Monday, December 8, 2014

Fisher: The Design of Experiments (4th ed., 1947), Chapter I

Fisher; from Judea Pearl's website.
Now, here's a revealing turn of phrase:
In the foregoing paragraphs the subject-matter of this book has been regarded from the point of view of an experimenter, who wishes to carry out his work competently, and having done so wishes to safeguard his results, so far as they are validly established, from ignorant criticism by different sorts of superior persons. (p. 3)
You could hardly spell out more explicitly the philosophy that lies behind Fisher's concept of statistics: It's a strategic ritual, not designed to ensure a result, but to protect against criticism.

Perfectly Rigorous and Unequivocal

Such protection only goes as far as the mathematical consensus on the validity of the logic. But Fisher goes on to state that "rigorous deductive argument" is possible even in the context of random events, citing gambling as a proof of concept:
The mere fact that inductive inferences are uncertain cannot, therefore, by accepted as precluding perfectly rigorous and unequivocal inference. (p. 4)
This seems to confuse the issues of probability and statistics, unless his argument here really only amounts to saying that distributions are non-stochastic entities.

Useless for Scientific Purposes

This leads him to a discussion of "inverse probability," which he gives three reasons for rejecting: First,
… advocates of inverse probability seem forced to regard mathematical probability, not as an objective quantity measured by observed frequencies, but as measuring merely psychological tendencies, theorems respecting which are useless for scientific purposes. (p. 6–7)
Second, Bayes' axiom (about the flat prior for a coin flip) is not self-evident, that is, the choice of prior is not unequivocal (p. 7).

Ever Since the Dawn of Man…

And third,
… inverse probability has been only very rarely used in the justification of conclusions from experimental facts, although the theory has been widely taught, and is widespread in the literature of probability. Whatever the reasons are which could give experimenters confidence that they can draw valid conclusions from their results, they seem to act just as powerfully whether the experimenter has heard of the theory of inverse probability or not. (p. 7)
That's a funny sociological proof, given that he has just rejected Bayesian statistics for its psychologism. But he himself sometimes seems to think that his statistics is a kind of theory of learning, whatever that means:
Men have always been capable of some mental processes of the kind we call "learning by experience." … Experimental observations are only experience carefully planned in advance, and designed to form a secure basis of new knowledge; (p. 8)

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