INDIVIDUALS AND MEASUREMENTS CONSIDERED. 35 



which the individuals who are to be discarded may be distinguished 

 from those who are to be retained in the series. They have said merely 

 that "all but 9 of the subjects could be grouped between two lines not 

 very far apart." 



Had not the authors designated by initials the men to be excluded 

 in this specific series of determinations it would have been impossible 

 for another writer to decide, without actual statistical criteria, which 

 should be thrown out. It is, therefore, quite out of the question to 

 divide any other series in a comparable manner without determining 

 (a) what shall be the slope of the lines which cut off the outlying mem- 

 bers of a series on the basis of height and weight, and (6) w^hat the 

 amount of separation of these lines shall be, i.e., what body-weights may 

 be allowed in any group of individuals of the same height, or vice versa. 



The selection of a criterion by which individuals are to be discarded 

 from a series 27 is so important a matter (if those in presumably good 

 health are to be discarded from control series on the basis of physical 

 configuration at all) that it seems worth while to go into the matter 

 in some detail. The individuals to be segregated are distributed in a 

 scatter diagram or a "correlation surface," according to the measure 

 of heights and weights. From this surface it is desired to cut off certain 

 areas, representing individuals of aberrant ratios of weight to height. 



Any line of division should take into account the general averages 

 for both stature and body-weight. We shall, therefore, select as a 

 standard a line which will pass through the intersection of these two 

 means. This establishes one position of the line. The slope must be 

 ascertained. This is determined by the correlation between the two 

 variables. Thus the equation required is given by 



or, taking the constants for the original 89 men from tables in this and 

 the following chapter, s = 172.449, a s = 7.8032, w = 64.334, a w = 10.7302, 

 r sw = 0.5320, and we have numerically, 



w= -61.818+0.732 s 



This is the axis of the swarm of observations represented by the line 

 A- A in diagram 1. 



In this diagram we have drawn the lines, D D, cutting off the indi- 

 viduals discarded by Gephart and Du Bois as exactly as we have been 

 able to do from their description of their method, but in a manner to 

 give them the benefit of every doubt concerning the position and 

 slope of the lines. These lines do not run parallel to the best-fitting 

 axis, A A, of the swarm of measurements distributed with regard to 



27 Obviously if subjects are to be ruled out of the class of " normals " available for use as 

 control subjects in comparison with pathological cases, it would be better to have them discarded 

 on the basis of logical criteria before rather than after the expenditure of time and labor necessary 

 to the determination of their basal metabolism. 



