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.

 

 


Pulling the multi-national story out, step by step

Reader Aleksander B. found this Economist chart difficult to understand.

Redo_multinat_1

Given the chart title, the reader is looking for a story about multinationals producing lower return on equity than local firms. The first item displayed indicates that multinationals out-performed local firms in the technology sector.

The pie charts on the right column provide additional information about the share of each sector by the type of firms. Is there a correlation between the share of multinationals, and their performance differential relative to local firms?

***

We can clean up the presentation. The first changes include using dots in place of pipes, removing the vertical gridlines, and pushing the zero line to the background:

Redo_multinat_2

The horizontal gridlines attached to the zero line can also be removed:

Redo_multinat_3

Now, we re-order the rows. Start with the aggregate "All sectors". Then, order sectors from the largest under-performance by multinationals to the smallest.

Redo_multinat_4

The pie charts focus only on the share of multinationals. Taking away the remainders speeds up our perception:

Redo_multinat_5

Help the reader understand the data by dividing the sectors into groups, organized by the performance differential:

Redo_multinat_6

For what it's worth, re-sort the sectors from largest to smallest share of multinationals:

Redo_multinat_7

Having created groups of sectors by share of multinationals, I simplify further by showing the average pie chart within each group:

Redo_multinat_8

***

To recap all the edits, here is an animated gif: (if it doesn't play automatically, click on it)

Redo_junkcharts_econmultinat

***

Judging from the last graphic, I am not sure there is much correlation between share of multinationals and the performance differentials. It's interesting that in aggregate, local firms and multinationals performed the same. The average hides the variability by sector: in some sectors, local firms out-performed multinationals, as the original chart title asserted.


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.

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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.

 

 


Powerful photos visualizing housing conditions in Hong Kong

I was going to react to Alberto's post about the New York Times's article about economic inequality in Hong Kong, which is proposed as one origin to explain the current protest movement. I agree that the best graphic in this set is the "photoviz" showing the "coffins" or "cages" that many residents live in, because of the population density. 

Nyt_hongkong_apartment_photoviz

Then I searched the archives, and found this old post from 2015 which is the perfect response to it. What's even better, that post was also inspired by Alberto.

The older post featured a wonderful campaign by human rights organization Society for Community Organization that uses photoviz to draw attention to the problem of housing conditions in Hong Kong. They organized a photography exhibit on this theme in 2014. They then updated the exhibit in 2016.

Here is one of the iconic photos by Benny Lam:

Soco_trapped_B1

I found more coverage of Benny's work here. There is also a book that we can flip on Vimeo.

In 2017, the South China Morning Post (SCMP) published drone footage showing the outside view of the apartment buildings.

***

What's missing is the visual comparison to the luxury condos where the top 1 percent live. For these, one can  visit the real estate sites, such as Sotheby's. Here is their "12 luxury homes for sales" page.

Another comparison: a 1000 sq feet apartment that sits between those extremes. The photo by John Butlin comes from SCMP's Post Magazine's feature on the apartment:

Butlin_scmp_home

***

Also check out my review of Alberto's fantastic, recent book, How Charts Lie.

Cairo_howchartslie_cover

 

 


What is a bad chart?

In the recent issue of Madolyn Smith’s Conversations with Data newsletter hosted by DataJournalism.com, she discusses “bad charts,” featuring submissions from several dataviz bloggers, including myself.

What is a “bad chart”? Based on this collection of curated "bad charts", it is not easy to nail down “bad-ness”. The common theme is the mismatch between the message intended by the designer and the message received by the reader, a classic error of communication. How such mismatch arises depends on the specific example. I am able to divide the “bad charts” into two groups: charts that are misinterpreted, and charts that are misleading.

 

Charts that are misinterpreted

The Causes of Death entry, submitted by Alberto Cairo, is a “well-designed” chart that requires “reading the story where it is inserted and the numerous caveats.” So readers may misinterpret the chart if they do not also partake the story at Our World in Data which runs over 1,500 words not including the appendix.

