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:

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.

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.

 

 

The windy path to the Rugby World Cup

When I first saw the following chart, I wondered whether it is really that challenging for these eight teams to get into the Rugby World Cup, currently playing in Japan:

Another visualization of the process conveys a similar message. Both of these are uploaded to Wikipedia.

(This one hasn't been updated and still contains blank entries.)

***

What are some of the key messages one would want the dataviz to deliver?

• For the eight countries that got in (not automatically), track their paths to the World Cup. How many competitions did they have to play?
• For those countries that failed to qualify, track their paths to the point that they were stopped. How many competitions did they play?
• What is the structure of the qualification rounds? (These are organized regionally, in addition to certain playoffs across regions.)
• How many countries had a chance to win one of the eight spots?
• Within each competition, how many teams participated? Did the winner immediately qualify, or face yet another hurdle? Did the losers immediately disqualify, or were they offered another chance?

Here's my take on this chart:

 

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.

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:

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.

Choosing between individuals and aggregates

Friend/reader Thomas B. alerted me to this paper that describes some of the key chart forms used by cancer researchers.

It strikes me that many of the "new" charts plot granular data at the individual level. This heatmap showing gene expressions show one column per patient:

This so-called swimmer plot shows one bar per patient:

This spider plot shows the progression of individual patients over time. Key events are marked with symbols.

These chart forms are distinguished from other ones that plot aggregated statistics: statistical averages, medians, subgroup averages, and so on.

One obvious limitation of such charts is their lack of scalability. The number of patients, the variability of the metric, and the timing of trends all drive up the amount of messiness.

I am left wondering what Question is being addressed by these plots. If we are concerned about treatment of an individual patient, then showing each line by itself would be clearer. If we are interested in the average trends of patients, then a chart that plots the overall average, or subgroup averages would be more accurate. If the interpretation of the individual's trend requires comparing with similar patients, then showing that individual's line against the subgroup average would be preferred.

When shown these charts of individual lines, readers are tempted to play the statistician - without using appropriate tools! Readers draw aggregate conclusions, performing the aggregation in their heads.

The authors of the paper note: "Spider plots only provide good visual qualitative assessment but do not allow for formal statistical inference." I agree with the second part. The first part is a fallacy - if the visual qualitative assessment is good enough, then no formal inference is necessary! The same argument is often made when people say they don't need advanced analysis because their simple analysis is "directionally accurate". When is something "directionally inaccurate"? How would one know?

Reference: Chia, Gedye, et. al., "Current and Evolving Methods to Visualize Biological Data in Cancer Research", JNCI, 2016, 108(8). (link)

***

Meteoreologists, whom I featured in the previous post, also have their own spider-like chart for hurricanes. They call it a spaghetti map:

Compare this to the "cone of uncertainty" map that was featured in the prior post:

These two charts build upon the same dataset. The cone map, as we discussed, shows the range of probable paths of the storm center, based on all simulations of all acceptable models for projection. The spaghetti map shows selected individual simulations. Each line is the most likely trajectory of the storm center as predicted by a single simulation from a single model.

The problem is that each predictive model type has its own historical accuracy (known as "skill"), and so the lines embody different levels of importance. Further, it's not immediately clear if all possible lines are drawn so any reader making conclusions of, say, the envelope containing x percent of these lines is likely to be fooled. Eyeballing the "cone" that contains x percent of the lines is not trivial either. We tend to naturally drift toward aggregate statistical conclusions without the benefit of appropriate tools.

Plots of individuals should be used to address the specific problem of assessing individuals.

As Dorian confounds meteorologists, we keep our minds clear on hurricane graphics, and discover correlation as our friend

As Hurricane Dorian threatens the southeastern coast of the U.S., forecasters are fretting about the lack of consensus among various predictive models used to predict the storm’s trajectory. The uncertainty of these models, as reflected in graphical displays, has been a controversial issue in the visualization community for some time.

Let’s start by reviewing a visual design that has captured meteorologists in recent years, something known as the cone map.

