Category Archives: Books

The Elements of Graphing Data, William S. Cleveland

Bill Cleveland is one of the founding figures in statistical graphics and data visualization. His two books, The Elements of Graphing Data and Visualizing Data, are classics in the field, still well-worth reading today.

Visualizing is about the use of graphics as a data analysis tool: how to check model fit by plotting residuals and so on. Elements, on the other hand, is about the graphics themselves and how we read them. Cleveland (co)-authored some of the seminal papers on human visual perception, including the often-cited Cleveland & McGill (1984), “Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods.” Plenty of authors doled out common-sense advice about graphics before then, and some even ran controlled experiments (say, comparing bars to pies). But Cleveland and colleagues were so influential because they set up a broader framework that is still experimentally-testable, but that encompasses the older experiments (say, encoding data by position vs length vs angle vs other things—so that bars and pies are special cases). This is just one approach to evaluating graphics, and it has limitations, but it’s better than many competing criteria, and much better than “because I said so” *coughtuftecough* ūüôā

In Elements, Cleveland summarizes his experimental research articles and expands on them, adding many helpful examples and summarizing the underlying principles. What cognitive tasks do graph readers perform? How do they relate to what we know about the strengths and weaknesses of the human visual system, from eye to brain? How do we apply this research-based knowledge, so that we encode data in the most effective way? How can we use guides (labels, axes, scales, etc.) to support graph comprehension instead of getting in the way? It’s a lovely mix of theory, experimental evidence, and practical advice including concrete examples.

Now, I’ll admit that (at least in the 1st edition of Elements) the graphics certainly aren’t beautiful: blocky all-caps fonts, black-and-white (not even grayscale), etc. Some data examples seem dated now (Cold War / nuclear winter predictions). The principles aren’t all coherent. Each new graph variant is given a name, leading to a “plot zoo” that the Grammar of Graphics folks would hate. Many examples, written for an audience of practicing scientists, may be too technical for lay readers (for whom I strongly recommend Naomi Robbins’ Creating More Effective Graphs, a friendlier re-packaging of Cleveland).

Nonetheless, I still found Elements a worthwhile read, and it made a big impact on the data visualization course I taught. Although the book is 30 years old, I still found many new-to-me insights, along with historical context for many aspects of R’s base graphics.

[Edit: I’ll post my notes on Visualizing Data separately.]

Below are my notes-to-self, with things-to-follow-up in bold:

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Roulette Wheel of Time

While we’re on crossovers between statistics and brick-sized fantasy novels, I remember taking some notes on references to math, logic, and probability in Robert Jordan’s Wheel of Time book series.

(I really can’t recommend the series. I enjoyed the first few books in middle school, but in a re-read last year they haven’t stood up to my childhood memories. The first is still fun but a blatant Tolkien ripoff; the rest are plodding and repetitive.)

Readers, can you recommend any good fantasy / sci-fi (or other fiction) that treats stats & math well?

The Dragon Reborn

A few of the characters discuss the difference between distributions that show clustering, uniformity, and randomness:

“It tells us it is all too neat,” Elayne said calmly. “What chance that thirteen women chosen solely because they were Darkfriends would be so neatly arrayed across age, across nations, across Ajahs? Shouldn’t there be perhaps three Reds, or four born in Cairhien, or just two the same age, if it was all chance? They had women to choose from or they could not have chosen so random a pattern. There are still Black Ajah in the Tower, or elsewhere we don’t know about. It must mean that.”

She’s suspicious of the very uniform distribution of demographic characteristics in the observed sample of 13 bad-guy characters. If turning evil happens at random, or at least is independent of these demographics, you’d expect some clusters to occur by chance in such a small sample—that’s why statistical theory exists, to help decide if apparent patterns are spurious. And if evil was associated with any demographic, you’d certainly expect to see some clusters. The complete absence of clustering (in fact, we see the opposite: dispersion) looks more like an experimental design, selecting observations that are as different as possible… implying there is a larger population to choose from than just these 13. Nice ūüėõ

There are also records of historical hypothesis testing of a magical artifact:

“Use unknown, save that channeling through it seems to suspend chance in some way, or twist it.” She began to read aloud. “‘Tossed coins presented the same face every time, and in one test landed balanced on edge one hundred times in a row. One thousand tosses of the dice produced five crowns one thousand times.'”

That’s a degenerate distribution right there.

