CHAPTER XIII 



CORRELATION 



When studying variability in its simplest form we take the 

 characters separately and determine how each behaves with 

 reference to itself alone ; that is, with reference to its own 

 range and type. 



SECTION I MEANING OF CORRELATION 



As the study proceeds, however, and is extended to other 

 particulars, it will be noted that certain characters tend to rise 

 and fall together, as if connected by some causative relation, 

 for example, length and weight of ears, or size and strength of 

 horses ; while others appear to vary quite independently of one 

 another, as stature and intellectual power in man, or color and 

 feeding quality in animals. 



The whole subject of correlation refers to that interrelation 

 between separate characters by which they tend, in some degree 

 at least, to move together. This relation is expressed in the 

 form of a ratio. Thus, if an increase of one character is always 

 followed by a corresponding and proportional increase in a re- 

 lated character, the correlation is said to be perfect and the 

 ratio is I. On the other hand, if an increase in one character 

 is followed by a corresponding and proportional decrease in a 

 related character, the correlation is said to be negative and the 

 ratio is i, or perfect negative correlation. Still again, if the 

 characters in question are absolutely indifferent the one to 

 the other, the correlation is said to be zero, indicating mere 

 association under the law of independent probability, without 

 causative relation of any kind. 



Examples of perfect correlation are furnished by such obvious 

 relations as those between the power of sight and the presence 

 of eyes ; the giving of milk and the presence of an udder ; the 



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