E.S.Pearson on a Gate, Mayo sketch
Today is Egon Pearson’s birthday (11 Aug., 1895-12 June, 1980); and here you see my scruffy sketch of him, at the start of my book, “Error and the Growth of Experimental Knowledge” (EGEK 1996). As Erich Lehmann put it in his EGEK review, Pearson is “the hero of Mayo’s story” because I found in his work, if only in brief discussions, hints, and examples, the key elements for an “inferential” or “evidential” interpretation of Neyman-Pearson theory of statistics. “Pearson and Pearson” statistics (both Egon, not Karl) would have looked very different from Neyman and Pearson statistics, I suspect. One of the few sources of E.S. Pearson’s statistical philosophy is his (1955) “Statistical Concepts in Their Relation to Reality”. It begins like this:
Controversies in the field of mathematical statistics seem largely to have arisen because statisticians have been unable to agree upon how theory is to provide, in terms of probability statements, the numerical measures most helpful to those who have to draw conclusions from observational data. We are concerned here with the ways in which mathematical theory may be put, as it were, into gear with the common processes of rational thought, and there seems no reason to suppose that there is one best way in which this can be done. If, therefore, Sir Ronald Fisher recapitulates and enlarges on his views upon statistical methods and scientific induction we can all only be grateful, but when he takes this opportunity to criticize the work of others through misapprehension of their views as he has done in his recent contribution to this Journal (Fisher 1955 “Scientific Methods and Scientific Induction” ), it is impossible to leave him altogether unanswered.
In the first place it seems unfortunate that much of Fisher’s criticism of Neyman and Pearson’s approach to the testing of statistical hypotheses should be built upon a “penetrating observation” ascribed to Professor G.A. Barnard, the assumption involved in which happens to be historically incorrect. There was no question of a difference in point of view having “originated” when Neyman “reinterpreted” Fisher’s early work on tests of significance “in terms of that technological and commercial apparatus which is known as an acceptance procedure”. There was no sudden descent upon British soil of Russian ideas regarding the function of science in relation to technology and to five-year plans. It was really much simpler–or worse. The original heresy, as we shall see, was a Pearson one!…
Indeed, to dispel the picture of the Russian technological bogey, I might recall how certain early ideas came into my head as I sat on a gate overlooking an experimental blackcurrant plot…!
To continue reading, “Statistical Concepts in Their Relation to Reality” click HERE.
See also Aris Spanos: “Egon Pearson’s Neglected Contributions to Statistics“.
Happy Birthday E.S. Pearson!
Error Statistics Philosophy 
Regarding the authors listed in the In the reference sections, one of these names is not like the others: G.A. Barnard, R.A. Fisher, H. Jeffreys, D.V. Lindley, J. Neyman, E.S. Pearson, K.D. Tocher.
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Who the heck was K.D. Tocher?
Corey: I thought you would know!
Interesting! I recall reading that 1955 paper by Fisher with all its `five year plan’ talk, and thinking that sounded weird. Pearson seems to be saying that this was a bit of a straw man.
But another aspect of Pearson’s paper confuses me, at the point he addresses 2 by 2 contingency tables. Is he rejecting the weak conditioning principle? E.g. as you have it in your Birnbaum papers: say you have an experiment with an antecedent random variable that affects the accuracy of the `second stage’ of a mixture experiment, once you know the outcome of the `antecedent’ bit then you have to `condition’ on that, i.e. you have to consider the accuracy relative to that (in your sampling distribution, you assume that the antecedent variable always comes out the way it did in the experiment you actually did).
Pearson talks about three different types of 2×2 table scenarios. The first I take it would be something like 100 plots of land with exactly 50 randomly chosen ones given pesticide treatment, and the outcome is infestation or not. Then both Pearson and Fisher would “condition” on the marginal total of 50 plots with and without pesticides (it’s type (i) in Pearson’s classification). There is no randomness in this marginal total.
But to take one other example (of type iii per Pearson’s list I think) if I surveyed 100 sewer rats for the presence of some disease, then tried to see if it’s presence was related to sex then the marginal total number of females might not be exactly 50. The actual number of females I find though is like the outcome of an `antecedent’ random variable and if I was Fisher I’m sure I would use the exact same method, conditioning on the marginal totals that I find be it 50 or 51 or 49 females or whatever. But Pearson implies that because if I repeated the whole experiment I would get different marginal totals then the same does not apply. Is that what he’s saying or am I misreading it?
James: I think Pearson’s point is that it depends on the context and question, and that we shouldn’t be making inferences in a recipe-like fashion.