NOVEMBEE 10, 1922] 



SCIENCE 



541 



SPECIAL ARTICLES 

 THE ORDER OF SCIENTIFIC MERIT 



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 'by ten of their leading colleagues. '^ 

 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 psychologist 

 and the ultimate object of tihe work is the study 

 of behavior with a view to advancing scientific 

 research, the psychologists may be used for 

 illustrations of method. William James was 

 jylaced 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 

 ithii'd, fourth and fifth were assigned, respect- 

 ively, positions of 4.0, 4.4 and 7.5, with pi-ob- 

 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 probable errors 

 increase 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 

 10.7 places for the last ten. Consequently No. 

 XL on the list would have about one chance in 

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

 numlber 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 errors. As 

 men who are about 6 ft. 2 in. tali are likely to 

 differ from each other about ten times as much 

 as men who are a1x)ut 5 ft. 8 in. tall, so the 

 more distinguished scientific men at the top of 

 the list differ from each other about ten times 

 as much as those toward the bottom, and a unit 



1 Science, November 23, November 30 and 

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

 The Science Press, 1910. 



can be adopted for measuring the differeaces. 

 This method for converting relative positions 

 into degrees of quantitative differences, which 

 was first used by the writer^ to measure sub- 

 jective differences in the intensity of lights has 

 proved to be of wide application. 



For a third selection of our thousand leading 

 men of science it seemed desiraible, 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 validity of votes appears 

 not to have been considered, yet the problem is 

 wide-reaching and is closely related to the 

 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 without 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 members? We do not know 

 the distribution of this "population," but if 

 from an urn containing 216 white and 216 black 

 balls, 8 are drawn, the chances are aibout 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 about evenly divided a 

 vote of that character will be obtained fix)m 

 the council; and on this basis the desirability 

 of a plebiscite vote may be decided. 



In 1916 iVIr. Wilson was elected president by 

 the vote in California, which was in his favor 

 by 466,300 to 462,394, giving him a majority 

 of 3,906. It might be supposed that this small 

 majority would readily have been reversed by 

 an indefinitely large electorate, but if the pop- 

 ulation were equally divided this would prob- 

 ably occur only once if an election were held 

 every day for a hundred years. 



If the members of a jm-y reached their deei- 



^ Philosophische Studien, 1902. See also 

 "Studies by the Method of Relative Position," 

 H. L. Hollingworth, in "The Psychologieal Ee- 

 searehes of James McKeen Cattell, " a review by 

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

 fifth anniversary of his professorship. New 

 York, 1914. 



