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Reprinted from Science, Nov. 10, 1922, Vol. LVI, No. 1454, pages 541-547 



THE ORDER OF SCIENTIFIC MERIT 



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In selecting groups of one thousand Amer- 

 ican men of. science for statistical study in 

 1903 and 1909, the workers in each of twelve 

 sciences were arranged in the order of merit for 

 their work bj^ ten of their leading eoUeagues.i 

 The average positions gave the order, and, as 

 there were ten observations of the position of 

 each individual, its probable error could be cal- 

 culated. 



As the writer of this paper is a psyeholc^ist 

 and the ultimate object of the work is the study 

 of behavior with a view to advancing scientifie 

 research, the psychologists may 'be used for 

 illustmtions of method. William James was 

 placed first in 1903 by the independent judg- 

 ment of each of the ten observers. The psy- 

 chologist who stood second had an average po- 

 sition of 3.7 with a probable error of 0.5; the 

 chances are even that his position was between 

 3.2 and 4.2. The psychologists who stood 

 third, fourth and fifth were assigned, respect- 

 ively, positions of 4.0, 4.4 and 7.5, with prob- 

 able errors of 0.5, 0.6 and 1.0. It follows that 

 the relative order of Nos. II, III and IV is not 

 determined definitely, whereas the chances are 

 some 10,000 to 1 that each of these stood below 

 No. I and above No. V. The protDable errors 

 inci"ease in size 'as the work of the men becomes 

 less significant; it is on the average 0.65 places 

 for the first ten of the fifty psychologists and 

 10J7 places for the last ten. Consequently No. 

 XL on the list would have aibout one chance iin 

 four of falling out of the group of fifty, if the 

 number participating in the arrangement had 

 been very large. 



The figures determine not only the validity 

 of the positions, but also the differences in 

 scientific merit among the psychologists, these 

 varying inversely as the probable eri'ors. As 

 men wlio are alwut 6 ft. 2 in. tal'l are likely to 

 differ from each other about ten times as much 



^ Science, November 23, November 30 and 

 December 6, 1906, "American Men of Science," 

 The Science Press, 1910. 



as men who are alK>ut 5 ft. 8 in. tall, >o, fhe 

 more distinguished scientific men at the top of 

 the list differ from each other alx)ut ten times 

 as much as those toward the bottom, and a unit 

 can be adopted fur measuring the differences. 

 This method for converting relative position.- 

 into degrees of quantitative differences, which 

 was first used by the writer^ to measure sub- 

 jective differences in the intensity of lights has 

 jjroveu to be of wide application. 



For a third selection of our thousand leading 

 men of science it .seemed desirable, in order to 

 avoid the inbreeding that might occur through 

 selection by a limited group, to obtain a gen- 

 eral vote from those competent, and, as before, 

 the new methodological problems have proved 

 to be of interest. The vailidity of votes appeai-s 

 not to have been considered, yet the problem is 

 wide-reaching and is closely related to tlie 

 drawing of balls from an urn, which has 

 largely occupied students of the theory of 

 probabilities. 



If, for example, the council of the American 

 Psychological Association, which consists of 

 eight members, decides witliout consultation in 

 favor of a given measure by a vote of 6 to 2, 

 how likely is this to represent the majority 

 opinion of the 432 membei-s? We do not know 

 the distribution of this "population," buit if 

 from an urn containing 216 white and 216 black 

 baills, 8 are drawn, the chances are ailx)ut one in 

 nine that 6 will be white and about one in 

 seven that 6 or more will be white. These may 

 be regarded as approximately the chances that 

 when the membership is a'bout evenly divided a 

 vote of that character will be obtained from 

 the council; and on this basis the desirability 

 of a plebiscite vote may be decided. 



2 Philosophuiche Studien, 1902. See also 



"Studies by the Method of Relative Position," 

 H. L. Hollingworth, in "The Psychological Re- 

 searches of James McKeen CatteH, " a review by 

 some of his pupils, on the occasion of the twenty- 

 fifth anniversary of his professorship. New 

 York, 1914. 



