12 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 



measure of the position of an individual in the whole series of measure- 

 ments. Values with the negative sign indicate a position below the 

 average, values with a positive sign a position above the average of 

 the series as a whole, while the numerical value gives at once the mag- 

 nitude of the deviation. 



Now remembering that (x x) and (y y) are values with signs, 

 it is clear that if we take the products of these deviations we shall have 

 positive products for all values with like signs and negative products for 

 the values of all deviations with unlike signs. Summing these products 

 with regard to sign for the whole series of individuals under investiga- 

 tion, the net total will be positive if the two measures x and y tend to 

 vary in the same direction, that is, if y tends to be above its mean value 

 in individuals in which x is above its mean value and y tends to lie 

 below its mean value in individuals in which x lies below its mean value. 



For example, the table for the athletes given above shows the actual 

 amount of the deviation of the weight and the daily heat-production 

 of each individual above or below the mean weight and mean heat- 

 production of the whole group of athletes. The fact that two positive 

 or two negative signs tend to occur together shows at a glance that there 

 is some correlation between body- weight and total heat-production. 

 The products of these deviations are given in table 2. 



TABLE 2. Products of deviations of body-weight and daily heat-production from 



their respective means. 



In 15 of the 16 cases the heat-production is larger than the average 

 heat-production when weight is larger than the average weight and 

 smaller than the average heat-production when weight is smaller than 

 the average. Summing the products with regard to sign, we have 



+48335.0-3.5 = +48331.5, 

 which divided by 16=3020.7188. 



