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I'm looking for examples of people who made some important contributions to the field, yet their original training was not in statistics and they may have learned it 'on the job'. I'm interested in details on how they finally ended up studying statistics.

I'm excluding centuries before 20th, because I guess the field was less complex back then, so it might have been easier to make contributions and to study "low hanging fruits" (but happy to be corrected here).

If the question has been closed because the definition of "formal training" is too broad, one can restrict it to "someone who didn't pursue a higher education degree in statistics or mathematics before making their contribution", if for some reason it's absolutely necessary to restrict the scope of the question with regard to this.

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This question has been cross posted at hsm: Who are some famous statisticians from the 20th and 21st centuries, who didn't have a formal training in statistics? and anyone who wanted to contribute to this question may visit hsm and do the same.

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    $\begingroup$ In the beginning of the 20th century, the statistics as a seperate field was only just established. So anybody that made contributions did not have an formal training in statistics. $\endgroup$
    – Sextus Empiricus
    Commented Jun 27 at 16:48
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    $\begingroup$ That should have ended this whole thread and I agree with @SextusEmpiricus. Then there are many who had started in other fields and later contributed in statistics, which, while exemplary, is not uncommon and this holds true for any other field too. $\endgroup$
    – User1865345
    Commented Jun 27 at 16:53
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    $\begingroup$ There is this anecdote re C. R. Rao who got his masters in Maths and wanted some employment opportunities and circumstances propelled him to learn statistics by only reading Biometrika at University of Calcutta. $\endgroup$
    – User1865345
    Commented Jun 27 at 16:56
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    $\begingroup$ A potential archetype example might be William Gosset who developed the t-test and the t-distribution in the 1910s. It seems like 'in the old days', when knowbody hat yet dibs on the early discoveries, science and mathematics was possible as a hobby. Like monks discovered the expansion of the universe or noble men discovered the atom in their garden shed. Nowadays a lot of science is stuck into large scale projects costing a lot of money, time and power (and rich people decide to make spaceX instead of meaningful science). The childish and naive approaches are gone and it is a full-time job. $\endgroup$
    – Sextus Empiricus
    Commented Jun 27 at 17:03
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    $\begingroup$ Strictly speaking Gosset did neither of those things, albeit many textbooks claim he did. The test he wrote about in 1908 is not the t-test, and does not have the t-distribution (albeit it's equivalent to a t-test, it rejects the same cases); Gosset (correctly) guessed the distribution of his statistic but couldn't prove it. The test we use was developed by Fisher (then a student, I think) around 1915 and the proof that it had a t-distribution was due to Fisher. The t-distribution was obtained by Lüroth in 1876 for a regression-related calculation (and found again by Edgeworth in 1883). $\endgroup$
    – Glen_b
    Commented Jun 28 at 1:38

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John Wilder Tukey (1915-2000) was one of the greatest statistical scientists of the twentieth century. Even that bare summary understates his achievements. His genius and his generosity were recognized early and often in elections to leading academies, major prizes, honorary degrees, and the like.

Tukey was mostly home-schooled by his parents as a prodigy. His first degree from Brown was in chemistry. His doctorate from Princeton was in topology. He fell into statistics as a result of government service in the Second World War. From 1945 he combined a position at Princeton with one at Bell Labs. He was highly active in consultancy and committee work, both governmental and private.

The recognition that he might have appreciated most was in the efforts of many colleagues and students to expound, apply, and expand on his statistical ideas. His work with others on the Fast Fourier Transform had a profound effect on computing in several fields. Especially from the middle 1970s, many of his ideas were built into texts and monographs as well as being applied to statistical and scientific problems in journal papers and reports.

A series of Collected Works reached eight volumes (1984-1994) before stalling, but remains invaluable, particularly for including many hitherto unpublished papers. A 1997 Festschrift growing out of celebrations of his 80th birthday has much interesting material on Tukey's life and work. After his death there were many celebratory and analytical papers on aspects of his work in leading statistical journals, notably Annals of Statistics, Statistical Science, and Technometrics.

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    $\begingroup$ Was it him who said something like "The first time I was in a statistics class I was there to teach it"? $\endgroup$
    – Igor F.
    Commented Jun 27 at 16:51
  • $\begingroup$ @Igor F That would have been accurate, I think, $\endgroup$
    – Nick Cox
    Commented Jun 27 at 17:43
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My view of the fun in science in the current world, is very cynical:

The modern academic world is very professional and institutional.

You can't make discoveries anymore by playing with dropping weights from towers, or accidentally finding radiation from a radioactive source on photosensitive plates.

