CORRELATION 465 



formulas stated in the last chapter. For the probable error in 

 the correlation coefficient use the formula 



V;/ 



Use of correlation coefficient. The correlation coefficient is a 

 good index of the mutual relation that exists between the char- 

 acters in question. If it is low, it indicates that they do not 

 depend very much upon each other; if it is high, it indicates 

 that they are in some 'way closely related ; and if it rises to 

 unity, this relation amounts to causation, that is, one is the 

 cause of the other, or else they are the joint effect of the same 

 causes. The practical advantage of this knowledge for purposes of 

 selection is obvious, especially when one character is easily seen 

 and readily examined and the other is not. An application of the 

 correlation table would correct many popular delusions on this 

 subject, as, for example, the selection of cows by the escutcheon. 



Shorter method for calculating r, the coefficient of correlation. 

 There is derived in the Appendix a formula which gives 



the same numerical value for r as - already used ; and 



n <T L <T W 



while its algebraic expression is a little more complicated, it is 

 much better adapted to numerical calculation, as it avoids the 

 use of decimals until almost the end of the work. In this respect 

 it is similar to the shorter method presented for calculating the 

 standard deviation. If applied to the case of the length and 

 weight of ears of corn the formula is 



/V r r \_L_ 



n C/ - ">,*,, 



where )/, D n l are deviations from our guess at the means instead 

 of deviations from the mean itself as D L and D w \ and C L and C, r 

 are the corrections applied to the guesses at the mean length 

 and weight respectively as used in the shorter method of finding 

 standard deviation. 



In other words, we find the standard deviation by the shorter 

 method explained on page 429. Then, in forming the sum of 

 products of deviations, we measure the deviations from the 

 guess instead of measuring them from the means, and divide as 



