‘Observations and Statistics. An Essay on the Theory of Errors of Observation and the First Principles of Statistics.,’ pp. 138-169 in: Transactions of the Cambridge Philosophical Society, Vol. XIV, Part II. Read May 25, 1885.
Cambridge: University Press, 1887. First edition, journal issue in never-bound sheets, of the first and most important of Edgeworth’s papers on the application of the statistical methods of the theory of errors to the social sciences and economics. “Of all the great economists in this book, he [Edgeworth] is (apart from Bernoulli and Slutsky) the only one to have made original contributions to mathematical statistics” (Blaug, Great Economists before Keynes (1986), pp. 69-71). “Francis Ysidro Edgeworth (1845-1926) was perhaps the statistician with the greatest mathematical abilities at the end of the 19th century” (Fischer, p. 122). “In 1883 began the series of papers that were to make [Edgeworth] the leading theorist of mathematical statistics of the latter half of the 19th century” (Stigler, The History of Statistics, p. 98). “He set himself to do at last what had been talked about and assumed possible for over a century but had never been accomplished: adapt the statistical methods of the theory of errors to the quantification of uncertainty in the social, particularly economic, sciences. In this he succeeded brilliantly” (ODNB). “Edgeworth's 1885 articles, particularly ‘Observations and statistics’ and ‘Methods of Statistics’, were widely noticed, both in England and on the continent, and until the end of the century when texts such as Bowley’s Elements of Statistics began to appear, they served as basic references for the theory and application of statistical techniques to social and economic data” (Stigler, p. 297). RBH lists no copy of this paper (in any form). “The type of questions Edgeworth sought to treat and the difficulties he saw in their treatment were described in an 1884 review of a posthumously published collection of Jevons’s papers, Investigations in Currency and Finance. Edgeworth commented upon the beautiful diagrams in the book, which he thought would assist the reader to estimate the probability that the differences in the averages for different weeks and months are not accidental: ‘The question which has been just indicated, one of the most delicate in statistics - namely, under what circumstances does a difference in figures correspond to a difference of fact - comes up often in these pages. Thus Mr. Jevons, comparing the amount of bills created in the different quarters of the year, speaks of a variation to the extent of about six percent. as ‘no great difference.’ On the other hand, he regards it as noteworthy that, ‘out of 79,794 bankruptcies which were gazetted from the beginning of 1806 to the end of 1860, 28,391 occurred in the second month of the quarter, 26,427 in the third month, and only 24,976 in the first month.’ No doubt a similar disparity between ‘heads’ and ‘tails’ in the result of so many throws of a coin would prove a cause, a want of symmetry in the coin. But our knowledge of the behaviour of tossed coins rests at bottom upon observation and experiments such as those which Mr. Jevons once performed. That what is true of games of chance is true of bankruptcies is not to be assumed without examination.’ “Edgeworth was to provide this examination. “Edgeworth’s key work on this topic was contained in a series of four papers read in the year 1885. The first of these, ‘Observations and statistics: An essay on the theory of errors of observation and the first principles of statistics,’ was read on 25 May 1885 to the Cambridge Philosophical Society. It concentrated on statistical theory and summarized and extended his work of the previous two years. The second paper, ‘Methods of statistics,’ was read a month later, on June 23, to the international gathering to celebrate the jubilee of the [Royal] Statistical Society. It was concerned with methodology and presented, through an extensive series of examples taken from all manner of fields, an exposition of the application and interpretation of significance tests for the comparison of means. Much of the material in these two papers was presented at least in outline in Edgeworth's evening classes in logic starting in April 1885. The third and fourth papers, ‘On methods of ascertaining variations in the rate of births, deaths, and marriages’ and ‘Progressive means,’ were read at meetings of the British Association in September and October. The third presented a remarkable analysis for two-way classifications that anticipated many ideas of the analysis of variance. The fourth article, ‘Progressive means,’ was a brief discussion of the use of linear least squares for detrending time series, including the estimation of the coefficients’ variabilities to permit significance tests for trend or comparisons of different series. “For Edgeworth the distinction between observations and statistics was an important one: ‘Observations and statistics agree in being quantities grouped about a Mean; they differ, in that the Mean of observations is real, of statistics is fictitious. The mean of observations is a cause, as it were the source from which diverging errors emanate. The mean of statistics is a description, a representative quantity put for a whole group, the best representative of the group, that quantity which, if we must in practice put one quantity for many, minimizes the error unavoidably attending such practice. Thus measurements by the reduction of which we ascertain a real time, number, distance are observations. Returns of prices, exports and imports, legitimate and illegitimate marriages or births and so forth, the averages of which constitute the premises of practical reasoning, are statistics. In short observations are different copies of one original; statistics are different originals affording one ‘generic portrait.’ Different measurements of the same man are observations; but measurements of different men, grouped round l'homme moyen, are primâ facie at least statistics’ (pp. 139-140) “Edgeworth’s aim was to apply the tools developed in the previous century for observations in astronomy and geodesy, where a more or less objectively defined goal made it possible to quantify and perhaps remove non-measurement error and meaningful to talk of the remaining variation as random error, to social and economic statistics where the goal was defined in terms of the measurements themselves and the size and character of the variation depended upon the classifications and subdivisions employed. To do this he first disassembled these tools to determine carefully what lay beneath them: What conditions, what assumptions, what interpretations lay behind their successful use? “‘Observations and statistics’ focused on one theoretical aspect of this problem, the choice of a best estimate of a mean. Although the problem was presented as one of estimation, the underlying motivation, the implicit use to which the mean would be put, was the comparison of different sets of statistics. Edgeworth examined the philosophical interpretations of probability as applied to inference. He gave careful consideration to the objective frequentist or sampling theory view (he called it ordinary induction, assumed inversion, or the indirect method), but in thee nd he adopted the inverse probability, or Bayesian, view after giving cogent refutations to criticisms of this view by Cournot, Boole, and Venn. Edgeworth gave qualified endorsement to the use of uniform prior distributions, but only when the prior was based on experience: ‘We have a rough general experience that one value of the measurable occurs as often as another at any rate between the limits with which we are practically concerned’ (p. 146). Like Laplace, Edgeworth embraced inverse probability for neither metaphysical (his priors were grounded on experience) nor dogmatic reasons. Like Laplace, Edgeworth was inconsistent in his application of inverse probability, reverting to sampling distributions when comparing means by significance tests. “In the selection of a best mean Edgeworth preferred choosing, with a general loss function that value that minimized the posterior expected loss. He extensively discussed the relationship between the population distribution (the ‘facility-curve’) and the best mean, his examples including the family of stable laws and others where averaging was detrimental, and densities where the median was to be preferred. He focused special attention upon the normal distribution (the ‘law of error’ or ‘probability-curve’) …” (Stigler, pp. 295-296). “Francis Ysidro Edgeworth (1845-1926) was perhaps the statistician with the greatest mathematical abilities at the end of the 19th century. Later on, however, he became prominent due to his work on economics rather than his statistical contributions … Edgeworth, who had originally studied ancient languages and law, acquired his mathematical skills as an autodidact mainly by reading the works of ‘classical’ authors like Laplace, Poisson, and Fourier. He did not become familiar with the analytical development of the beginning modern era. Regarding his stochastic concepts and analytic methods, Edgeworth was especially influenced by apparently very carefully reading Laplace’s [Théorie analytique des Probabilités, 1812]. The latter’s remarks on possible alternatives to the method of least squares for parameter estimation were adopted by Edgeworth and further advanced, in particular in context with his frequent discussions of non-normal distributions. As a consequence of his autodidactic education, Edgeworth cultivated an analytic style which reminds one of the 18th rather than the early 20th century. His presentation of mathematical issues was often sketchy and not always straightforward. Altogether, these circumstances make his statistical work quite difficult to read. On the other hand, his permanent readiness to advance the discussion of statistical models far beyond their momentary practical applicability give his contributions a very modern touch. Born in Edgeworthstown, County Longford, into a leading Irish family, Edgeworth studied classics at Trinity College, Dublin and then literae humaniores at Oxford, graduating in 1869. He then studied law, and was called to the bar in 1877. After leaving Oxford, and while studying law, he also undertook an intense programme of self-study in mathematics. “In 1879 Edgeworth became in effect an apprentice in economic theory to his friend and neighbour William Stanley Jevons. Starting from scratch, he learned economics so well and so fast that in 1881 he published his masterpiece Mathematical Psychics. Although its reviewers Jevons and Marshall praised the book, neither showed any understanding of the profound ‘economical calculus’ that is its heart, a positive analysis of exchange in both market and non-market settings. In the latter, the possibility of coalitions between the various parties to the exchange poses severe and quite novel analytical difficulties, but even so Edgeworth was able to reach deep and highly non-intuitive theorems about relations between non-market and market exchange … “For whatever reasons (and one can think of several), soon after Mathematical Psychics appeared Edgeworth changed course completely, and in 1883 began the series of papers that were to make him the leading theorist of mathematical statistics of the latter half of the 19th century … but, as with his economics, his achievements were consistently underrated for many years. Only after 1975 did sympathetic criticism by Stephen Stigler and others lead to proper evaluation of Edgeworth’s contributions, which culminated in 1996 in three large volumes (ed. C. R. McCann) which reprint nearly all his papers on statistics and probability” (ODNB). Fischer, A History of the Central Limit Theorem, 2011. Stigler, ‘Francis Ysidro Edgeworth, Statistician,’ Journal of the Royal Statistical Society, Series A, 141 (1978), pp. 287-322.
4to (289 x 225 mm), pp. [iv] 71-209 [blank]. Original unbound and unopened sheets and original printed wrappers. A virtually mint copy.
Item #6405
Price: $500.00
