Did Neyman really say of Fisher’s work, “It’s easy to get the right answer if you never define what the question is,” and did Fisher really describe Neyman as “a theorem-proving poseur who wouldn’t recognized real data if it bit him in the ass”?

To answer the question in the title of this post: Of course not. Fisher is English. They say arse, not ass.

But here’s a quote that is floating around. Joseph Wilson quotes science reporter Regina Nuzzo:

Neyman called some of Fisher’s work mathematically “worse than useless”; Fisher called Neyman’s approach “childish” and “horrifying [for] intellectual freedom in the west”

and psychologist Gerd Gigerenzer:

Neyman, also with reference to the issue of power, called some of Fisher’s testing methods “worse than useless” in a mathematically specifiable sense

The latter quote seems to derive from this line of philosopher Ian Hacking from 1965:

The likelihood test in the situation just described is a sort of which, in the literature, has been called worse than useless. Its power is less than its size.

But, as Wilson notes, the “worse than useless” idea was floating around for quite awhile before then:

[Erich] Lehmann, who received his doctorial thesis from Neyman in 1946, casually called likelihood ratio tests whose power was less than its size ”worse than useless” in 1948.

I liked Erich Lehmann. He was one of the few people in the Berkeley stat dept who were nice to me when I was there in the 1990s. Perhaps surprisingly given his theoretical reputation, he seemed to get the idea that applied Bayesian statistics could be both useful and nontrivial. He didn’t share the attitude of his colleagues that probability modeling is suspect, the moment it comes in contact with the data.

Did Neyman really call some of Fisher’s work mathematically “worse than useless”?

I passed this question over to statistician and historian Steve Stigler, who replied:

Yes, Neyman and Fisher took small verbal potshots at each other after 1935 on several occasions, and as such this remark would not be a big deal. But is it accurate? A quick look tells me:

1) In a 1950 Annals of Math Stat paper, “Some principles of the theory of testing hypotheses,” Erich Lehmann twice uses the phrase, as in, “Cases exist, in which the likelihood ratio test is not only unsatisfactory but worse than useless, and hence the likelihood ratio principle is not reliable.” Of course this was not a comment directed at Fisher specifically or even at a corpus of his work, only a reflection of the view that LRs themselves were not always to be trusted, and Fisher would no doubt have disowned the uses in the specific cases given. I gather Lehmann wrote the same thing earlier as well.

2) Hacking I think had exactly this statement in mind when he wrote, “The likelihood test in the situation just described is a sort of which, in the literature, has been called worse than useless. Its power is less than its size.”

3) But it is certainly not aimed at Fisher’s work in any general sense, and it is not to be attributed to Neyman without citation, even though I suspect Neyman would endorse it, and may even have said or written it in the sense used by Lehmann. It is addressed at the idea that LR alone solves all problems, which is not something Fisher would have said.

So there you have it. In any case, I think Nuzzo’s statement gets the point across. Even if Neyman did not make this particular statement, he and Fisher insulted each others’ work in enough other places that I think the general sense of Nuzzo’s statement is correct.

The post Did Neyman really say of Fisher’s work, “It’s easy to get the right answer if you never define what the question is,” and did Fisher really describe Neyman as “a theorem-proving poseur who wouldn’t recognized real data if it bit him in the ass”? appeared first on Statistical Modeling, Causal Inference, and Social Science.