702 



SCIENCE. 



[N. S. Vol. XXIV. No. 622. 



position falls between the grades of XXXIV. 

 and L. and that there is one chance in four 

 that he does not belong among our fifty lead- 

 ing psychologists. The increase in the size 

 of the probable errors is irregular, it being 

 more difficult to assign a position to some 

 men than to others. 



It will be noted that the psychologists fall 

 into groups, the first twenty being set off from 

 the next group, though the two groups are 

 bridged over by three cases. At this point 

 also the probable errors become almost sud- 

 denly about three times as large. There are 

 altogether about 200 psychologists in the 

 country, and it looks as if the first tenth 

 forms a separate group of leaders. There is 

 a similar, though less marked group of the 

 first twenty astronomers, but these groups 

 seem to be partly accidental. There is, how- 

 ever, as shown below, an inflection point in 

 the curve of distribution after about the first 

 tenth of our scientific men. The first twenty 

 psychologists fall into four distinct groups, 

 and there are groupings in the other sciences. 

 They do not, however, appear to be sufficiently 

 marked to lead us to distinguish species, such 

 as men of genius and men of talent. It is, 

 however, possible that the complicated condi- 

 tions may ultimately be analyzed so as to give 

 such groups. 



The probable errors not only tell the accu- 

 racy with which the psychologists can be ar- 

 ranged in the order of merit, but they also 

 measure the differences between them. This, 

 indeed, I regard as the most important result 

 of this paper, as science is advanced chiefly 

 by the extension of quantitative methods, and 

 it might not have been foreseen that it would 

 be possible to measure degrees of scientific 

 merit. Our data are concerned with the recog- 

 nition of scientific performance, not with ab- 

 stract ability, if such a thing is conceivable. 

 Merit is in perforraance, not in non-perform- 

 ance, and expert judgment is the best, and in 

 the last resort the only, criterion of perform- 

 ance. 



The difference in scientific merit between 

 any two of the psychologists whose positions 

 and probable errors are shown in the chart is 

 directly as the distance between them and 



inversely as their probable errors. If two of 

 them are close together on the scale, and if 

 the probable errors are large, the difference 

 between them is small, and conversely. 



If the psychologists II. and III. were sepa- 

 rated by 0.5 and their probable errors were 

 0.5, as is approximately the case, then the 

 difference between them is so small that there 

 is one chance in four that the position of III. 

 is above the grade of II. If again the psy- 

 chologists XL. and XLIX. were separated by 

 6 and their probable errors were 6, as is ap- 

 proximately the case, then there is again one 

 chance in four that the true position of 

 XLIX. is above the grade of XL. The dif- 

 ference between II. and III. is thus about the 

 same as that between XL. and XLIX. 



If we take the fifty psychologists in groups 

 of 10, and thus partly eliminate the chance 

 variations, the average probable errors of the 

 five groups are 0.7, 1.8, 4.2, 6.8, 6.2. These 

 probable errors are subject to a correction for 

 the range covered by the grades. Thus the 

 first ten cover a range of about eleven points, 

 and the last ten a range of about six points, 

 and the differences between the psychologists 

 at the top of the list would be nearly twice as 

 great as between those at the bottom of the 

 list if the probable errors were the same. 

 When we take account of both factors, the 

 probable errors in the five groups are 0.6, 1.9, 

 1.8, 6.4 and lO.Y. While the probable errors 

 are determined with a considerable degree of 

 exactness, which is itself measured, the ranges 

 covered by the grades seem to depend on the 

 special conditions in the science; they are not 

 the same in the different sciences, and their 

 validity can not be determined with any 

 exactness. Subject, however, to a consider- 

 able probable error, the range of merit covered 

 by the fifty psychologists is inversely as the 

 figures given, and reduced to a scale of 100 

 would be: 55.6, lT.5, 18.5, 5.2 and 3.2. 



Thus we can say that the psychologists at 

 the top of the list are likely to differ from 

 each other about 18 times as much as the 

 psychologists at the bottom of the list. We 

 have no zero point from which we can meas- 

 ure psychological merit. Men who are 6 ft. 

 2 in. tall are likely to differ from each other 



