54 GENETICS IN RELATION TO AGRICULTURE 



His formula is the one now generally used. If the coefficient of corre- 

 lation equal r, 

 Then 



<W|/ 1 \ 



n I \ffxffyf 



We know the work of computing the standard deviation is lessened 

 by using the short method. Hence this method should be employed in 

 computing the correlation coefficient. Qn the basis of assumed means 

 from which the deviations are d' x and d' y we have 



/I,(d' x d'y) \ / 1 \ 



r ty = (- - - w x w v ) (--) 



\ n I \(Tx<T,j' 



from which we read the following rule: 



To compute the coefficient of correlation, multiply the x and y 

 deviations from G for each class; summate the products and divide by 

 n ; from the quotient subtract the product of the two correction factors; 

 divide this difference by the product of the two standard deviations. 



The application of this formula is based upon the correlation table 

 and is illustrated in the case of total yield of plant in grams and 

 number of culms per plant for Sixty Day oats (Fig. 26). 



Interpretation of the Coefficient of Correlation. King gives the 

 following rules for the interpretation of the coefficient of correlation 

 according to its relation to the probable error: 



1. If r is less than the probable error, there is no evidence whatever 

 of correlation. 



2. If r is more than six times the size of the probable error, the 

 existence of correlation is a practical certainty. 



3. In cases where the probable error is relatively small: 



(a) If r is less than 0.3 the correlation cannot be considered at all 

 marked. 



(6) If r is above 0.5 there is decided correlation. 



Applying these rules to the case of variation in yield as related 

 to number of culms we see that r is over 40 times the probable error and 

 under rule 3, the probable error being relatively small, since r = 0.7 +, 

 there is very decided correlation. Referring now to relation of number 

 of culms per plant to average height of plant (Fig. 23) we find that 

 r = 0.042 0.034 from which it is clear that there is little if any indi- 

 cation of correlation. 



Biometricians consider the correlation coefficient the most powerful 

 tool the agricultural investigator can have since it is a most excellent 

 measure and is applicable to an immense range of variables. Remember- 

 ing that this constant is an index of the mutual relation that exists 

 between the variations of any two characters, we realize that, if it is 