Mat, the lucky-gambler character, also talks of luck going in his favor more often where there’s more randomness: he always wins at dice, usually at card games, and rarely at games like “stones” (basically Go). It’d be good fodder for a short story set in our own world—a character who realizes he’s no braniac but incredibly lucky and so seeks out luck-based situations. What else could you do, besides the obvious lottery tickets and casinos?

The Shadow Rising

I was impressed by Elayne’s budding ability to think like a statistician in the previous book, but she returns to more simplistic thinking in this book. The characters ponder murder motives (p.157):

“They were killed because they talked […] Or to stop them from it […] They might have been killed simply to punish them for being captured […] Three possibilities, and only one says the Black Ajah knows they revealed a word. Since all three are equal, the chances are that they do not know.”

Oh, Elayne. There are well-known problems with the principle of insufficient reason. Your approach to logic may get you into trouble yet.

Lord of Chaos

The description of Caemlyn’s chief clerk and census-taker Halwin Norry is hamfisted and a missed opportunity:

Rand … was not certain anything was real to Norry except the numbers in his ledgers. He recited the number of deaths during the week and the price of turnips carted in from the countryside in the same dusty tone, arranged the daily burials of penniless friendless refugees with no more horror and no more joy than he showed hiring masons to check the repair of the city walls. Illian was just another land to him, not the abode of Sammael, and Rand just another ruler.

If anything, Norry sounds like an admirable professional! Official statisticians must be as objective and politically disinterested as possible; else the rulers can make whatever “decisions” they like but there’ll be no way to accurately carry them out when you don’t know what resources you actually have on hand nor how severe the problem really is. It’d be fascinating to see how Norry actually gets runs a war-time census—perhaps with scrying help from the local magic users? But here Jordan is just sneering down. Such a shame.

Knife of Dreams

There are a few ridiculous scenes of White Ajah logicians arguing; I should have noted them down. I’m not sure if Jordan really believes mathematicians and logicians talk like this, or whether his tongue is in cheek and he’s just joking, but man, it’s a grotesque caricature. Someday I’d love to see a popular book describe the kind of arguments mathematicians actually have with each other. But this isn’t it.

Statistics Done Wrong, Alex Reinhart

Hats off to my classmate Alex Reinhart for publishing his first book! Statistics Done Wrong: The Woefully Complete Guide [website, publisher, Amazon] came out this month. It’s a well-written, funny, and useful guide to the most common problems in statistical practice today.

Although most of his examples are geared towards experimental science, most of it is just as valid for readers working in social science, data journalism [if Alberto Cairo likes your book it must be good!], conducting surveys or polls, business analytics, or any other “data science” situation where you’re using a data sample to learn something about the broader world.

This is NOT a how-to book about plugging numbers into the formulas for t-tests and confidence intervals. Rather, the focus is on interpreting these seemingly-arcane statistical results correctly; and on designing your data collection process (experiment, survey, etc.) well in the first place, so that your data analysis will be as straightforward as possible. For example, he really brings home points like these:

  • Before you even collect any data, if your planned sample size is too small, you simply can’t expect to learn anything from your study. “The power will be too low,” i.e. the estimates will be too imprecise to be useful.
  • For each analysis you do, it’s important to understand commonly-misinterpreted statistical concepts such as p-values, confidence intervals, etc.; else you’re going to mislead yourself about what you can learn from the data.
  • If you run a ton of analyses overall and only publish the ones that came out significant, such data-fishing will mostly produce effects that just happened (by chance, in your particular sample) to look bigger than they really are… so you’re fooling yourself and your readers if you don’t account for this problem, leading to bad science and possibly harmful conclusions.

Admittedly, Alex’s physicist background shows in a few spots, when he implies that physicists do everything better ūüôā (e.g. see my notes below on p.49, p.93, and p.122.)
XKCD: Physicists
Seriously though, the advice is good. You can find the correct formulas in any Stats 101 textbook. But Alex’s book is a concise reminder of how to plan a study and to understand the numbers you’re running, full of humor and meaningful, lively case studies.

Highlights and notes-to-self below the break:
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Dataclysm, Christian Rudder

In between project deadlines and homework assignments, I enjoyed taking a break to read¬†Christian Rudder’s Dataclysm. (That’s right, my¬†pleasure-reading break from statistics grad school textbooks¬†is… a different book¬†about statistics. I think I have a problem. Please suggest some good fiction!)