Ourworldindata_causesofdeath

The map of Canada, submitted by Highsoft, highlights in green the provinces where the majority of residents are members of the First Nations. The “bad” is that readers may incorrectly “infer that a sizable part of the Canadian population is First Nations.”

Highsoft_CanadaFirstNations

In these two examples, the graphic is considered adequate and yet the reader fails to glean the message intended by the designer.

 

Charts that are misleading

Two fellow bloggers, Cole Knaflic and Jon Schwabish, offer the advice to start bars at zero (here's my take on this rule). The “bad” is the distortion introduced when encoding the data into the visual elements.

The Color-blindness pictogram, submitted by Severino Ribecca, commits a similar faux pas. To compare the rates among men and women, the pictograms should use the same baseline.

Colourblindness_pictogram

In these examples, readers who correctly read the charts nonetheless leave with the wrong message. (We assume the designer does not intend to distort the data.) The readers misinterpret the data without misinterpreting the graphics.

 

Using the Trifecta Checkup

In the Trifecta Checkup framework, these problems are second-level problems, represented by the green arrows linking up the three corners. (Click here to learn more about using the Trifecta Checkup.)

Trifectacheckup_img

The visual design of the Causes of Death chart is not under question, and the intended message of the author is clearly articulated in the text. Our concern is that the reader must go outside the graphic to learn the full message. This suggests a problem related to the syncing between the visual design and the message (the QV edge).

By contrast, in the Color Blindness graphic, the data are not under question, nor is the use of pictograms. Our concern is how the data got turned into figurines. This suggests a problem related to the syncing between the data and the visual (the DV edge).

***

When you complain about a misleading chart, or a chart being misinterpreted, what do you really mean? Is it a visual design problem? a data problem? Or is it a syncing problem between two components?


Clarifying comparisons in censored cohort data: UK housing affordability

If you're pondering over the following chart for five minutes or more, don't be ashamed. I took longer than that.

Ft_ukgenerationalhousing

The chart accompanied a Financial Times article about inter-generational fairness in the U.K. To cut to the chase, a recently released study found that younger generations are spending substantially higher proportions of their incomes to pay for housing costs. The FT article is here (behind paywall). FT actually slightly modified the original chart, which I pulled from the Home Affront report by the Intergenerational Commission.

Uk_generational_propincomehousing

One stumbling block is to figure out what is plotted on the horizontal axis. The label "Age" has gone missing. Even though I am familiar with cohort analysis (here, generational analysis), it took effort to understand why the lines are not uniformly growing in lengths. Typically, the older generation is observed for a longer period of time, and thus should have a longer line.

In particular, the orange line, representing people born before 1895 only shows up for a five-year range, from ages 70 to 75. This was confusing because surely these people have lived through ages 20 to 70. I'm assuming the "left censoring" (missing data on the left side) is because of non-existence of old records.

The dataset is also right-censored (missing data on the right side). This occurs with the younger generations (the top three lines) because those cohorts have not yet reached certain ages. The interpretation is further complicated by the range of birth years in each cohort but let me not go there.

TL;DR ... each line represents a generation of Britons, defined by their birth years. The generations are compared by how much of their incomes did they spend on housing costs. The twist is that we control for age, meaning that we compare these generations at the same age (i.e. at each life stage).

***

Here is my version of the same chart:

Junkcharts_redo_ukgenerationalhousing_1

Here are some of the key edits:

  • Vertical blocks are introduced to break up the analysis by life stage. These guide readers to compare the lines vertically i.e. across generations
  • The generations are explicitly described as cohorts by birth years
  • The labels for the generations are placed next to the lines
  • Gridlines are pushed to the back
  • The age axis is explicitly labeled
  • Age labels are thinned
  • A hierarchy on colors
  • The line segments with incomplete records are dimmed

The harmful effect of colors can be seen below. This chart is the same as the one above, except for retaining the colors of the original chart:

Junkcharts_redo_ukgenerationalhousing_2

 

 


Clearing a forest of labels

This chart by the Financial Times has a strong message, and I like a lot about it:

Ft-europe-growth

The countries are by and large aligned along a diagonal, with the poorer countries growing strongly between 2007-2019 while the richer countries suffered negative growth.

