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.

Announcement: Advancing your data skills, Fall 2019

Interrupting the flow of dataviz with the following announcement.

If you're looking to shore up your data skills, modernize your skill set, or know someone looking for hands-on, high-touch instruction in Machine Learning, R, Cloud Computing, Data Quality, Digital Analytics,  A/B Testing and Financial Analysis, Principal Analytics Prep is offering evening classes this Fall. Click here to learn about our courses. 

Our instructors are industry veterans with 10+ years of practical industry experience. And class size is capped to 10, ensuring a high-touch learning environment.



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.

Blog receives a facelift


After a number of years, I finally took time this long weekend to refresh the blog design. I hope you like it.

The key changes are:

  • This design is responsive, so mobile users should have a better experience.
  • The Welcome message that was pinned to the top has been moved to the top navigation menu. Someone complained about that a long time ago, and I can finally say it's now fixed.
  • The Search box is shown at the top (for non-mobile users), which is another request from some time ago.
  • Many of the links on the side have been updated or made secure.

Comment below if you encounter any problems, especially if you're using mobile.