That naive experimental phase is over. Such science is dead, and the ashes have become completely academic with large institutions and teams crawling around like an ant nest (and are powered by outsider incentives like economical powers).

Individuals have very little meaning anymore.

So important statisticians...

  • First they started out as mathematicians like the Bernoullis and Gauss or Laplace, who did some mathematics on probability (and this flavour of statistician has remained, with mathematicians remaining influential).
  • Second you got pioneers in specific fields that developed new techniques different from the initial mathematical approaches. Biology/agriculture/genetics/eugenics was a particularly fruitful fields for developments in statistics (Karl Pearson, Ronald Fisher, Sewall Wright, etc.), other fields are geophysics (Harold Jeffreys).
  • Third you got the statisticians that learned the job from prior statisticians.
  • Nowadays all the statisticians work within an established framework.

Like in many other fields, the first developments came from polymaths and the last developments came from specialists. In between you find outsiders that made developments along side specialist. In the 21th century I believe that we have already past the phase where the two coincide.

Possibly in AI or data science there might be novelties that come from outside the statistics field. But also in that field it seems difficult to make an achievement without proper initial training, and the developments occur in small steps and based on team developments.

To speak about individual contributions, already now it is difficult (who discovered the first proof of the Higgs Boson?). I guess that several decades from now we won't do that anymore.

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    $\begingroup$ Good if sardonic overview. I wouldn't use genetics and Pearson in the same sentence. Yes, he was very interested in biological questions. But his work was in many ways indifferent or hostile to genetics as developed by people who worked under that heading. (This comment is not about eugenics. Many people who worked in statistics wide sense were concerned about eugenics in the late 19th and early 20th century. That included socialists such as JBS Haldane as well as conservatives like RA Fisher. I won't join in the unhistorical criticism of their work.) $\endgroup$
    – Nick Cox
    Commented Jun 27 at 17:50
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    $\begingroup$ @NickCox I was searching for an 'outsider' and Wright came first to my mind, that was how genetics came to my mind and it sparked the idea that a lot of that early statistics is agriculture, genetics, biology, and somehow I feel that these are related fields (at least in characteristics, it is not exact science like physics or chemistry). In the brackets I combined on purpose the well known Pearson and Fisher with slightly less well known Wright to stress that all that work in the early 20th was all the time subjective to other fields, like biology, or ... genetics. $\endgroup$
    – Sextus Empiricus
    Commented Jun 27 at 17:57
  • $\begingroup$ Sewall Wright was a very distinguished biologist himself. IIRC, he named the coefficient of determination. $\endgroup$
    – Nick Cox
    Commented Jun 28 at 12:13
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    $\begingroup$ @NickCox Sewall Wright definitily made a long lasting contribution which can be seen in the $R^2$ value. Yet, his development of the method of path coefficients never got popular. Was that idea not good enough or was he too much outsider from the rest of statistics? I might be wrong, but to me he appears as a bystander or a person that passed by with a contribution, but did not devote their entire career to the statistics. $\endgroup$
    – Sextus Empiricus
    Commented Jun 28 at 12:44
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Statistics is closely related to fields like mathematics, econometrics, etc. and many contributions to statistics come from researcher whose formal education was in one of these disciplines.

In terms of a statistician without a formal degree in statistics or any closely related field, I think it would be hard to find someone more influential than James Robins who has made significant contributions to causal inference, i.e. G-estimation, doubly robust estimation, etc.

See this article in Statistical Science for a thorough overview of his contributions. The article begins by noting that

Robins majored in mathematics at Harvard College, but then, in the spirit of the times, left college to pursue more activist social and political goals. Several years later, Robins enrolled in Medical School at Washington University in St. Louis, graduating in 1976. His M.D. degree remains his only degree, other than his high school diploma.

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  • $\begingroup$ He didn’t earn a bachelor’s degree in math? $\endgroup$
    – Dave
    Commented Jun 27 at 16:38
  • $\begingroup$ No, he dropped out which is why "his M.D. degree remains his only degree." $\endgroup$
    – num_39
    Commented Jun 27 at 19:28
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Frank Wilcoxon (of the Wilcoxon tests) was a chemist.

Milton Friedman (of the Friedman test was an economist), as was Leslie Godfrey (of the Breusch-Pagan-Godfrey test) [I used to work with him, which is why I mention this test].

Carlo Bonferroni (according to Wikipedia) originally studied music.

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    $\begingroup$ Bonferroni studied music initially but then switched to mathematics. $\endgroup$
    – mdewey
    Commented Jun 30 at 16:18
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From the Bayesian camp: Edwin T. Jaynes (physics) and John Skilling (physics).

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