METHODS OF STATISTICAL ANALYSIS. 23 



first and second powers and the products for the specific individual, or 

 the sum of these values for the group of individuals, may be subtracted 

 from the original value of 2(x), 2(z 2 ), ZQ/), 2(?/ 2 ) and *L(xy) and the 

 means, standard deviations, and correlation be redetermined on the 

 basis of the reduced A r . 



This has been the method followed in the calculations of the present 

 study. We have used the original measurements as published in the 

 fundamental tables, pp. 38-47, without modification or grouping. This 

 has necessitated rather heavy arithmetical work, since the squares 

 and products have been very large. The course has, however, the merit 

 of introducing no error not already inherent in the data. 



As an illustration of method we again take the constants for body- 

 weight and daily heat-production in our smallest series, the 16 athletes. 

 The values required are given in table 3. These give 



2(t0) =1181.1 Z^ 2 ) =89836.41 N = 16 



= w = 73.8188 <r w = \/2(w*)/N-ti* = 12.8670 



Z(/0 =30025 Z(/i 2 ) =57305137 



/i = 1876.5625 <r h =245.1209 



Z(wft) =2264739.6 2(wh)/N = 141546.225 



and finally 



_ 141546.225 - (73.8188 X 1876.5625) _ Q 95?? 



12.8670X245.1209 

 l-r 2 = 0.0828 E r = 0.0140 



That in presenting our results we have retained more figures than 

 are really significant for physiological work is quite as clear to ourselves 

 as to anyone who may desire to lop off the constants. But we have 

 borne continually in mind the fact that these constants may in many 

 instances be required for further calculation. It has seemed desirable, 

 therefore, to retain a number of places sufficiently large to enable 

 those who care to do so to check particular phases of our work without 

 going back to the raw data. 



