This is an exchange between Professor David Johnstone (University of Sydney) and I some time ago.
Jagdish Gangolly:
Your call for a dialogue between statistics and
philosophy of science is very timely, and extremely important considering
the importance that statistics, both in its probabilistic and
non-probabilistic incarnations, has gained ever since the computational
advances of the past three decades or so. Let me share a few of my
conjectures regarding the cause of this schism between statistics and
philosophy, and consider a few areas where they can share in mutual
reflection. However, reflection in statistics, like in accounting of late
and unlike in philosophy, has been on short order for quite a while. And it
is always easier to pick the low hanging fruit. Albert Einstein once
remarked, ""I have little patience with scientists who take a board of wood,
look for the thinnest part and drill a great number of holes where drilling
is easy".
1.
Early statisticians were practitioners of the art,
most serving as consultants of sorts. Gosset worked for Guiness, GEP Box did
most of his early work for Imperial Chemical Industries (ICI), Fisher worked
at Rothamsted Experimental Station, Loeve was an actuary at University of
Lyon... As practitioners, statisticians almost always had their feet in one
of the domains in science: Fisher was a biologist, Gossett was a chemist,
Box was a chemist, ... Their research was down to earth, and while
statistics was always regarded the turf of mathematicians, their status
within mathematics was the same as that of accountants in liberal arts
colleges today, slightly above that of athletics. Of course, the individuals
with stature were expected to be mathematicians in their own right.
All that changed with the work of Kolmogorov (1933,
Moscow State, http://www.socsci.uci.edu/~bskyrms/bio/readings/kolmogorov_theory_of_probability_small.pdf),
Loeve (1960, Berkeley), Doob(1953, Illinois), and Dynkin(1963, Moscow State
and Cornell). They provided mathematical foundations for earlier work of
practitioners, and especially Kolmogorov provided axiomatic foundations for
probability theory. In the process, their work unified statistics into a
coherent mass of knowledge. (Perhaps there is a lesson here for us
accountants). A collateral effect was the schism in the field between the
theoreticians and the practitioners (of which we accountants must be wary)
that has continued to this date. We can see a parallel between accounting
and statistics here too.
2.
Early controversies in statistics had to do with
embedding statistical methods in decision theory (Fisher was against, Neyman
and Pearson were for it), and whether the foundations for statistics had to
be deductive or inductive (frequentists were for the former, Bayesians were
for the latter). These debates were not just technical, and had
underpinnings in philosophy, especially philosophy of mathematics (after
all, the early contributors to the field were mathematicians: Gauss, Fermat,
Pascal, Laplace, deMoivre, ...). For example, when the Fisher-Neyman/Pearson
debates had ranged, Neyman was invited by the philosopher Jakko Hintikka to
write a paper for the journal Synthese ( "Frequentist probability and
Frequentist statistics", 1977).
3.
Since the early statisticians were practitioners,
their orientation was usually normative: in sample theory, regression,
design of experiments,.... The mathematisation of statistics and later work
of people like Tukey, raised the prominence of descriptive (especially
axiomatic) in the field. However, the recent developments in datamining have
swung the balance again in favour of the normative.
4. Foundational issues in statistics have always
been philosophical. And treatment of probability has been profoundly
philosophical (see for example http://en.wikipedia.org/wiki/Probability_interpretations).
____________________________________
David Johnstone:
In reply to your points: (1) the early development
of statistics by Gossett and Fisher was as a means to an end, i.e. to design
and interpret experiments that helped to resolve practical issues, like
whether fertilizers were effective and different genetic strains of crops
were superior. This left results testable in the real world laboratory, by
the farmers, so the pressure to get it right rather than just publish was
on. Gossett by the way was an old fashioned English scholar who spent as
much time fishing and working in his workshop as doing mathematics. This
practical bent comes out in his work.
(2) Neman’s effort to make statistics “deductive”
was always his weak point, and he went to great lengths to evade this issue.
I wrote a paper on Neyman’s interpretations of tests, as in trying to
understand him I got frustrated by his inconsistency and evasiveness over
his many papers. In more than one place, he wrote that to “accept” the null
is to “act as if it is true”, and to reject it is to “act as if it is
false”. This is ridiculous in scientific contexts, since to act as if
something is decided 100% you would never draw another sample - your work
would be done on that hypothesis.
(3) On the issue of normative versus descriptive,
as in accounting research, Harold Jeffreys had a great line in his book, “he
said that if we observe a child add 2 and 2 to get 5, we don’t change the
laws of arithmetic”. He was very anti learning about the world by watching
people rather than doing abstract theory. BTW I own his personal copy of his
3rd edition. A few years ago I went to buy this book on Bookfinder, and
found it available in a secondhand bookshop in Cambridge. I rand them
instantly when I saw that they said whose book it was, and they told me that
Mrs Jeffreys had just died and Harold’s books had come in, and that the 1st
edition was sold the day before.
(4) I adore your line that “Foundational issues in
statistics have always been philosophical”. .... So must they be in
accounting, in relation to how to construct income and net assets measures
that are sound and meaningful. Note however that just because we accept
something needs philosophical footing doesn’t mean that we will find or
agree on that footing. I recently received a comment on a paper of mine from
an accounting referee. The comment was basically that the effect of
information on the cost of capital “could not be revealed by philosophy”
(i.e. by probability theory etc.). Rather, this is an empirical issue. Apart
from ignoring all the existing theory on this matter in accounting and
finance, the comment is symptomatic of the way that “empirical findings”
have been elevated to the top shelf, and theory, or worse, “thought pieces”,
are not really science. There is so much wrong with this extreme but common
view, including of course that every empirical finding stands on a model or
a priori view. Indeed, remember that every null hypothesis that was ever
rejected might have been rejected because the model (not the hypothesis) was
wrong. People naively believe that a bad model or bad experimental design
just reduces power (makes it harder to reject the null) but the mathematical
fact is that it can go either way, and error in the model or sample design
can make rejection of the null almost certain.