So, Rudder is one of the founders of dating site OkCupid and its quirky, data-driven research blog. His new book is very readable—each short, catchy chapter was hard to put down. I like how he gently alludes to the statistical details¬†for nerds like myself, in a way that shouldn’t¬†overwhelm lay readers. The clean,¬†Tufte-minimalist graphs work quite well and are accompanied by clear writeups. Some of the insights are basically repeats of material already on the blog, but with a cleaner writeup, though there’s plenty of new stuff too. Whether or not you agree with all of his¬†conclusions [edit: see Cathy O’Neil’s valid¬†critiques¬†of the stats¬†analyses here],¬†the book sets¬†a good example to follow for anyone interested in¬†data- or evidence-based popular science writing.

Most of all, I loved his description of statistical precision:

Ironically, with research like this, precision is often less appropriate than a generalization. That’s why I often round findings to the nearest 5 or 10 and the words ‘roughly’ and ‘approximately’ and ‘about’ appear frequently in these pages. When you see in some article that ‘89.6 percent’ of people do x, the real finding is that ‘many’ or ‘nearly all’ or ‘roughly 90 percent’ of them do it, it’s just that the writer probably thought the decimals sounded cooler and more authoritative. The next time a scientist runs the numbers, perhaps the outcome will be 85.2 percent. The next time, maybe it’s 93.4. Look out at the churning ocean and ask yourself exactly which whitecap is ‘sea level.’ It’s a pointless exercise at best. At worst, it’s a misleading one.

I might use that next time I teach.

The description of how academics hunt for data is also spot on: “Data sets move through the research community like yeti—I have a bunch of interesting stuff but I can’t say from where; I heard someone at Temple has tons of Amazon reviews; I think L has a scrape of Facebook.

Sorry I didn’t take many notes this time, but Alberto Cairo’s post on the book links to a few¬†more detailed reviews.

What the Best College Teachers Do, Ken Bain

Although CMU has no school of education, it does have strong support for those of us who’d like to become better educators, not just better researchers. There’s the Eberly Center, which bridges the research-about-education that happens on campus, to the education-of-researchers for which most of us are here. And there’s the brand-new¬†Simon Initiative—I’m not fully sure yet what it entails, but I enjoyed the inaugural lecture by Carl Wieman on improving science education.

Amidst all this, I’ve started teaching a summer course (36-309, Experimental Design). While preparing to teach, I’ve read Ken Bain’s What the Best College Teachers Do (recommended by CMU’s¬†Sciences Teaching Club).

Much of the content is about convincing you to adopt the mindset of a good teachers: You should be interested in the students’ understanding, not just in getting them to regurgitate facts or plug & chug formulas. You should be patient with learners of different types and levels. Assessments for the sake of getting feedback should be frequent and separate from assessments for the sake of labeling the student with a final grade. You want the students to become able to learn independently, so train them to think constructively about their own learning.

Mostly, this is stuff I already agreed with. I really like Bain’s high-level ideas. But I wish there would have been more concrete illustrations of how these ideas work in practice. Practical examples could have replaced a lot of the fluffy language about the opening the students’ minds and hearts, etc.

Still, there are a couple of lists of explicit questions to use when planning your course. No list can cover everything you need to consider—but still, it doesn’t hurt to use such a list, to ensure that at least you haven’t overlooked what’s on it.

Bain also has some lists of “types of learners” or “developmental stages of learning.” It’s often unhelpful to pigeonhole individual students into one bucket or another… but it can be useful to treat these archetypes as if they were¬†user personas, and¬†consider how your lesson plan will work for these users.

Some of these lists, and other excessive notes-to-self, below the break.

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How to Listen to and Understand Great Music, Robert Greenberg

These are just notes to myself on an audio course I got from the library. Nothing about statistics or R here ūüôā

I’ve spent the past few months listening to Robert Greenberg’s How to Listen to and Understand Great Music, 3rd Edition as I walk to and from school. I’ve played classical music for years (in school bands and orchestras as well as at home), so I’d picked up a fair bit about its history, but I hoped this survey course would fill in some gaps.

Below are some notes-to-self, though my appetite for note-taking got weaker and eventually petered out halfway through the course. (Not because the course got boring—just because the semester got busy!)
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Visual Revelations, Howard Wainer

I’m starting to recognize several clusters of data visualization books. These include:

(Of course this list calls out for a flowchart or something to visualize it!)

