Nigel Smeeton writes:
I see from the old online post, “The greatest works of statistics never published,” that there is interest in EJG Pitman’s Notes on Non-Parametric Statistical Inference.
Working from a poor online scan of the Notes, EJG Pitman’s early papers, and with the assistance of Jim Pitman and a US librarian, I have been able to resurrect the document and create a pdf file, now included in the Mimeo Series held by the North Carolina State University library.
I took a quick look and I’d say it’s more of historical interest than anything else. It’s all about hypothesis testing (sample bits: “We may have to decide from samples whether the distributions of two chance variables X and Y are the same or different” and “The question we wish to decide is ‘Is the mean of the population zero or not? Does the mean of the sample differ significantly from zero?'”), which I guess was what academic statisticians were mostly concerned with back in 1949.
Still, historical interest isn’t nothing, so I’m sharing it here. Enjoy.
“historical interest isn’t nothing,” indeed. Of no historical interest — that’s really nothing. “Chance variables” reminded me that Doob and Feller settled the question of using “chance variables” vs “random variables” by flipping a coin. Doob lost, but at least he had some support from Pitman.
Roger:
Regarding the only-of-historical-interest thing, I suspect that some of the problem was that these people were basically mathematicians, and they thought of their job as to solve problems that were set by others. As far as they’d been told, statistics was hypothesis testing, so that’s what they did. We all do this to some extent—it’s impossible to completely start from scratch—but when the ideas are so old-fashioned as in the Pitman document, the problems of starting with a received problem become more clear.
I find the following excerpt delightful:
I call this form of test “closed” because in applying it we do not go outside the
observations and make suppositions about populations from which they have been drawn.
The probability distributions which we consider are determined completely by the
observations themselves. We shall discuss several tests of this closed form but they all have
this in common. We may express it thus. A crime has been committed. Various natural
agencies and the statistician are known to have been present. The question is who did it?
Now the statistician is always regarded as the villain of the piece. Suspicion always
falls on him. In contrast to the best principles of political and social justice he is assumed to
be guilty until he can establish his innocence. He is accused of tying irrelevant labels around
the necks of supposed causes and facing up the appearance of crime, when, in fact nothing of
any importance has really occurred. The null hypothesis is that the statistician is guilty..
Glancing through the 100+ citations, the document has most commonly been used as a reference for Pitman asymptotic relative efficiency (see p.54). It also contains a clear account of Pitman’s randomization test for two independent samples (pp. 35-37).