SCIENCE 



The situation may be illustrated by an in- 

 stance of general irapor'tance. Death rates, 

 birth rates and marriage rates are continually 

 used, but always witliout probable errors. 

 Thus, for example, the Bureau of the Census 

 issues weekly a bulletin that contains the death 

 rates of the leading cities of the United States, 

 but the figures have no meaning because one 

 does not know whether the different rates ai'e 

 due to chance fluctuations with a limited popu- 

 lation or to causes such as a large proportion 

 of infants or an epidemic of influenza.^ If the 

 average death rate is 12 per thousand, in a city 

 of 100,000 population there will be about 23 

 deaths in a week. If black and white balls in 

 indefinitely large numbers are distributed in 

 the ratio of 23 black to 99,977 white and 

 100,000 are drawn, the most probable number 

 of black balls is 23, but one time in four there 

 will be more than 27, Thus the recorded death 

 rate for a week for a city of 100,000 will nor- 

 mally fluctuate. If it is on the average 12, it 

 will in half the weeks be approximately either 

 as large as 15 or as small as 9. 



If the death rate exceeds 15 in two consecu- 

 tive weeks then the chances are fifteen out of 

 sixteen that it is due to some cause such as an 

 epidemic. The conditions are obviously of 

 practical importance for physicians and health 

 officers. The situation for death rates is nicely 

 illustrated by the illustration that has been 

 used of the distribution of black and white 

 balls in an urn. If the population of the 



6 In the last report received (for the week end- 

 ing September 2, 1922) the death rate of New 

 Haven is given as 5.8 and of Houston as 13.9. In 

 the same week a year ago the death rate of New 

 Haven was 10 and of Houston 7.6. Without 

 probable errors these figures give no useful 

 information in regard to the conditions in the two 

 cities. 



country were 100,000,000 and the death rate 

 were 12 (as it should be, but is not), then 

 1,200,000 people would die during a year. 

 Axiong 100,000,000 black and white balls tliere 

 are 1,200,000 black. But if we draw 100,000 

 (?'. e., take a town of that population) there 

 will be a chance fluctuation as described above. 

 It is also the case that the ])alls are not com- 

 pletely mixed, there being more black balls in 

 some part of the uim than others. In some 

 places we shall draw a larger proportion of 

 black balls. When there is a negro population 

 or a tenement house population or a large pop- 

 ulation of very young or very old people, there 

 are relatively more black balls. There are tem- 

 porarily more black balls in one place when 

 there is an epidemic or the like. In that case 

 we have the analogy of the black balls attract- 

 ing one another. 



This paper has been written to explain the 

 methods used to select the thousand leading 

 American men of science by votes. The psy- 

 chologists have been taken as an example; if 

 space and time permitted tables and curves 

 might be given for the other sciences and a 

 study of the data might yield results of inter- 

 est. Such treatment must, however, be post- 

 poned or left to others. The object of the 

 present paper will be accomplished if it makes 

 clear that the scientific men have been selected 

 and placed in the order of merit for their work 

 by valid objective methods and that the meth- 

 ods used have wnde application. In a subse- 

 quent paper the distribution of the scientifie 

 men will be considered with special reference 

 to the changes that have occurred in the course 

 of ten years. 



J. McKeen Cattell 



Tfie Psychological Corporation, 

 August 1, 1922 