A small issue with the chart is the thick forest of text - redundant text. The sub-title, the axis titles, the quadrant labels, and the left-right-half labels all repeat the same things. In the following chart, I simplify the text:

Redo_fteuropegrowth_text

Typically, I don't put axis titles as a sub-header (or, header of the graphic) but as this may be part of the FT style, I respected it.


Re-thinking a standard business chart of stock purchases and sales

Here is a typical business chart.

Cetera_amd_chart

A possible story here: institutional investors are generally buying AMD stock, except in Q3 2018.

Let's give this chart a three-step treatment.

STEP 1: The Basics

Remove the data labels, which stand sideways awkwardly, and are redundant given the axis labels. If the audience includes people who want to take the underlying data, then supply a separate data table. It's easier to copy and paste from, and doing so removes clutter from the visual.

The value axis is probably created by an algorithm - hard to imagine someone deliberately placing axis labels  $262 million apart.

The gridlines are optional.

Redo_amdinstitution_1

STEP 2: Intermediate

Simplify and re-organize the time axis labels; show the quarter and year structure. The years need not repeat.

Align the vocabulary on the chart. The legend mentions "inflows and outflows" while the chart title uses the words "buying and selling". Inflows is buying; outflows is selling.

Redo_amdinstitution_2

STEP 3: Advanced

This type of data presents an interesting design challenge. Arguably the most important metric is the net purchases (or the net flow), i.e. inflows minus outflows. And yet, the chart form leaves this element in the gaps, visually.

The outflows are numerically opposite to inflows. The sign of the flow is encoded in the color scheme. An outflow still points upwards. This isn't a criticism, but rather a limitation of the chart form. If the red bars are made to point downwards to indicate negative flow, then the "net flow" is almost impossible to visually compute!

Putting the columns side by side allows the reader to visually compute the gap, but it is hard to visually compare gaps from quarter to quarter because each gap is hanging off a different baseline.

The following graphic solves this issue by focusing the chart on the net flows. The buying and selling are still plotted but are deliberately pushed to the side:

Redo_amd_1

The structure of the data is such that the gray and pink sections are "symmetric" around the brown columns. A purist may consider removing one of these columns. In other words:

Redo_amd_2

Here, the gray columns represent gross purchases while the brown columns display net purchases. The reader is then asked to infer the gross selling, which is the difference between the two column heights.

We are almost back to the original chart, except that the net buying is brought to the foreground while the gross selling is pushed to the background.

 


Pay levels in the U.S.

The Wall Street Journal published a graphic showing the median pay levels at "most" public companies in the U.S. here.

Wsj_mediancompanypay

People who attended my dataviz seminar might recognize the similarity with the graphic showing internet download speeds by different broadband technologies. It's a clean, clear way of showing multiple comparisons on the same chart.

You can see the distribution of pay levels of companies within each industry grouping, and the vertical lines showing the sector medians allow comparison across sectors. The median pay levels are quite similar with the energy sector leaning higher, and consumer sector leaning lower.

The consumer sector is extremely heavy on the low side of the pay range. Companies like Universal, Abercrombie, Skechers, Mattel, Gap, etc. all pay at least half their employees less than $6,000. The data is sourced to MyLogIQ. I have no knowledge of how reliable or valid the data are. It's curious to me that Dunkin Brands showed a median of $110K while Starbucks showed $13K.

Wsj_medianpay_dunkinstarbucks

***

I like the interactive features.

The window control lets the user zoom in to different parts of the pay range. This is necessary because of the extremely high salaries. The control doubles as a presentation of the overall distribution of median salaries.

The text box can be used to add data labels to specific companies.

***

See previous discussion of WSJ Graphics.

 


Seeking simplicity in complex data: Bloomberg's dataviz on UK gender pay gap

Bloomberg featured a thought-provoking dataviz that illustrates the pay gap by gender in the U.K. The dataset underlying this effort is complex, and the designers did a good job simplifying the data for ease of comprehension.

