1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

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1 Oscar Sheynin History of Statistics Berlin, 2012 ISBN 978-3 ...

observations, Boscovich applied a similar test with respect to absolutedeviations and that Herschel independently (1805) made use of it whendetermining the Sun’s movement (again § 6.3.2-3).Herschel (1817/1912, p. 579) wrongly indicated that any starpromiscuously chosen […] out of [14,000 stars of the first sevenmagnitudes] is not likely to differ much from a certain mean size of them all.With regard to size, the stars are incredibly different; that mean value is aworthless quantity, and, in general, stochastic statements, made in theabsence of data, are hardly useful. However, it occurred that the stars, evenearlier than the asteroids, had been considered as elements of a singlepopulation (in the last-mentioned instance, wrongly).Stellar statistics really originated in the mid-19 th century with the study ofthe proper motions of hundreds of stars (until 1842, when astronomersstarted to use the Doppler’s invention, only in the directions perpendicularto the appropriate lines of sight). The calculated mean proper motions forstars of a given magnitude proved, however, almost meaningless sincemagnitudes depended on distances. Beginning with W. Herschel,astronomers thought that the proper motions were random, but theyunderstood randomness in different ways. Newcomb (1902) assumed thattheir projections on an arbitrary axis were normally distributed. He derived,although without providing any calculations, the density laws of theirprojections on an arbitrary plane and their own distribution. Both wereconnected with the χ 2 distribution.The general statistical study of the starry heaven became more importantthan a precise determination of the parameters of some star (Hill & Elkin1884, p. 191):The great Cosmical questions to be answered are not so much what is theprecise parallax of this or that particular star, but – What are the averageparallaxes of those of the first, second, third and fourth magnituderespectively, compared with those of lesser magnitude? [And] Whatconnection does there subsist between the parallax of a star and the amountand direction of its proper motion or can it be proved that there is no suchconnection or relation?Then, Kapteyn (1906b; 1909) described a stochastic picture of the stellaruniverse by the laws of distribution of the (random!) parameters, parallaxesand peculiar motions, of the stars. He (1906a) also initiated the study of thestarry heaven by [stratified] sampling; here is a passage from a letter that hereceived in 1904 on this subject from one of his colleagues and inserted onhis p. 67:As in making a contour map, we might take the height of points at thecorners of squares a hundred meters on a side, but we should also take thetop of each hill, the bottom of each lake, […], and other distinctive points.In statistics, sampling became recognized at about the same time, althoughnot without serious resistance (You Poh Seng 1951) and its most activepartisan was Kiaer, also see § 10.7-2.The compilation of vast numerical materials (catalogues, yearbooks) wasalso of a statistical nature. Sometimes this direction of work had been104

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