Howard Wainer’s Visual Revelations falls in this last category. And it’s no surprise Wainer’s book emulates Tufte’s, given how often the author refers back to Tufte’s work (including comments like “As Edward Tufte told me once…”). And The Visual Display of Quantitative Information is still probably the best introduction to the genre. But Visual Revelations is different enough to be a worthwhile read too if you enjoy such books, as I do.

Most of all, I appreciated that Wainer presents many bad graph examples found “in the wild” and follows them with improvements of his own. Not all are successful, but even so I find this approach very helpful for learning to critique and improve my own graphics. (Tufte’s classic book critiques plenty, but spends less time on before-and-after redesigns. On the other hand, Kosslyn’s book is full of redesigns, but his “before” graphs are largely made up by him to illustrate a specific point, rather than real graphics created by someone else.)

Of course, Wainer covers the classics like John Snow’s cholera map and Minard’s plot of Napoleon’s march on Russia (well-trodden by now, but perhaps less so in 1997?). But I was pleased to find some fascinating new-to-me graphics. In particular, the Mann Gulch Fire section (p. 65-68) gave me shivers: it’s not a flashy graphic, but it tells a terrifying story and tells it well.
[Edit: I should point out that¬†Snow’s and Minard’s plots are so well-known today largely thanks to Wainer’s own efforts.¬†I also meant to mention that Wainer is the man who helped bring into print an English translation of Jacques Bertin’s seminal¬†Semiology of Graphics and a replica volume of William Playfair’s Commercial and Political Atlas and Statistical Breviary. He has done amazing work at unearthing and popularizing many lost gems of historical¬†data visualization!
See also¬†Alberto Cairo’s review of a more recent¬†Wainer book.]

Finally, Wainer’s tone overall is also much lighter and more humorous than Tufte’s. His first section gives detailed advice on how to make a bad graph, for example. I enjoyed Wainer’s jokes, though some might prefer more gravitas.

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Statistical Inference, Michael Oakes; and “Likelihood inference”

You may be familiar with the long-running divide between Classical or Frequentist (a.k.a. Neyman-Pearson) and Bayesian statisticians. (If not, here’s a simplistic overview.) The schism is being smoothed over, and many statisticians I know are pragmatists who feel free to use either approach depending on the problem at hand.

However, when I read Gerard van Belle’s Statistical Rules of Thumb, I was surprised by his brief mention of three distinct schools of inference: Neyman-Pearson, Bayesian, and Likelihood. I hadn’t heard of the third, so I followed van Belle’s reference to Michael Oakes’ book Statistical Inference: A Commentary for the Social and Behavioural Sciences.

Why should you care what school of inference you use? Well, it’s a framework that guides how you think about science: this includes the methods you choose to use and, crucially, how you interpret your results. Many Frequentist methods have a Bayesian analogue that will give the same numerical result on any given dataset, but the implications you can draw are quite different. Frequentism is the version taught traditionally in Stat101, but if you show someone the results of your data analysis, most people’s interpretation will be closer to the Bayesian interpretation than the Frequentist. So I was curious how “Likelihood inference” compares to these other two.

Below I summarize what I learned from Oakes about Likelihood inference. I close with some good points from the rest of Oakes’ book, which is largely about the misuse of null hypothesis significance testing (NHST) and a suggestion to publish effect size estimates instead.

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A Theory of Data, Clyde Coombs

Earlier I’ve quoted Leland Wilkinson¬†in¬†The Grammar of Graphics, where he recommends Clyde Coombs’ book A Theory of Data:

…in a landmark book, now out of print and seldom read by statisticians, Coombs (1964) ‚Ķ believed that the prevalent practice of modeling based on cases-by-variables data layouts often prevents researchers from considering more parsimonious structural theories and keeps them from noticing meaningful patterns in their data.

I checked out Coombs’ book through interlibrary loan and haven’t had time to read it thoroughly before the due date. But even from skimming it on the train a few days, I can see why Wilkinson recommends it.

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Most-cited books on list of lists of data visualization readings

As part of the resources for his online data visualization course, Alberto Cairo has posted several lists of recommended readings:

Some of these links lead to other excellent recommended-readings lists:

I figured I should focus on reading the book suggestions that came up more than once across these lists. Below is the ranking; it’s by author rather than book,¬†since some authors were suggested with multiple¬†books. So many good books!

The list, by number of citations per author: Continue reading