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5~atistics, -1 her. and Now EDWIN B. WILSON* I learned of the year 1839 very early in life. It was the year of my father's birth. He was not a statistician but a student of the Greek and Latin classics, and my schoolina like that of most of my contemporaries who were fitting for college was chiefly classical. There was Greek and Latin, arithmetic, algebra and geometry, and a modern languabe but no science. The first data I read in the preschool days were in the marbins of the Bible. The creation was in 4.001. B.C., already in the agricultural age. The ancient Jewish historian had not heard of the pre-agricultural ages, but he may have been no worse off than the chronolo;ist Bishop Ussher (Usher) of 1581-1656 whose biblical chronoloay was published shortly before his death. Tl:e cosmogonists are always giving us dates for future cos- mobonists to revise. Then there was the universal flood that destroyed all animal life except for the inhabitants of Noah's ark in 2349 B. C., an event of which we are far from certain, albeit sure it did not occur at that time. And Joseph went down into Egypt in 1729 and, being a smart fellow, was well received only to have his whole tribe driven out in the exodus of 1460. By this date the chronologist may perhaps be not more than 250 years off. ~r,~1 p -. There are the more recent statisttical estimates by our best demographers which turned~o~t none too accurate. Sometime around 1937 fl'rae-'bf'edt planner, President Roosevelt, asked his National Resources Committee to forecast our population to 1980 so plans could be made for taking care of it. The best demographers were then Thompson and Whelpton of the Scripps Foundation for Research in Population. In great detail, as was desired, they made 7 forecasts on seven different sets of hypoth- eses assuming thN past characteristics of the population known up to 1935, leading by extrapolation to the 7 tlistributions thev found. Leaving out the detail of age distribution, I give only the totals for the whole United States. The actual census fi;ures for 1940, 1950, 1960, to the nearest million are 132, 151, 179. The forecast for 1940 was naturally about right. For 1950 the 7 fore- casts varied from 136 to 144, with the census at 151 icell, above the highest. For 1960 the 7 forecasts were from 137 to 155, but 179 was the census figure, and this was above the highest estimate for 1980, which was 174. The details can be found in the first chapter of that 305 page quarto Government monograph "The Prob- lems of a Chanf;ing Population". The sibnificance of the participial adjective Changing was that, relatively speak- ing, children were to be fewer and old folks more plenti- ful than in the past. * Dr. Wilson died on December 28, 1964, one month after pre- senting these remarks at the Boston Anniversary Meeting of ASA. See the memorial article on'Dr. Wilson by Jane Worcester in this issue. Well, the adjective was right, the abe distribution cltan,ed. Not long ago I received from Health, Education and Welfare an advertisement for their "Trends" in which they, too, gave population forecasts probably by able demographers of the present beneration. For 1980 there are 4 in number, varying from 231 to 273. Possibly this sort of statistical work can be done better now than 37 years a;o. The increase from 179 in 1960 lies between 52 and 94 which allows a variation of 29°fo to 54% during the 20 years 1960 to 1980; whereas Thompson and Whelpton basing or. 1935 at 127 allowed only a variation of 8% to 22% for the 25 years from 1935 to 1960. The HEW forecasters are clearly far more cau- tious, much nearer to saying "we can't forecast". By 1980 Changing may still be a good adjective-enough room has been allowed to make quite a difference-but what the 1980 figure will be we do not know. ana~ After graduation from Harvard I went to Yale where-' 1839'came to mean the year of birth of J. Willard Gibbs, the great mathematical physicist, with whom I worked. He was working intensively on the preparation of his book "Elementary Principles of Statistical Mechanics", which appeared in 1902 as one of the volumes in celebra- tion of Yale's Bicentennial. Statistical here means proba- bilistic, as in the kinetic theory of gases; it did not imply data. And elementary did not mean easy. Professor Boussinesque with whom I studied in Paris in 1902-3 said that he had a copy of the book and it would prob- ably take him 5 years to absorb its full significance. The volume came out just before the quantum theory; it was written in terms of' the current dynamics, butl so fundamental was the, analysis that it was actually useful when the quantum theory came along. In point of fact, however, there was one point at which Gibbs' theory did not check with the facts, and he well knew it; the ratio of the specific heats of polyatomic gases indicated fewer degrees of freedom in the molecule than the dynamical theory implied, a matter I had heard Gibbs say had troubled him for 30 years without his seeing any way to explain it. He died in 1903; had he lived another decade, he would have seen the quantum theory explain it. f When I turned my attention to that very diflicult field of medical, public health and socia' -' ;tistics, 1839 came .. up again as the year of birth o: ::;at great, versatile genius Charles S. Peirce-logician, mathematician, beode- sist and philosopher. I had known of his work in logic and mathematics when I was a very young instructor in mathematics at Yale before I was transferred to teach- ina tlle work in mathematical physics of Willard Gibbs after his death. But what interested me in the - 1920s at the Harvard School of'Public Health in Peirce's work , was his paper "On, the Theory of Errors Of Observa- ; 37 E