If asked to explain this map, most of us trace a line through the middle of the cone understood to be the center of the storm, the “cone” as the areas near the storm center that are affected, and the warmer colors (red, orange) as indicating higher levels of impact. [Note: We will  design for this type of map circa 2000s.]

The above interpretation is complete, and feasible. Nevertheless, the data used to make the map are forward-looking, not historical. It is still possible to stick to the same interpretation by substituting historical measurement of impact with its projection. As such, the “warmer” regions are projected to suffer worse damage from the storm than the “cooler” regions (yellow).

After I replace the text that was removed from the map (see below), you may notice the color legend, which discloses that the colors on the map encode probabilities, not storm intensity. The text further explains that the chart shows the most probable path of the center of the storm – while the coloring shows the probability that the storm center will reach specific areas.

***

When reading a data graphic, we rarely first look for text about how to read the chart. In the case of the cone map, those who didn’t seek out the instructions may form one of these misunderstandings:

1. For someone living in the yellow-shaded areas, the map does not say that the impact of the storm is projected to be lighter; it’s that the center of the storm has a lower chance of passing right through. If, however, the storm does pay a visit, the intensity of the winds will reach hurricane grade.
2. For someone living outside the cone, the map does not say that the storm will definitely bypass you; it’s that the chance of a direct hit is below the threshold needed to show up on the cone map. Thee threshold is set to attain 66% accurate. The actual paths of storms are expected to stay inside the cone two out of three times.

Adding to the confusion, other designers have produced cone maps in which color is encoding projections of wind speeds. Here is the one for Dorian.

This map displays essentially what we thought the first cone map was showing.

One way to differentiate the two maps is to roll time forward, and imagine what the maps should look like after the storm has passed through. In the wind-speed map (shown below right), we will see a cone of damage, with warmer colors indicating regions that experienced stronger winds.

In the storm-center map (below right), we should see a single curve, showing the exact trajectory of the center of the storm. In other words, the cone of uncertainty dissipates over time, just like the storm itself.

 

After scientists learned that readers were misinterpreting the cone maps, they started to issue warnings, and also re-designed the cone map. The cone map now comes with a black-box health warning right up top. Also, in the storm-center cone map, color is no longer used. The National Hurricane Center even made a youtube pointing out the dos and donts of using the cone map.

***

The conclusion drawn from misreading the cone map isn’t as devastating as it’s made out to be. This is because the two issues are correlated. Since wind speeds are likely to be stronger nearer to the center of the storm, if one lives in a region that has a low chance of being a direct hit, then that region is also likely to experience lower average wind speeds than those nearer to the projected center of the storm’s path.

Alberto Cairo has written often about these maps, and in his upcoming book, How Charts Lie, there is a nice section addressing his work with colleagues at the University of Miami on improving public understanding of these hurricane graphics. I highly recommended Cairo’s book here.

P.S. [9/5/2019] Alberto also put out a post about the hurricane cone map.

 

 

 

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.)

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.

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.

 

 

This Wimbledon beauty will be ageless

This Financial Times chart paints the picture of the emerging trend in Wimbledon men’s tennis: the average age of players has been rising, and hits 30 years old for the first time ever in 2019.

The chart works brilliantly. Let's look at the design decisions that contributed to its success.

The chart contains a good amount of data and the presentation is carefully layered, with the layers nicely tied to some visual cues.

Readers are drawn immediately to the average line, which conveys the key statistical finding. The blue dot  reinforces the key message, aided by the dotted line drawn at 30 years old. The single data label that shows a number also highlights the message.

Next, readers may notice the large font that is applied to selected players. This device draws attention to the human stories behind the dry data. Knowledgable fans may recall fondly when Borg, Becker and Chang burst onto the scene as teenagers.

 

Then, readers may pick up on the ticker-tape data that display the spread of ages of Wimbledon players in any given year. There is some shading involved, not clearly explained, but we surmise that it illustrates the range of ages of most of the contestants. In a sense, the range of probable ages and the average age tell the same story. The current trend of rising ages began around 2005.

