Content warning: this is the most arrogant article I’ve written in a long time. I ask you to bear with me, because I think it is an important observation to discuss. Unfortunately, I lack the clarity of mind to make it more approachable: the article is arrogant because I am dumb, not because of the subject matter itself.

Hopefully, someone else can run with this and do a better job than I.

It’s hard to write directly about something which one don’t know what it is, so we will proceed by analogy and example.

Back in the 1500s shipping insurance was priced under the assumption that if you just knew enough about the voyage, you could tell for certain whether it would be successful or not, barring the will of God. Thus, when asked to insure a shipment, the underwriter would thoroughly investigate things like the captain’s experience, ship maintenance status, size of crew rations, recency of navigational charts, etc. After much research, they would conclude either that the shipment ought to be successful, or that it ought not to be. They arrived at a logical, binary conclusion: either the shipment will make it (based on all we know) or it will not. Then they quoted a price based on whether or not the shipment would make it.

This type of logical reasoning leads to a normative perspective of what the future ought to look like. Combined with the idea that every case is unique, this is typical of a lack of statistical illiteracy. The statistically illiterate predicts what the future will look like based on detailed knowledge and logical sequences of events. Given that we hadn’t yet invented statistics in the 1500s, it is not surprising our insurer would think that way.

Of course, even underwriters at the time knew that sometimes ships that ought to make it run into a surprise storm and sink. Similarly, ships that ought not to make it are sometimes lucky and arrive safely. To the 1500s insurer, these are expressions of the will of God, and are incalculable annoyances, rather than factors to consider when pricing.

This is similar to how a gambler in the 1500s could tell you that dice were designed to land on each number equally often – but would refuse to give you a probability for the next throw, because the outcome of any given throw is “not uncertain, just unknown”: God has predetermined a specific number for each throw, and we have no way of knowing how God makes that selection.1¹ This distinction between the uncertain and unknown still happens among the statistically illiterate today.

The revolution in mindset that happened in the 1600s and 1700s was that one could ignore most of what made a shipment unique and instead price the insurance based on what a primitive reference class of shipments had in common, inferring general success propensities from that. Insurers that did this outprofited those that did not, in part because they were able to set a more accurate price on the insurance, and in part because they spent less on investigating each individual voyage.

I like the mid-1800s quote from Lecky commenting on the rise of rationalism, saying

My object in the present work has been to trace the history of the spirit of Rationalism: by which I understand not any class of definite doctrines or criticisms, but rather a certain cast of thought, or bias of reasoning, which has during the last three centuries gained a marked ascendancy in Europe […]

[Rationalism] leads men […] to subordinate dogmatic theology to the dictates of reason and conscience […] It predisposes men […] to attribute all kinds of phenomena to natural rather than miraculous causes. [It] diminishes the influence of fear as the motive of duty [and] establishes the supremacy of conscience.

I believe we are now in the early days of a similar movement, namely the rise of empiricism. Borrowing Lecky’s words, we could use almost the same passage to describe this change.

The spirit of Empiricism, by which I understand not any class of definite doctrines or criticisms, but rather a certain cast of thought, or bias of reasoning, which will during the next three centuries gain a marked ascendancy worldwide.

Empiricism leads people to subordinate reason and conscience to the dictates of process variation and indeterminism. It predisposes people to attribute all kinds of phenomena to intervention by a large number of variables rather than direct causes. It diminishes the influence of assumption as the motive of duty and establishes the supremacy of studying the outcome.

This captures many of the things I think are covered by statistical literacy:

• It is not a specific set of techniques or doctrines, but rather a general mindset.
• It emphasises how logic alone might not lead us to the right conclusions, because there are different things at play in reality than in our mental models.
• It suggests that we choose actions by carefully studying outcomes rather than based on what ought to yield the best outcome.
• It tells us that differences in outcomes may not be a signal of differences in controllable antecedents: it is often just the natural variation of the process.

If my idea of statistical literacy is accurate, my readership should fall roughly into three categories in their reactions to the above:

1. “Yes! Thank you. That’s exactly what I’ve been trying to say and it’s so frustrating when people don’t get it!”
2. “Sure, that makes sense.”
3. “Are you crazy? Subordinate reason and conscience? No way. If the gas mileage of a car is 40 miles per gallon, and I drive 20 miles, I will have used half a gallon of gas. This is just logic and you can’t deny that.”

The first category (“Yes!”) will consist of people who are statistically literate. The third category (“No!”) will attract people who are not statistically literate. I don’t know about the middle ground – I think it could attract open-minded but not yet very statistically literate people.

The devious thing about statistical literacy is that people who don’t have it seem to not know they don’t have it – not even when someone points out that statistical literacy is a thing that not all people have. To someone who is not statistically literate, statistical reasoning sounds like the ramblings of someone confused and illogical.

To be clear: I’m not knocking on anyone here. As I’ve previously admitted, I wasn’t statistically literate until fairly recently. I didn’t become statistically literate because I tried to. I mean, how could I? I didn’t even know it was a thing. It just happened by accident when I read lots of books on varied topics inside and outside statistics. Out of nowhere, I discovered I had this new lens through which I could look at the world and see it all differently.2² This lens is still something I’m polishing and discovering more ways in which it can be useful.

