The Movements of Countrymen 113 



the 100 rural counties, while the farm increase, in the same 

 county, is more than the average, then the one deviation is 

 plus and the other minus and a negative relationship is in- 

 dicated. This degree of relationship between the pairs of 

 observations is clearer still in the fifth column, which is ob- 

 tained by multiplying the two deviations together. In the 

 event that both population and farm increase are either 

 above or below the average, the product of the deviations is 

 a plus quantity. In the event, however, that the deviations 

 are in opposite directions from their averages, as in Talbot 

 (the fifth county in the table), their product is minus. In 

 the event both deviations are large, the product is of course 

 a large quantity, in the event one is large and the other 

 small, the product is a smaller quantity, and in the event 

 both deviations are small, the product is so small as to be 

 relatively insignificant. Examination of Column V, which 

 lists these products, reveals that there are only sixteen of the 

 100 counties for which the deviations did not agree in sign, 

 and for which the product is a minus quantity. Many of 

 these are very small products, and the sum of all the minus 

 products deducted from the sum of all the plus products 

 leaves a very large postive number. 



This, in such a large number of cases, is indicative of a 

 strong positive relationship between the two observations. 

 But it may be given a more definite quantitative value by 

 the method of correlation. By this method the relationship 

 expressed in Table 17 is reduced to a coefficient which can- 

 not be numerically greater than plus or minus 1. The closer 

 the coefficient is to plus one, the greater the degree of posi- 

 tive relationship between the phenomena observed. The 

 closer it is to minus one the greater the degree of negative 

 relationship, and the closer it is to zero, the more doubtful 

 the relationship. 



In this case the coefficient arrived at as indicative of the 

 relationship between increase in Negro population and in- 

 crease in independent Negro farmers was .811. The rela- 



