed by taking the average of the beginning years and the average of the ending years. This indicates a desire to allow comparisons between each definition and the average range.
  • The bars are ordered by the ending birth year (right edge).

The underlying issue is how to display uncertainty. The interest here is not just to feature the "average" definition of a millennial but to show the range of definitions.

***

In making my chart, I apply a different way to find the "average" range. Given any year, say 1990, what is the chance that it is included in any of the definitions? In other words, what proportion of the definitions include that year? In the following chart, the darker the color, the more likely that year is included by the "average" opinion.

Redo_junkcharts_cnbcmillennials

I ordered the bars from shortest to the longest so there is no need to annotate them. Based on this analysis, 90 percent (or higher) of the sources list 19651985 to 1993 as part of the range while 70 percent (or higher) list 19611981 to 1996 as part of the range.

 

 


Does this chart tell the sordid tale of TI's decline?

The Hustle has an interesting article on the demise of the TI calculator, which is popular in business circles. The article uses this bar chart:

Hustle_ti_calculator_chart

From a Trifecta Checkup perspective, this is a Type DV chart. (See this guide to the Trifecta Checkup.)

The chart addresses a nice question: is the TI graphing calculator a victim of new technologies?

The visual design is marred by the use of the calculator images. The images add nothing to our understanding and create potential for confusion. Here is a version without the images for comparison.

Redo_junkcharts_hustlet1calc

The gridlines are placed to reveal the steepness of the decline. The sales in 2019 will likely be half those of 2014.

What about the Data? This would have been straightforward if the revenues shown are sales of the TI calculator. But according to the subtitle, the data include a whole lot more than calculators - it's the "other revenues" category in the financial reports of Texas Instrument which markets the TI. 

It requires a leap of faith to believe this data. It is entirely possible that TI calculator sales increased while total "other revenues" decreased! The decline of TI calculator could be more drastic than shown here. We simply don't have enough data to say for sure.

 

P.S. [10/3/2019] Fixed TI.

 

 


Tennis greats at the top of their game

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.

Tableautennisnumberones

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:

Redo_junkcharts_no1tennisplayers

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.


Women workers taken for a loop or four

I was drawn to the following chart in Business Insider because of the calendar metaphor. (The accompanying article is here.)

Businessinsider_payday

Sometimes, the calendar helps readers grasp concepts faster but I'm afraid the usage here slows us down.

The underlying data consist of just four numbers: the wage gaps between race and gender in the U.S., considered simply from an aggregate median personal income perspective. The analyst adopts the median annual salary of a white male worker as a baseline. Then, s/he imputes the number of extra days that others must work to attain the same level of income. For example, the median Asian female worker must work 64 extra days (at her daily salary level) to match the white guy's annual pay. Meanwhile, Hispanic female workers must work 324 days extra.

There are a host of reasons why the calendar metaphor backfired.

Firstly, it draws attention to an uncomfortable detail of the analysis - which papers over the fact that weekends or public holidays are counted as workdays. The coloring of the boxes compounds this issue. (And the designer also got confused and slipped up when applying the purple color for Hispanic women.)

Secondly, the calendar focuses on Year 2 while Year 1 lurks in the background - white men have to work to get that income (roughly $46,000 in 2017 according to the Census Bureau).

Thirdly, the calendar view exposes another sore point around the underlying analysis. In reality, the white male workers are continuing to earn wages during Year 2.

The realism of the calendar clashes with the hypothetical nature of the analysis.

***

One can just use a bar chart, comparing the number of extra days needed. The calendar design can be considered a set of overlapping bars, wrapped around the shape of a calendar.

The staid bars do not bring to life the extra toil - the message is that these women have to work harder to get the same amount of pay. This led me to a different metaphor - the white men got to the destination in a straight line but the women must go around loops (extra days) before reaching the same endpoint.

Redo_businessinsider_racegenderpaygap

While the above is a rough sketch, I made sure that the total length of the lines including the loops roughly matches the total number of days the women needed to work to earn $46,000.

***

The above discussion focuses solely on the V(isual) corner of the Trifecta Checkup, but this data visualization is also interesting from the D(ata) perspective. Statisticians won't like such a simple analysis that ignores, among other things, the different mix of jobs and industries underlying these aggregate pay figures.

Now go to my other post on the sister (book) blog for a discussion of the underlying analysis.