What is the correct value of X in the sentence, “The t test is the Xth most important statistical method in science”?

Jack Murtagh has lots of interesting math news articles here. I recommend them.

But I disagree with his (or his editor’s) claim that the t test is “the most important statistical method in science.” Sure, the t test has been used a lot, and it’s important for historical reasons, and it’s a mathematical or statistical breakthrough to use distribution theory to account for the uncertainty in the estimate of the standard deviation–but, for all practical purposes, just about any reasonable approximate solution to that particular problem would be just fine. If you want to define “important” in terms of its value in statistical design and analysis, rather than its historical success, I think you’d have to put the t test way down on the list.

Maybe the t test is the hundredth-most important statistical method in science?

I feel like it wouldn’t be hard to come up with 99 more important methods.

As with ranking sports greats, you have to make some adjustment for progress over time. Your local neighborhood grandmaster could presumably kick Paul Morphy’s ass, but I wouldn’t want my list of 100 greatest players to be constrained to the past 20 years.

For example, what do I think is the single most important statistical method in science? Least-squares fitting, maybe. The second most important statistical method? Probability theory. The third most important statistical method? The scatterplot. The fourth most important statistical method? I’m not sure. But somewhere in the top hundred would be randomization, confidence intervals, hypothesis testing, Bayesian inference, survey weighting, the analysis of variance, logistic regression, . . . . We do need to reserve space for modern methods such as multiple imputation, deep learning, instrumental variables, MRP (ok, maybe that doesn’t belong in the top hundred, but let’s keep it in the top thousand, huh?), the fast Fourier transform, the Kalman filter, the grid of graphs . . . ummm, I dunno, I guess I’ll also have to include some methods that I personally loathe and which indeed I think have had negative influence (boxplots, the so-called Fisher exact test, one-sided hypothesis tests, BIC, various other bad ideas) . . . I think the t test might end up around 100th place. It’s a method that’s been applied a zillion times, that’s for sure, but in practical terms it’s such a minor advance on the z test. It’s a tough call. The t test has had practical import, but I’d say its main impact has been conceptual, in that it gives theorists and applied researchers alike the idea that they can do exact inference. Which maybe isn’t such a good thing! But it’s been influential, that’s for sure.