Salsburg, D. 2001.
``
The Lady Tasting Tea
-- How statistics revolutionized science
in the twentieth century''.
Owl Book.
Chapter 11. Hypothesis Testing
(continuation)
The frequentist definition of probability
The climb of the Neyman-Pearson formulation to the
pinnacle of statistics did not go unchallenged. Fisher
attacked it from its inception and continued to attack
it for the rest of his life. In 1955, he published a paper
entitled ``Statistical Methods and Scientific Induction''
in the Journal of the Royal
Statistical Society, and he expanded on this with
his last book, Statistical Methods
and Scientific Inference. In the late 1960s, David
Cox, soon to be the editor of
Biometrika,
published a trenchant analysis of how hypothesis tests
are actually used in science, showing that Neyman's
frequentist interpretation was inappropriate to what is
actually done. In the 1980s, W. Edwards Deming attacked
the entire idea of hypothesis testing as nonsensical.
(We shall come back to Deming's influence on statistic
in chapter 24.) Year after year, articles continue to
appear in the statistical literature that find new faults
with the Neyman-Pearson formulation as frozen in the
textbooks.
Neyman himself took no part in the canonization of the
Neyman-Pearson formulation of hypothesis testing. As early
as 1935, in an article he published (in French) in the
Bulletin de la Société
Mathématique de France, he raised serious
doubts about whether optimum hypothesis tests could be
found. In his later papers, Neyman seldom made use of
hypothesis tests directly. His statistical approaches
usually involved deriving probability distributions from
theoretical principles and then estimating the parameters
from the data.
Until R.A. Fisher died in 1962, Neyman was under constant
attack by this acerbic genius. Everything Neyman did was
grist for Fisher's criticism. If Neyman succeeded in
showing a proof of some obscure Fisherian statement,
Fisher attacked him for misunderstanding what he had
written. If Neyman expanded on a Fisherian idea, Fisher
attacked him for taking the theory down a useless path.
Neyman never responded in kind, either in print of, if
we are to believe those who worked with him, in private.
In an interview toward the end of his life, Neyman
described a time in the 1950s when he was about to
present a paper in French at an international meeting.
As he went to the podium, he realized that Fisher was
in the audience. While presenting the paper, he steeled
himself for the attacks he knew would come. He knew that
Fisher would pounce upon some unimportant minor aspect
of the paper and tear it and Neyman to pieces. Neyman
finished and waited for questions from the audience. A
few came. But Fisher never stirred, never said a word.
Later, Neyman discovered that Fisher could not speak
French.
