Appendix E 419 



for number of pods. This product is always subtracted from the 



2P. 

 quotient of ' 



66.20 - (1.88 X - 1.56) = 69.1328. 



Now this corrected deviation must be secured in terms of the 

 standard deviations for each character, and hence this quantity 

 69.1328 is to be divided by the product of both standard devia- 

 tions : 



69:1328 



14.9789 X 12.0360 



. 3835. 



We have now finally arrived at our correlation coefficient, 

 designated universally by the letter r, the formula for the deter- 

 mination of which is as follows : 



Correlation Coefficient (r) = 



o- 2 



Like all other constants the correlation coefficient must be 

 accompanied by its probable error, the formula for the finding 

 of which is as follows : 



- 6745 (! - r2 



Solving this for our correlation coefficient, we find the prob- 

 able error to be .0257. 



The amount of confidence which can be placed in the corre- 

 lation coefficient depends upon the size of its probable error 

 largely. Biometricians say that in order to be of much value, 

 the coefficient must be from five to ten times as great as its 

 probable error. But whether the coefficient shows a high, low, 

 or intermediate degree of correlation between the two charac- 

 ters measured depends entirely upon its position with reference 

 to its two limits, and + 1 or and - 1. According to the 



