NOVEMEEK 16, 1922] 



SCIENCE 



545 



about one sixth. Tlie probable error of posi- 

 tion at the bottom of the group of flftj- is 3.6; 

 there are thus only three or four for whom 

 there would be as much as one chance in four 

 of being dropped from the list if the arrange- 

 ment were made by an indefiniteh- large elec- 

 torate of the same character. 



In the first study of the psychologists, the 

 probable error at the lower ejid of Ihe fifty 

 was 10.7, that is, there wei-e 10 or 11 for whom 

 there was one chance in four that they should 

 not be included on the list. There were then 

 ten arj'augements in order of merit; now there 

 are eighty votes. The probable error decreases 

 as the square root of the number of observa- 

 tions, and the probable errors in ithe two eases, 

 other things being equal, should be about as 

 3 : 1, which is in fact almost exactly the ease. 

 The probable error of a single vote for the 

 psychologists low in the group of fifty at the 

 present time is thus the same as by order of 

 merit in tlie group of 1903. 



In the first study, however, we were con- 

 cerned with the upper quartile, and we are 

 now concerned with the upper decile of the 

 group of American psychologists. If we as- 

 sume disti-ibutions in accordance with the curve 

 of error, the men who now stand at the bottom 

 of the fifty in the present selection will be as 

 able as those who stood about twenty in the 

 lirst arrangement. An examination of the rela- 

 tive ijositions of the individuals who are in 

 each of the two arrangements indicates that 

 this tends to be the ease. The probable error 

 at the bottom of the fifty selected by votes 

 should be in the neighborhood of those who 

 stood about twenty in the first arrangements. 

 This would make a single vote one half as 

 valid (the ratio of the ijrobable errors in the 

 first arrangement for those near the bottom of 

 the fourth hundred and in the tenth hundred 

 of the thousand being 6-1 : 125) as a single 

 judgment of order of merit. The figures given 

 should, however, be regarded as indications of 

 method rather than as exact determinations, 

 for they are subject to various errors. 



The average position of the survivors of the 

 first group of psychologisis in the arrangement 

 of 1903 was (after deaths have been eliminated) 

 4; it is now for the same individuals 14.8. 



Those in the four following groups of ten have 

 dropped, respectively, from 11.5 to IS.l; 20 to 

 27.4; 29.5 to 59.2, and 39.5 to 64.9. This 

 drop in position is on the average less than 

 would be expected if the 10,000 scientific men 

 of to-day are as able and have as good oppor- 

 tunity as the 4,000 scientific men of 1903. The 

 inference is that as the total number increases 

 the pi-oportion of men of distinction decreases. 

 This may be due to the fact that men of special 

 ability find their level apart from the size of 

 the group or because the scientific career 

 attracts less able men or gives them less oppor- 

 tunity than formerly. Both factors are prob- 

 ably present; it is apparent that the situation 

 deserves further investigation. In the pre- 

 vious study it was shown that in the increased 

 competition of a five-year period, those Ijetween 

 40 and 44 years of age remained on the average 

 about stationary; those below 40 gained; those 

 aljove 44 lost, ihe loss being in direct propor- 

 tion to the age. 



As the work of the men becomes more im- 

 portant, the diJierences between the indi- 

 viduals as measured by the probable error of 

 position become greater, the distribution cor- 

 responding in a general way to the upper end 

 of the curve of error. In the case of the votes 

 there are complications, for the votes for dif- 

 ferent men do not have the same weight. The 

 ten ■ A\4io receive the most votes receive nearly 

 all the votes, and in the eases of the few who 

 do not vote for them poor judgment or an error 

 in cheeking is indicated. Some votes mean that 

 a psychologist stands first or near the top of the 

 lisit, whereas others mean that he is barely 

 included. Consecjuently the order and the 

 probable errors in the case of such a vote for 

 one half of the group do not have great validity 

 for the upper part of the distribution. The 

 order is obtained in a satisfactory ananner by 

 the douljle vote, but this introduces further 

 complications in the probable error. In all 

 cases of votes, we have asymmetrical distribu- 

 tions and skew curves. The quantitative rela- 

 tions should be worked out in the first instance 

 for less comj>lieai:ed material than that with 

 which we are' here concerned. 



In nearly all cases in which probable errors 

 have been applied to psychological data, the 



