A reporter asked me for a quote regarding the importance of statistics. But, after thinking about it for a moment, I decided that statistics isn’t so important at all. A world without statistics wouldn’t be much different from the world we have now.

What would be missing, in a world without statistics?

Science would be pretty much ok. Newton didn’t need statistics for his theories of gravity, motion, and light, nor did Einstein need statistics for the theory of relativity. Thermodynamics and quantum mechanics are fundamentally statistical, but lots of progress could’ve been made in these areas without statistics. The second law of thermodynamics is an observable fact, ditto the two-slit experiment and various experimental results revealing the nature of the atom. The A-bomb and, almost certainly, the H-bomb, maybe these would never have been invented without statistics, but on balance I think most people would feel that the world would be a better place without these particular scientific developments. Without statistics, we could forget about discovering the Hibbs boson etc, but that doesn’t seem like such a loss for humanity.

At a more applied level, statistics helped to win World War 2, most notably in cracking the Enigma code but also in various operations-research efforts. And it’s my impression that “our” statistics were better than “their” statistics. So that’s something.

Where would civilian technology be without statistics? I’m not sure. I don’t have a sense of how necessary statistics was for quantum theory. In a world without statistics, would the study of quantum physics have progressed far enough so that transistors were invented? This one, I don’t know. And without statistics we wouldn’t have modern quality control, so maybe we’d still be driving around in AMC Gremlins and the like. Scary thought, but not a huge deal, I’d think. No transistors, though, that would make a difference in my life. No transistors, no blogging! And I guess we could also forget about various unequivocally beneficial technological innovations such as modern pacemakers, hearing aids, cochlear implants, and Clippy.

Modern biomedicine uses lots and lots of statistics, but would medicine be so much worse without it? I don’t think so, at least not yet. You don’t need statistics to see that penicillin works, nor to see that mosquitos transmit disease and that nets keep the mosquitos out. Without statistics, I assume that various mistakes would get into the system, various ineffective treatments that people think are effective, etc. But on balance I doubt these would be huge mistakes, and the big ones would eventually get caught, with careful record-keeping even without statistical inference and adjustments. Without statistics, biologists would not be able to sequence the gene, and I assume they’d be much slower at developing tools such as tests that allow you to check for chromosomal abnormalities in amnio. I doubt all these things add up to much yet, but I guess there’s promise for the future. Statistics is also necessary for a lot of drug development—right now my colleagues and I are working on a pharmacodynamic model of dosing—but, again, without any of this, it’s not clear the world would be *so* much different.

The Poverty Lab team use statistics and randomized experiments to see what works to help the lives of poor people around the world. That’s cool but I’m not ultimately convinced this all makes a difference in the big picture. Or, to put it another way, I suspect that the statistical validation serves mostly as a way to build political consensus for economic policies that will be effective in sharing the wealth. By demonstrating in a scientific way that Treatment X is effective, this supports the idea that there is a way to help the sort of people who live in what Nicholas Wade would describe as “tribal” societies. So, sure, fine, but in this case the benefits of the statistical methods are somewhat indirect.

Without statistics, we wouldn’t have most of the papers in “Psychological Science,” but I could handle that. Piaget didn’t need any statistics, and I think the modern successors of Piaget could’ve done pretty much what they’ve done without statistics, just by careful observation of major transitions.

Careful observation and precise measurement can be done, with or without statistical methods. Indeed, researchers often use statistics as a *substitute* for careful observation and precise measurement. That is a horrible thing to do, and if you have a clear understanding of statistical theory, you can see why. But statistics is hard, and lots of researchers (and journal editors, news reporters, etc.) don’t have that understanding. When statistics is used as a substitute for, rather than an adjunct to, scientific measurement, we get problems.

OK, here’s another one: no statistics, no psychometrics. That’s too bad but one could make the argument that, on the whole, psychometrics has done more harm than good (value-added assessment, anyone?). Don’t get me wrong—I like psychometrics, and a strong argument could be made that it’s done more good than harm—but my point here is that the net benefit is not clear; a case would have to be made.

Polling. Can’t do it well without statistics. But, would a world without polling be so horrible? Much as I hate to admit it, I don’t think so. Don’t get me wrong, I think polling is on balance a good thing—I agree with George Gallup that measurement of public opinion is an important part of the modern democratic process—but I wouldn’t want to hang too much of the benefits of statistics on this one use, given that I expect lots of people would argue that opinion polls do more harm than good in politics.

**The alternative to good statistics is . . .**

Perhaps the most important benefits of statistics come not from the direct use of statistical methods in science and technology, but rather in helping us learn about the world. Statisticians from Francis Galton and Ronald Fisher onward have used statistics to give us a much deeper understanding of human and biological variation. I can’t see how any non-statistical, mechanistic model of the world could reproduce that level of understanding. Forget about p-values, Bayesian inference, and the rest: here I’m simply talking about the nature of correlation and variation.

For a more humble example, consider Bill James. Baseball is a silly example, sure, but the point is to see how much understanding has been gained in this area through statistical measurement and comparison. As James so memorably wrote, the alternative to good statistics is not “no statistics,” it’s “bad statistics.” James wrote about baseball commentators who would make asinine arguments which they would back up by picking out numbers without context. In politics, the equivalent might be a proudly humanistic pundit such as New York Times columnist David Brooks supporting his views by just making up numbers or featuring various “too good to be true” statistics and not checking them.

So here’s one benefit to the formal study of statistics: Without any statistics, there still would be *numbers*, along with people trying to interpret them.

Could governments and large businesses be managed well without statistics? I’m not sure. Given that half the U.S. Congress seems willing to shut down the government from time to time, it’s not clear than any agreement on the numbers will have much to do with political action. Similarly, all the statistics in the world don’t seem to be stopping the euro-zone from drifting. But maybe things would be much worse without a common core of statistical agreement. I don’t know; unfortunately this seems like the sort of causal question that is too difficult for statistics to answer.

Finally, one way that statistics is potentially having a huge impact in our lives is through the measurement of global warming and all the rest. But I’m guessing that a lot of this could be done with a pre-statistical understanding. The basic physics is already there, as would be the careful measurements. Statistical modeling is certainly relevant to the study of climate change—if you’re trying to reconstruct historical climate conditions from tree-ring data, it’s tough enough to do it *with* statistical modeling, I can’t imagine how it could be done otherwise—but the basic patterns of carbon dioxide, temperature, melting ice, etc., are apparent in any case. And, even with statistics, much uncertainty remains.

**Summary**

When I started writing this post, I was thinking that statistics doesn’t really matter, but I think that’s because I was focusing on some of the more highly-publicized but less beneficial applications of statistics: the use of statistical experimentation and inference to get p-values for tabloid-bait scientific papers, or for Google, Amazon, etc., to perfect their techniques for squeezing money out of their customers or, even at best, to test a medical treatment that increases survival rate for some rare disease by 2 percentage points. But statistics is central to how we think about the world. I still think that statistics is much less central to our lives than, say, chemistry. But it ain’t nothing.