414 Plant-Breeding 



measure it to be 80 cm. also, we could no more predict the 

 number of pods it bears than if we had not measured it at all. 

 Here, then, we say there is no relationship whatever between 

 length of plant and number of pods, or, in other words, the cor- 

 relation is 0. 



Now suppose a third case, in which we find that invariably 

 the longest plant bears the fewest pods, and the shortest the 

 most. Here we could say the relationship is fixed or absolute 

 too, but in an opposite, or negative manner, and accordingly, 

 the correlation would be expressed by 1 . 



But now turning back to the first supposition, where it was 

 assumed that one pod was borne for each centimeter length, 

 suppose that the relationship were not so definite. Suppose 

 that one pod occurs not for every centimeter, but sometimes for 

 a little more than a centimeter, sometimes for a little less ; then 

 the relationship, though not absolute, is high, and the degree 

 to which this relationship approaches the perfect 100 % relation- 

 ship will express the correlation between the two characters. 

 The correlation coefficient, in other words, would fall between 

 and + 1. 



We rarely find characters or organs in an organism to be 

 absolutely related; usually they are associated in a more or 

 less intermediate degree, somewhere between and + 1, or 

 and 1. The degree to which they are associated, or corre- 

 lated, if it can be determined in an exact manner and expressed 

 by a mathematical constant, should be an index of the degree 

 for which one is the cause of the other, or the probability of 

 finding the other when we know the first is present. This may 

 be of importance sometimes to the breeder because some easily 

 seen character may be responsible for, or indicative of, the 

 presence of a desired, but unseen character. Thus a certain 

 shaped kernel of corn (one with a large germ) is known to run 

 high in oil content, one with large endosperm high in starch. 

 To select kernels with large germs is much easier than to analyze 



