CORRELATION 459 



Arrays of a correlation table. In this table each ear is 

 recorded in the proper square to represent both its weight and 

 its length. This being the case, all the ears of the same weight 

 that are also of the same length are recorded together in the 

 same square. This means that the various rows are frequency 

 distributions of weight with respect to length (as i, 6, n, 26, 

 11, 8, 6, i, the frequency distribution corresponding to the 

 length 6.5 inches), and all the columns are frequency distributions 

 of length with respect to weight. Such frequency distributions 

 with respect to a correlated character are technically known as 

 "arrays." The entire table, therefore, may be looked upon as 

 made up of two systems of parallel arrays with respect to the 

 two characters in question. They are in no respect different from 

 any other frequency distributions ; and their means, standard 

 deviations, variability, and other determinations are calculated 

 by the same methods as given in the last chapter. 



SECTION IV THE CORRELATION COEFFICIENT 



A mere inspection of the correlation table just given suggests 

 that, in general, short ears are light ears, and that long ears are 

 heavy ears ; but what we seek is a statistical constant which 

 will be a measure of this correlation, and which indicates to 

 what extent the weight of ears can be predicted from their 

 lengths. The coefficient of correlation is such a constant, and 

 when determined it will be denoted by r. 



A discussion of the mathematical theory of correlation will 

 be given in the Appendix, but it should be said here, as before, 

 that the coefficient always takes some value between + i and 

 -i. If r==+ i, there is said to be perfect positive correla- 

 tion; that is, the two characters are causally connected. If 

 r i there is perfect negative correlation; that is, they 

 are mutually exclusive. If no correlation exists, r = o^. indicat- 

 ing the two characters as being indifferent to each other and 

 moving independently. In nearly all cases some actual correla- 

 tion exists, and, in a general way, we may say that the correla- 

 tion should be judged by the value which r takes between zero 

 and unity. 