The whole thing reminds me of the idea Scott Alexander proposed about missing developmental milestones. This certainly seems like one of them: either someone taught you to think statistically, and it seems like second nature, or you never learned it, and then you don’t know what’s missing.

This leads into another important point: I’m certainly not claiming any one person is incapable of statistical literacy. I think it’s generally within reach of most people I meet. But, as formal operational thought is described in Scott Alexander’s article, statistical literacy

is more complexly difficult than earlier modes of thought and will be used in a culture in a publicly shared way only if that culture has developed techniques for training people in its use.

Our culture has yet to develop techniques for training large amounts of people in statistical literacy. Our elementary school teachers know how to train students in reading, writing, and basic logical reasoning. But I believe most of them are not statistically literate. This means

• They will not give students examples of when the race was not to the swift.3³ From Ecclesiastes 9:11. In the King James Bible, this is phrased as “I returned, and saw under the sun, that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.” I noticed that in the International Children’s Bible, it starts with “I also realized something else here on earth that is senseless: The fast runner does not always win the race. […]” Hah! Senseless! Statstical illiteracy!
• They will not observe the battle against entropy in seating choices in the classroom.
• They will neglect reference class propensities as the largest source of variation and latch on to concrete details.
• They will attribute differences in outcomes to differences in aptitude/skill/perseverence, even when there are several other environmental factors that have much larger influence on the outcome.
• They will pretend mathematical models apply cleanly to real-world problems, even when significant sources of error make very rough approximations more appropriate.
• They will not treat student performance as an error-laden sample from a hypothetical population.4⁴ I think it was Deming who, as a rule, gave a passing grade to everyone in his class, because as long as he was doing a passable job of teaching, any problems in learning is unlikely to rest with factors the student can control. He used tests not as a way to fail students, but as a way to calibrate how well he was teaching the material. He used students as measuring devices for his teaching skill, acknowledging that sometimes individual students don’t fairly represent his abilities but on aggregate, they will.
• They will not allow students to indicate their confidence in all alternatives of a multiple-choice question.
• Although they may tell you “correlation does not mean causation”, they will readily conclude a causal link exists when presented with any slightly more complicated real-world correlation.

And if the teachers do not see these things, if the teachers are not statistically literate, how on Earth are they going to teach it to their students?

I suspect this will improve with time. Statistical reasoning wasn’t even invented 400 years ago. Unlike verbal language and art, it is not an innately human thing to do. Like logical reasoning, it will take time for it to spread, and it will do so at first slowly, then suddenly. I think it will, in the next few centuries, become as important a marker of civilisation as actual literacy and numeracy is today.

Once one starts looking for it, differences in statistical literacy pop up everywhere. Dan Luu writes that he is “looking at data” better than others (my emphasis):

For the past three years, the main skill I’ve been applying and improving is something you might call “looking at data”; the term is in quotes because I don’t know of a good term for it. I don’t think it’s what most people would think of as “statistics”, in that I don’t often need to do anything […] sophisticated.

I know the term for it: statistical literacy. Dan, you are practicing your statistical literacy.

When the data are difficult and uncooperative, statistical literacy is needed to look at it in a way that improves decisions – or at least does not make them worse. Dan Luu goes further and notes that most people who are not statistically literate don’t even bother collecting the data in the first place: When people attempt to data-drive despite lacking statistical literacy, they often end up flailing about and making things worse, eventually giving up on the idea and reverting to decisions based on logic and/or faith.

All of this happens in a world that is turning increasingly statistical. Many of our productivity-enhancing technologies these days incorporate statistical reasoning to make decisions when presented with wobbly information. Our obsession with determinism in software systems is, I think, a temporary fad, just as it was in science.

What originally prompted this article out of months of thinking from my end was Cedric Chin over at Commoncog publishing an article on Becoming Data Driven, From First Principles. That is an excellent article which just might help nudge a predisposed organisation into statistical literacy.

As I mentioned, I have also read a lot of books that nudged me in the right direction, but I’m not yet at a point where I can make a concrete recommendation. I hope to re-read and review some of them over the coming year, which would hopefully put me in a better spot to recommend.

I’m also hoping that I can carve out some time to try to measure people’s statistical literacy, which would help me pinpoint exactly what it is about, and thus allow for the construction of an effective curriculum.

Because the thing is, all of these words are meaningless in the sense that they are just a wild man’s speculation. I have not gone through the trouble Lecky did when he chronicled the rise of rationalism.

On the flip side, the hypothesis fuzzily outlined in this article should be testable. If I’m correct about statistical literacy, it should be possible to design a questionnaire with psychometric reliability and validity, with diverse questions that all seem to measure a construct that sounds like statistical literacy.

I don’t know exactly what the items in the questionnaire would be. I have some ideas and I’ve run a few trial surveys (massive thanks to my incredibly helpful test subjects!), but not arrived at anything concrete yet. If someone would donate me large amounts of money I would love to actively research this subject. In the mean time, I can only think about it in my spare time and sometimes write about it online.