The Cartoon Guide to Statistics

Written by Larry Gonick & Woollcott Smith

Note: This is based on the “Revised and Updated Edition”.

Deriving, and learning when to apply, statistical formulas is always going to be difficult. It turns out that including cartoons does not make it any easier.

I would put statistics writing into three general categories: teaching statistical literacy, e.g., How To Lie With Statistics; deriving the principles of statistical concepts, e.g., any college-level textbook; and applying statistical methods, e.g., an academic study. The Cartoon Guide To Statistics tries to do a bit of all three of these, and is worse off for it. The guide covers probability, random variables, sampling, confidence intervals, hypothesis testing, experimental design, and regression in just over 200 pages.

I’m unsure who the guide is written for, but I imagine it would be appropriate for a high school statistics class. I don’t think it would be particularly valuable for someone learning statistics for the first time, with this as their only resource. Chapters too frequently end with the derivation of a formula, and not enough applications of the formula to demonstrate its usefulness. Personally, I would prefer a greater focus on reinforcement through a set of exercises - at least 2 to 3 worked-through applications per concept.

The examples range widely, from the usual coin flips and dice rolls to polling, quality control, and health studies. I don’t care at all for probability explained through gambling applications, or the height of students, even though they possess properties that make them easy to use for statistics examples. I thought that this guide spent far too long stuck in coin flips, for example, without connecting them to more interesting applications.

And lastly, on the topic of examples, the goal of a statistics book should give you the ability to determine what type of problem you have, and whether it can be approached through statistical methods. A Cartoon Guide to Statistics is best as a quick, visually interesting survey of different types of methods, but I don’t recommend it if you have a specific problem that you are curious about solving. This is why I feel that statistics are best taught within the context of a certain domain, rather than as a general set of methods. Sure, the book hints at more complex statistical methods or how certain formulas might have to be adapted - but what I would have liked to see is a list of examples and exercises that you could actually do yourself, where what’s been presented in each chapter does apply.

The cartoons, at their best, help illustrate the examples; at worst, they distract me from the statistics. In some chapters, recurring characters create a thin narrative wrapper around solving a problem end-to-end, almost acting as checkpoints separating steps within each problem. I think this is a good use of the cartoons - this approach continually asserts that statistical analysis a method to answer a question, without losing sight of the question that gets people interested in statistics. And of course, sometimes explanations are easier to understand through visual drawings, like Venn diagrams or data visualizations.

An effective use of the illustrations is to explain the intuition behind confidence intervals, as shown below.

Turning each page, my eyes immediately go to the drawings, and I read them out of order. Many of the cartoons are just little funny characters with short quips about the current topic that I felt almost detracted from the book; space could have been slightly better used to further explain mathematical formulas or definitions instead of a witty comment about how confusing the formula is (which happens very often in the book). The subject material is likely too advanced for most kids, but many of the jokes feel targeted toward young children.

As the math gets simpler, the book gets better. Cartoons don’t add much to derivations, but they work well in the context of how to visualize data. And notably, the text still does nearly all of the heavy lifting in the book. If you took out nearly all of the cartoons, you would not lose any key information that hindered your understanding. But the book doesn’t always present concepts in the context of real life scenarios that apply to the general population, instead using hypothetical questions that are not memorable or immediately useful. The statistics behind political polling and the racial bias in jury selection court case presented in later chapters were good examples that the authors worked through - I would just like even more, perhaps with guided exercises that get the reader involved in the calculations.

Overall, if you are teaching statistics and want to use a visual aid, I think this book would be useful in a classroom. You can pull out a few specific chapters and work through them, or assign them as digestible readings. However, if you’re learning on your own, I think you would be better off with another book. Decide what you want to learn - how to interpret statistics or how to use and apply them yourself? If it’s the former, I’d recommend Naked Statistics; if the latter, take an online course. But no need for cartoons.