 

Finally, a key data processing decision is disclosed in chart header and sub-header. The chart only plots the players who reached the fourth round (16). Like most decisions involved in data analysis, this choice has both desirable and undesirable effects. I like it because it thins out the data. The chart would have appeared more cluttered otherwise, in a negative way.

The removal of players eliminated in the early rounds limits the conclusion that one can draw from the chart. We are tempted to generalize the finding, saying that the average men’s player has increased in age – that was what I said in the first paragraph. Thinking about that for a second, I am not so sure the general statement is valid.

The overall field might have gone younger or not grown older, even as the older players assert their presence in the tournament. (This article provides side evidence that the conjecture might be true: the author looked at the average age of players in the top 100 ATP ranking versus top 1000, and learned that the average age of the top 1000 has barely shifted while the top 100 players have definitely grown older.)

So kudos to these reporters for writing a careful headline that stays true to the analysis.

I also found this video at FT that discussed the chart.

***

This chart about Wimbledon players hits the Trifecta. It has an interesting – to some, surprising – message (Q). It demonstrates thoughtful processing and analysis of the data (D). And the visual design fits well with its intended message (V). (For a comprehensive guide to the Trifecta Checkup, see here.)

Too much of a good thing

Several of us discussed this data visualization over twitter last week. The dataviz by Aero Data Lab is called “A Bird’s Eye View of Pharmaceutical Research and Development”. There is a separate discussion on STAT News.

Here is the top section of the chart:

We faced a number of hurdles in understanding this chart as there is so much going on. The size of the shapes is perhaps the first thing readers notice, followed by where the shapes are located along the horizontal (time) axis. After that, readers may see the color of the shapes, and finally, the different shapes (circles, triangles,...).

It would help to have a legend explaining the sizes, shapes and colors. These were explained within the text. The size encodes the number of test subjects in the clinical trials. The color encodes pharmaceutical companies, of which the graphic focuses on 10 major ones. Circles represent completed trials, crosses inside circles represent terminated trials, triangles represent trials that are still active and recruiting, and squares for other statuses.

The vertical axis presents another challenge. It shows the disease conditions being investigated. As a lay-person, I cannot comprehend the logic of the order. With over 800 conditions, it became impossible to find a particular condition. The search function on my browser skipped over the entire graphic. I believe the order is based on some established taxonomy.

***

In creating the alternative shown below, I stayed close to the original intent of the dataviz, retaining all the dimensions of the dataset. Instead of the fancy dot plot, I used an enhanced data table. The encoding methods reflect what I’d like my readers to notice first. The color shading reflects the size of each clinical trial. The pharmaceutical companies are represented by their first initials. The status of the trial is shown by a dot, a cross or a square.

Here is a sketch of this concept showing just the top 10 rows.

Certain conditions attracted much more investment. Certain pharmas are placing bets on cures for certain conditions. For example, Novartis is heavily into research on Meningnitis, meningococcal while GSK has spent quite a bit on researching "bacterial infections."

It's hot even in Alaska

A twitter user pointed to the following chart, which shows that Alaska has experienced extreme heat this summer, with the July statewide average temperature shattering the previous record;

This column chart is clear in its primary message: the red column shows that the average temperature this year is quite a bit higher than the next highest temperature, recorded in July 2004. The error bar is useful for statistically-literate people - the uncertainty is (presumably) due to measurement errors. (If a similar error bar is drawn for the July 2004 column, these bars probably overlap a bit.)

The chart violates one of the rules of making column charts - the vertical axis is truncated at 53F, thus the heights or areas of the columns shouldn't be compared. This violation was recently nominated by two dataviz bloggers when asked about "bad charts" (see here).

Now look at the horizontal axis. These are the years of the top 20 temperature records, ordered from highest to lowest. The months are almost always July except for the year 2004 when all three summer months entered the top 20. I find it hard to make sense of these dates when they are jumping around.

In the following version, I plotted the 20 temperatures on a chronological axis. Color is used to divide the 20 data points into four groups. The chart is meant to be read top to bottom. 

 

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.

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.

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:

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: