Statistics can be used for good, and they can be used for bad. But used they must be, for us to have a shot at understanding our world.
It is easy to feel that today we live in a world drowned by numbers. Convincing-sounding statistics are hurled at us from all directions at once – from friends and family, from the media, from your boss and your accountant. As a species, we seem to measure almost everything we can.
I usually relegate these overenthusiastic notions about our numbers-addicted world to the inability to lift one’s preoccupied gaze from the concerns of the present. Energetically gathering numbers for insight into the world is something we’ve done for a long time – the Victorians, a century-and-a-half ago, were experts at it.
Today, of course, numbers are much more available than they were for the contemporaries of Florence Nightingale or Karl Pearson, collected as they are by professional statisticians, assembled in widely accessible databases, and presented in colorful graphs left and right. That places extra demands on the consumer of numbers – us – to be equipped enough to see through them, to distill what they are actually saying.
The British economist, Financial Times columnist, and host of the BBC show More or Less, has produced a handy guidebook to help us with this extraordinarily important task. With How to Make the World Add Up: Ten Rules for Thinking Differently About Numbers, Harford has refined crucial statistical concepts into an easy-to-read and entertaining manual.
I recently read King’s College psychologist Stuart Ritchie’s comprehensive book on why so much science is wrong, and there’s a lot of overlap with Harford’s book. While Ritchie does a great job explaining complicated statistics and uncovering the worst excesses of the Replication Crisis, his topic is dense, thorough, and difficult, aimed as it is at a more professional audience. Harford, following the creed of his BBC show to make sense, nuance, and debunk numbers in the news, targets a wider audience.
The material used by Ritchie and Harford is often the same – ridiculously so, in using the exact same stories: Abraham Wald during World War II, Amy Cuddy’s power poses, Kahneman’s stance of psychological priming, the magazine Literary Digest’s spectacular misjudged prediction of the 1936 election, and many more. With even a little bit of training in statistics, much of Harford’s well-written prose can be skipped; frequently did I find myself jumping paragraphs or entire pages.
The advantage to this approach is, of course, that if you come to the confusing world of statistics with no previous training – and without having read similar books like Ritchie’s – Harford’s book is an excellent start. Harford includes the same substantive material, warnings and lessons, but in condensed portions and accessible language. Besides, you can pick up Harford’s book at any time, reading a few pages here and there, and still walk away with a treasure trove of useful knowledge of how to decipher the world of numbers.
Harford’s devotion to figuring out – and displaying – the truth is admirable and important. Of course, few people set out to conceal the truth, and instead end up misreading or misinterpreting numbers, or fall prey to their own emotions. He opens his book with a story from the art world in the 1940s – unconventional perhaps for what is a tale of numbers and how to read them. Han van Meegeren, a prankster, Nazi collaborator, and Dutch art forger, expertly catered to the art expert Abraham Bredius’ bias. Van Meegeren went to great pains to craft a painting that would convince Bredius he had discovered a long-lost Vermeer (Johannes Vermeer, one of the most shining stars of 17th century art). The story highlights the power of motivated reasoning: Bredius desperately wanted to uncover an unknown Vermeer, providing the unproved connection to the late-Renaissance Italian painter Caravaggio that Bredius had suspected all his life.
You wouldn’t think that an obscure instance of fraudulent art in mid-twentieth century Holland has much to do with a book on statistics – but it works, and remarkably well. Harford weaves the story of Bredius’ misattributing the Vermeer painting into the entire book, returning to it as an illustration of two or three rules. The lesson Harford takes from this more than half-century old story is that emotions rule our judgments much more than we’re normally willing to accept – and it doesn’t seem to go away with more training or experience. The more knowledge we have about a topic, the better we seem to be able to fool ourselves into interpreting available data in a way that supports our preconceived case. To a non-expert eye, the van Meegeren fake was nothing like a Vermeer; only in Bredius’ skilled eyes could it become one.
While clear, Harford’s ten rules are a bit odd. Several could be merged into a single rule. Rule 3 (“Avoid premature enumeration”) and 9 (“Misinformation can be beautiful too”) are the same: don’t take a number or graph for granted – always look into the nuance. Similarly, Rules 5 and 6 could have been merged into a chapter on selection – what numbers are missing and what was overlooked when gathering them. Rule 7 is not a rule at all but a well-meaning call of appreciation for the hard work that statisticians do behind the scenes; Rule 8 is an extended opinion piece about big data and whether private information should be accessible to the wider public.
The really good ones are the first (“Search your feelings,” where we first encounter the Bredius story), the second (“Ponder your personal experience,” not because n=1 is an argument, but because it gives you a first-pass plausibility test), and the fourth (“Step back and enjoy the view”), which I’ve called Always Be Comparing Thy Numbers, following the late Hans Rosling’s advice. The rest can be effectively merged or removed altogether. That would leave us with a more handy five rules instead of ten, which Harford himself admits is a little cliché: ten rules look good and rigorous, and have the aura of commandments.
Another problem, especially when I’ve just finished Ritchie’s at times brutal takedown of psychological results that won’t replicate, is how often Harford relies on an unnuanced conclusion of psychological experiments. Much of psychology lies in shambles, and I’d be thoroughly surprised if some of the studies that Harford discusses emerge unscathed. Confusingly, he also uses “replicate” and “reproduce” interchangeably, even though the former refers to experiments that explore the same research question with new data or subjects, and the latter imitate the original research with its own data.
A less substantive but more annoying tendency is for Harford to wave his woke credentials – especially on climate change, where he often abandons his comfortable shed of statistical seriousness in favor of evangelism. Ironically nested in a discussion of motivated reasoning, Harford uses an odd and needlessly complicated sleight of hand to make his case. Anthropogenic climate change is a scientific fact, he writes, and continues: “Scientific evidence is scientific evidence. Our beliefs about climate change shouldn’t skew left or right.” Because they do, he concludes that we let our political positions inform our opinion on factual matters.
Except that climate change isn’t a one-dimensional scientific fact: it’s only partly a factual matter, operating on at least three different levels of disagreement. Let me illustrate with a simple sentence: Human activity causes the Earth to warm, posing serious risks to biodiversity and human civilization.
- The first part is factual, but includes a causal connection in a complex system, so details quickly get fuzzy and inconclusive.
- “posing serious:” this is ambiguous and undefined – how serious? Many erudite writers and scientists who are pushing back at the alarmism of the environmentalist movement make persuasive arguments for why it won’t be particularly serious, or at least much overshadowed by other factors (as does the Intergovernmental Panel on Climate Change itself).
- “risks to biodiversity and human civilization” – this is a value judgment of what matters most to humans (eco-processes, biodiversity, hunger, economic growth, human life) over which reasonable people can probably disagree.
When I put it like that it gets much clearer that “innocent” claims about climate change are neither innocent nor primarily about climate change facts. Only to an evangelizing convert can ambiguity and value judgments so successfully be turned into obviously factual claims.
Despite these flaws, I share Harford’s deep commitment to figuring out what’s true. His calls for keeping an open mind, for being curious about scientific questions, results, and numbers, for carefully noticing your emotions on a topic – all supremely useful advice from which most of us can benefit. Abandoning or doubting all statistics you encounter is not wise or clever; it’s giving up logic and evidence in a complicated world. It’s a “retreat into believing whatever makes us feel good.”
Let’s not do that.