Jul

18

 The book The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century is a one person historical account of the greatest statisticians.

While one may quibble with the authors choice of who the greatest statisticians where or how much he wrote on the statisticians he personally knew, its strength is also because this book is written by a student of R. A. Fischer. a statistician known for introducing statistical research methods into science and furthering Galton's regression analysis.

The "lady tasting tea" is a test if a lady can taste if tea is mixed into milk or if milk is mixed into tea. Highly recommended for those that love history and/ or statistics.

David Lillienfeld writes: 

Let's stop this myth. Fisher's contribution to research methods was in "translating" Pearson. Pearson had actually derived the mathematical formulation well before Fisher, and that Fisher "stole" (from Pearson's view) what became the F test and the like was the basis for a long-standing animosity between the two. Bringing in statistical methods into science was the work of others, not Fisher.

Pearson started that task in the early 1900s for biology and medicine, work continued by Major Greenwood (Pearson's protege, though some might argue that Egon Pearson, Karl Pearson's son, of Neyman-Pearson Lemma fame among other things, took on that role ) and then A Bradford Hill (Greenwood's protege). Hill was among the first tobacco-lung cancer studies (frequently not noted is that Richard Doll was Hill's protege).

Hill was also the genius behind the first modern randomized trial, the MRC Streptomycin Trial in 1948 (conducted as a randomized trial to eliminate bias and not to allow for significance testing). (The trial was necessitated by the cost of streptomycin as a treatment for TB and the essential bankruptcy of Britain post WW2. If the drug didn't "work", the British government didn't want the expense of buying it.) In the US, it was Harold Dorn's work bringing stats into medical research. Dorn and Hill studied together in 1933-5 under Pearson (Egon, not Karl) in London. That was just before Hill published his book on statistics in medical research, which itself translated Pearson for medical researchers.

On the social science side, there was F. Stuart Chapin methodologically, and a bunch of students of Franklin Gittings on the pure stats side. (Gitting's statistical empiricism contrasted with the case-study methods championed at the University of Chicago—which wouldn't change until Sam Stouffer went to it from the University of Wisconsin, where he was the thesis advisor to Harold Dorn.

These were all statisticians, with the exception of Chapin, who strode the fence between stats and subject matter.

Fisher's fame derived out of a book that allowed people to understand Pearson's accomplishments, significant but hardly the person to bring stats into scientific research.

Frank Yates, Fisher's contemporary and teacher to Bill Cochran (of Cochran's theorem—the basis of all contingency table analyses since about 1940 (and yes, Fisher's exact test is still sometimes used, but not anywhere near as much as the tests deriving off of Cochran's work, including log-likelihood, Mantel-Haenszel (also known as Cochran-Mantel-Haenszel today), as well as sampling and queuing theory). That work (Cochran's) had as much to do with bringing "modern" stats into science as Fisher did—but he didn't write much. Yates is also significant in the development of the analysis of variance, but the foundational work there was Fisher's. The AoV was important for agriculture and some laboratory work, though some might argue that Student (Gossett)—another student of Pearon's was the more significant figure there—it is, after all, Student's t-test, not Fisher's t-test. It was the F-test which was named for Fisher.

Fisher was the Richard Feynman of stats, though some might argue, reasonably, that Cochran's book (aka Snedecor and Cochran) taught at least two or three magnitudes more people in science about stats than Fisher ever did, holds as much claim to that title as Fisher did. Cochran went to the US because he and Fisher had quite a falling out after Cochran published what has become known as Cochran's Theorem (which demonstrated, among other things, that the sum of a series of chi-squares was a chi-square and that one could thereby combine contingency tables for analytic purposes).

That was 1938, and the Cochran-Mantel-Haenszel work started in 1954—M-H was 1959). Cochran told me that he and Fisher were good friends before that, sharing a "smoke and afternoon tea" together. (Cochran was well along in suffering from strokes by the time I got to know him, so he might have that history a bit wrong, though Tony Hill agreed with Cochran's recollections—Cochran was well known in London by 1936/7.) Cochran's great "sin" was his refusal to "genuflect" (his word) before the "alter of Fisher" when he published this theorem and stating that the idea was Fisher's—Cochran said it was not. Interesting is that aside from Fisher's exact test, he never did much with contingency tables.

Fisher was a genius, but his impact in stats has been way overblown in its significance (pun intended), much as Feynman was a phenomenal teacher—rainbows on the blackboard—but his impact on physics was normative, not transformative. Pearson has a stronger claim to being the person who brought statistics, notably mathematical statistics, into scientific research, though as the above discussion suggests, he was seminal but hardly alone.

anonymous writes: 

Fisher's Fundamental Theorem of Natural Selection, from his 1930 work, "The Genetical Theory of Natural Selection," which speaks to the relationship of "the relationship of "increase in fitness," (the aggregate of the means, we can think of this as) and "variance," states:

"The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time."

But Fisher was, in looking at the natural world, only therefore considering a narrow band of the spectrum — things, for whatever reasons, are "bound" in the natural world (for example, if I double my height, I end up squaring my weight in order to maintain proportionality, and my legs buckle under the weight [they are probably close to do so now]). Further I contend, this same mechanism, which we only see a sliver of the spectrum manifesting in the natural world (and the overarching question then becomes "why?") manifests in spread of a population of bacteria, spread of disease within cells of an organism, or spread of infected individuals within a population, to the growth rate of national deficits (the idea, to my great satisfaction, having FINALLY found an ear and an excitement with the powers who can do something about this on an international level), and, as we've seen in trading (and which demonstrates that variance in returns is equivalent to negative returns, not to "risk.") The following graphic, which I hope comes through, illuminates the idea:

The black curved line is the average, compounded growth rate (the average [geometric] rate of population growth, what Fisher calls "the increase in fitness of a population"), the hypotenuse, the mean growth in population size per period, the base of the triangles, the variance in growth in those periods. Clearly, Fisher saw in the natural world, a sliver, to the left of the peak of this mathematical relationship.

In very many things, we see this relationship over and over, but often because of natural bounds, we see but a sliver (trading, being an abstraction [until the margin department calls] however, experiences the full spectrum).


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