Appendix E 413 



one is the cause of the other or else both are dependent upon 

 the same cause. 



Two phenomena are causally connected if any one of the 

 following four cases is true : 



(1) If, when the first is present, the second is invariably present 

 also. 



(2) If, when the first increases in amount, the second also in- 

 variably increases a proportional amount. 



(3) If, when the first is absent, the second is invariably absent 

 also. 



(4) If, when the first decreases in amount, the second also 

 invariably decreases a proportional amount. 



Because a fixed or absolute relationship exists in each of the 

 four cases the correlation between the two phenomena is said 

 to be perfect, but in the first two cases it is positive in nature, 

 in the second two negative in nature. If absolutely no relation 

 existed between the two phenomena, the correlation would be 

 zero. . 



Now, in the bean problem used in the preceding exercise, it 

 might be asked, "Is there any fixed relation between the length 

 of plant and its number of pods?" Suppose, for example, that 

 if on selecting a plant from the whole lot, it was found to be a 

 long one, could we then say, on this information only, that it will 

 be found to bear a great number of pods? If so, we are assum- 

 ing that some relation exists between the two characters. 



Let us, for the sake of illustration, suppose that each bean 

 plant bears one pod for every centimeter in length. Because in 

 this case there exists a fixed or absolute relationship, the corre- 

 lation is said to be perfect, and is expressed by 100 %, or more 

 usually simply by unity (1). 



Now, suppose, however, that on selecting 300 plants averag- 

 ing 80 cm. in length, we find the first 100 plants to bear an 

 average of 50 pods per plant, the second 25 pods, and the third 

 10, it is clear that if we select one more plant at random and 



