510 FREDERICK S. HAMMETT. 



Turning now to the method of analysis I can do no better than 

 to quote directly from Miner (3): "A coefficient of correlation 

 measures the degree to which two variables are associated, taking 

 the value + I when a deviation of one variable from its mean is 

 always associated with a proportional deviation of the other in 

 the same direction, decreasing as the intensity of the association 

 decreases until for complete independence of the two variables it 

 takes the value o, and again increasing in numerical value, but 

 with a negative sign for increasing intensity of association where 

 deviations of one variable in one direction are coupled with 

 deviations of the other variable in the opposite direction. Thus 

 the absolute magnitude of a coefficient of correlation measures the 

 intensity of the association of two variables, while its sign indi- 

 cates whether as one variable changes the average values of the 

 other variable change in the same or opposite directions. The 

 possible range of values is from + i to - i." 



The coefficient of correlation does not of itself indicate which 

 is the dependent and which the independent variable. This must 

 be determined by other means. The simple or zero order corre- 

 lation between any pair of variables is not representative of 

 their association uncomplicated by assumed interferences derived 

 from the other variables. In order to obtain such an uncompli- 

 cated index it is necessary to determine the correlation between 

 any given pair of variables when the others are held constant. 

 This is done by the method of partial correlation. 



Now it is conceivable that the weight association between brain 

 and spinal cord is factored by the general size factors carried by 

 the body weight and possibly by the body length, particularly in 

 the case of the spinal cord. Hence the elimination of these 

 general factors for size by stabilization for body weight and 

 length, is essential if we are to obtain the uncomplicated associ- 

 ation between the brain and the spinal cord. That is to say the 

 association free from the general body size factors. This has 

 been done as succeeding paragraphs will show. 



In order that the values obtained by the method of partial 

 correlation be valid it is necessary that all the zero order re- 

 gressions be linear, and that the number of observations in each 

 of the zero order tables be fairly large as compared with the 



