METHODS OF STATISTICAL ANALYSIS. 11 



basis by expressing them as percentages of their respective means. 

 Thus, if x represents heat produced per 24 hours and y represents 

 pulse-rate, it is quite impossible to say from a comparison of a x and a u 

 whether pulse-rate or heat-production is the more variable character. 

 But if the two standard deviations be expressed as percentages of 

 their respective means, 



y = IQOff, y _ 100(T V 



x y 



it is possible to determine which of the two characters is relatively 

 more variable. 



Thus in the case of the measurements of body-weight and total 

 heat-production given above, the relative variabilities are : 



v _100<r t , y ..lOOfffc 



' W 'ft 



w h 



or numerically 



245. 



- 8 



This relative variation constant is known as the coefficient of varia- 

 tion. It shows in the present case that the body-weight of the athletes 

 is about 4.4 per cent more variable than their daily heat-production. 



We now turn to the problem of the measurement of interdependence 

 or correlation. 



Remembering that we are seeking a measure of the degree of inter- 

 relationship of the magnitudes of two variables, it is first necessary 

 to adopt a standard with which individual measures of body-weight, 

 body-surface, metabolism, pulse-rate, or other variables may be com- 

 pared in order to determine their place in their own series. Such a 

 standard is furnished by the average value of the character in the series 

 of individuals available. This arithmetical mean has the advantage 

 for metabolism work that it has been regularly used as a standard 

 value by various workers. The only difference between our use of the 

 mean and that of some other writers on metabolism is that the average 

 value which we employ as a standard is always the average for the 

 particular series of individuals under consideration, not an average for 

 some selected standard series. Thus, in working with athletes, vege- 

 tarians, or all normal men the averages employed as standards are 

 those for athletes, vegetarians, or for all normal men, as the case may be. 



Let x be the measure of any physical or physiological characteristic 

 of an individual, y the measure of any other physical or physiological 

 characteristic for example, oxygen consumption, carbon-dioxide out- 

 put, or calories of heat-production, in the same individual. Then if 

 we designate by bars the average values of these two characteristics in 

 the series of individuals dealt with, (x x), (yy) furnish at once the 



