COEEELATION" AS APPLIED TO FARM-SURVEY DATA. 5 



is the standard deviation of the first variable; and Cy the standard 

 deviation of the second. The vakie of " r " will always be between 

 +1 and —1, +1 indicating perfect positive correlation, and —1 

 perfect negative correlation; and to be significant, the value should 

 be appreciably greater than its probable error. 



Er 



±■6745(1-7''') 



(11) 



In the example, r=-\-.277, and its probable error is ±.076, so there 

 was a tendency for the heavier calves to return a greater profit, but 

 the correlation is by no means perfect. 



PARTIAL CORRELATION. 



A study in which many factors are concerned is not complete 

 until it is determined whether or not an apparent correlation, meas- 

 ured in the manner explained above, is due to the fact that each 

 of the two variables (or factors) under consideration is correlated 

 with another or even several other variables. For instance, in the 

 data under consideration there is apparently a high correlation be- 

 tween the weight of the calves and the value per hundredweight 

 received for them (7'=-j-.56), and the question now arises if heavier 

 calves really do demand a higher price on the market. This corre- 

 lation might be due entirely or in part to the fact that the heavier 

 calves in the records obtained were sold at a later date, and that 

 the price of cattle in general was higher later in the season; that 

 is, the correlation exhibited here might be due to the fact that both 

 weight and price are correlated with date of sale. 



In a problem of this type, where it is necessary to consider simul- 

 taneously the relation between three variables and to determine the 

 correlation between any two, a coefficient of net or partial correlation^ 

 can be determined by the formula — 



Calling the three variables a, b, and c, the terms of the formula are : 

 Tab'c is the coefficient of net correlation between a and &, when the 

 effect of c is considered ; Tab is the ordinary coefficient of gross corre- 

 lation between a and b and is obtained as explained above ; Tac and r&c 

 are the coefficients of gross correlation between a and c and h and c, 

 respectively. Continuing with the example above, let us endeavor to 

 determine the degree of correlation between weight and value per 

 hundredweight, after taking into account any effect that date of sale 

 might have had. In other words, we seek an answer to the question : 



1 Yule, G. U. : " Introduction to the Theory of Statistics," p. 229 et seq. 



