Statistical inference

Descriptive statistics summarize the data in front of you; inference reaches past it, to a claim about the world the data were drawn from. R. A. Fisher's *Statistical Methods for Research Workers* (1925) put a portable version of this in every scientist's hands. State a *null hypothesis* — that there is no real effect, that she is only guessing. Then work out how surprising your actual data would be *if* the null were true, and report that surprise as a *p-value*. If the data would be very unlikely under "no effect," you have grounds to reject "no effect." Fisher offered p = 0.05 — a one-in-twenty result — as a convenient line for "worth taking seriously." That arbitrary threshold, chosen for convenience in this one book, still governs much of what science is willing to publish.

It let small, carefully arranged experiments deliver trustworthy general conclusions, and it turned "but chance could have produced this" from a debating tactic into a number. Fisher's companion volume, *The Design of Experiments* (1935), supplied the other half — randomization, replication, and blocking, the rules for arranging a study so that its statistics are valid in the first place. Together they converted whole fields from the accumulation of anecdote into controlled inference. The randomized controlled trial in medicine, the factorial experiment in agriculture and industry, and the empirical spine of modern psychology and economics all descend directly from these two books.

Statistical inference gave us the randomized controlled trial, industrial quality control and the design of experiments, econometrics, and the statistical foundation under every empirical science. Fisher's method of maximum likelihood — choose the model that makes the observed data most probable — is the direct ancestor of how modern machine-learning models are fit to data. Almost any modern sentence of the form "the effect was significant" is a debt to a woman tasting tea at Rothamsted.