tions" in the Report of the Superintendent of the U. S. . Coast Survey for 1870, in which 24 series of about 500 reaction times were listed. It is not too easy to come by a large series of a large number of observations for statistical analysis. The results of working up the series (published in Proc. \atl. Acad. Sci., vol. 15, pp. 120-5, 1929) showed that the 24 frequency functions were definitely skew by the ordinary tests, had practically uncontrolled values of the-kurtosis, and that on the whole the medians were as well determined as the means, and finally that the daily means or medians and their stand- ard deviations varied very much more than they should have by the usual sampling formulas and even by those expressed in terms of the fourth moment instead of using those depending only on the standard deviation and the assumption of normality. How it was that Peirce could have considered that he was proving the normal law I had no idea. Besides these three birth dates there was one event in 1839 in addition to that which we are celebrating today which has been of great statistical significance to me. I refer to the letter dated February 28 from Gauss to Bessel, a fellow professor of astronomy who had sent Gauss some work he had done on errors of observation. As we all know, Gauss had published his Theoria lblotus in 1809 using the normal law but in his Theoria Combin- ationis in 1823 had pursued a different course. In his letter of 1839 he wrote that he had never publicly ex- plained why he had ";ab8}~doned the metaphysics applied to the method of least squ~r~es" in his discussion of errors of observation in 1809 and~replaced it by the principle ~ ~imis obnoxiae). I will not of least cost (errorabu's`mzn, quote the whole pairagraph given on pp. 523-4 of the Briefwechsel xwischen Gauss und Bessel. Gauss had be- come not only a very great mathematician but a dis- tinguished scientist. I do not believe I knew when our Association started jectandi, often cited as the first on probability, and wrote Leibniz asking if he could not treat an observed rate as a probability. You know what Leibniz replied-that be could not, because although there were recurrences in Nature they were never exact. The trouble with statistics is that it is so very old and still consists of data which have no common laws that are of much use in interpreting it. Vital statistics, economic statistics, social statistics, meteorological sta- tistics, astronomical statistics, etc., all depend for their proper interpretation upon the state of knowledge in their respective fields of observation, and often upon the knowl- edge in detaill of some small part of the large field, much more than upon mathematical calculations as Leib- niz told Bernoulli; indeed it often happens that one can- not make the proper observation or even the proper cal- culations upon them unless one has a great deal of back- ground of knowled ;e. It is getting easier to make the calculations, what with the decimal notation, logarithms, slide rules, desk com- puting machines, and the great computing machines which are getting larger in capacity as they get smaller in size due to min„a, iaturization. The question is: Are we ~' getting smarter as fast as our tools are improving or are we becoming more likely to cut ourselves intellectually to bits with the increasing sharpness of the tools? Statistics was statistics long before there was mathema- tical probability, and statistics will remain statistics in the sense that we need better data the better our equip- ment to handle it. Many fields of statistical study today, as always, have very little demonstrated background of controllable causation. I will close with a quotation from Yule's essay "The Function of Statistical Method in Scientific Investigation" (Industrial Fatigue Research Board, No. 28, 14 pp., H.M.S.O., London, 1924). The unhappy statistician has to try to disentangle the effect from the ravelled skein with which he is presented. No easy matter this, very often; and a matter demanding , not merely a knowledge of method, but all the qualities that an investigator can possess-strong common sense, caution, reasoning power and imagination. And when he has come to his conclusion the statistician must not forget his caution; he should not be dogmatic. "You can prove -anything by statistics" is a common gibe. Its contrary is more nearly true-you can never prove anything by sta- tistics. The statistician is dealing with most complex cases of multiple causation. He may show that the facts are in accordance with this hypothesis or that. But it is quite another thing to show that all other possible hypotheses are excluded, and that the facts do not admit of any inter- at the time I was its president 35 years ago, and I do' not now know who were those who started it or why . they did so. Insofar as they were practical men interested . in affairs, whether public or their own, they probably were not interested in theory so much as in practice. In this sense statistics is indeed very old. There was John Graunt back in 1662 who- wrote that remarkable book on Vital Statistics, though not so called, of which the three hundredth anniversary was celebrated by the Royal Society two years ago this month. This was consid- . erably before Jacques Bernoulli was writing his Ars Con- , 38 The American Statistician, April, 1965 pretatiori other than . the particular one he may have in ' mind.