U.K. companies are required to submit data on salaries and bonuses by gender, and by pay quartiles. The dataset is incomplete, since some companies are slow to report, and the analyst decided not to merge companies that changed names.

Companies are classified into industry groups. Readers who read Chapter 3 of Numbers Rule Your World (link) should ask whether these group differences are meaningful by themselves, without controlling for seniority, job titles, etc. The chapter features one method used by the educational testing industry to take a more nuanced analysis of group differences.

***

The Bloomberg visualization has two sections. In the top section, each company is represented by the percent difference between average female pay and average male pay. Then the companies within a given industry is shown in a histogram. The histograms provide a view of the disparity between companies within a given industry. The black line represents the relative proportion of companies in a given industry that have no gender pay gap but it’s the weight of the histogram on either side of the black line that carries the graphic’s message.

This is the histogram for arts, entertainment and recreation.

Bloomberg_genderpaygap_arts

The spread within this industry is very wide, especially on the left side of the black line. A large proportion of these companies pay women less on average than men, and how much less is highly variable. There is one extreme positive value: Chelsea FC Foundation that pays the average female about 40% more than the average male.

This is the histogram for the public sector.

Bloomberg_genderpaygap_public
It is a much tighter distribution, meaning that the pay gaps vary less from organization to organization (this statement ignores the possibility that there are outliers not visible on this graphic). Again, the vast majority of entities in this sector pay women less than men on average.

***

The second part of the visualization look at the quartile data. The employees of each company are divided into four equal-sized groups, based on their wages. Think of these groups as the Top 25% Earners, the Second 25%, etc. Within each group, the analyst looks at the proportion of women. If gender is independent of pay, then we should expect the proportions of women to be about the same for all four quartiles. (This analysis considers gender to be the only explainer for pay gaps. This is a problem I've called xyopia, that frames a complex multivariate issue as a bivariate problem involving one outcome and one explanatory variable. Chapter 3 of Numbers Rule Your World (link) discusses how statisticians approach this issue.)

Bloomberg_genderpaygap_public_pieOn the right is the chart for the public sector. This is a pie chart used as a container. Every pie has four equal-sized slices representing the four quartiles of pay.

The female proportion is encoded in both the size and color of the pie slices. The size encoding is more precise while the color encoding has only 4 levels so it provides a “binned” summary view of the same data.

For the public sector, the lighter-colored slice shows the top 25% earners, and its light color means the proportion of women in the top 25% earners group is between 30 and 50 percent. As we move clockwise around the pie, the slices represent the 2nd, 3rd and bottom 25% earners, and women form 50 to 70 percent of each of those three quartiles.

To read this chart properly, the reader must first do one calculation. Women represent about 60% of the top 25% earners in the public sector. Is that good or bad? This depends on the overall representation of women in the public sector. If the sector employs 75 percent women overall, then the 60 percent does not look good but if it employs 40 percent women, then the same value of 60% tells us that the female employees are disproportionately found in the top 25% earners.

That means the reader must compare each value in the pie chart against the overall proportion of women, which is learned from the average of the four quartiles.

***

In the chart below, I make this relative comparison explicit. The overall proportion of women in each industry is shown using an open dot. Then the graphic displays two bars, one for the Top 25% earners, and one for the Bottom 25% earners. The bars show the gap between those quartiles and the overall female proportion. For the top earners, the size of the red bars shows the degree of under-representation of women while for the bottom earners, the size of the gray bars shows the degree of over-representation of women.

Redo_junkcharts_bloombergukgendergap

The net sum of the bar lengths is a plausible measure of gender inequality.

The industries are sorted from the ones employing fewer women (at the top) to the ones employing the most women (at the bottom). An alternative is to sort by total bar lengths. In the original Bloomberg chart - the small multiples of pie charts, the industries are sorted by the proportion of women in the bottom 25% pay quartile, from smallest to largest.

In making this dataviz, I elected to ignore the middle 50%. This is not a problem since any quartile above the average must be compensated by a different quartile below the average.

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The challenge of complex datasets is discovering simple ways to convey the underlying message. This usually requires quite a bit of upfront analytics, data transformation, and lots of sketching.