Jan. 3, 1921 



Correlation and Causation 



579 



the degree of direct determination by radiation, but determination by 

 some factor other than wind or temperature with which radiation is 

 correlated. 



One should not attempt to apply in general a causal interpretation to 

 solutions by the direct methods. In these cases, determination can usu- 

 ally be used only in the sense in which it can be said that knowledge of 

 the effect determines the probable value of the cause. This is the sense 

 in which Pearson's formula for multiple regression must be interpreted. 

 If W, T', and R' are given deviations of wind, temperature, and radiation 

 from their mean values, the most probable value of the wet-bulb depres- 

 sion, B', is given by the following formula: 



B' W . R' T 



This formula can only be used for conditions which are similar to those 

 for which the values of the path coefficients were calculated. If path 

 coefficients were calculated in a sys- 

 tem which truly represented the 

 causal relations, the formula would 

 give the value of the wet-bulb de- 

 pression under any set of conditions 

 in so far as it is determined by the 

 factors considered. 



The causal factors which actually 

 determine wet-bulb depression are 

 temperature, absolute humidity (H), 

 and wind velocity (fig. 15). Radia- 

 tion can be introduced into the scheme 

 as a factor correlated with these causal factors. Wind velocity is cor- 

 related to such a very slight extent with temperature and radiation that 

 its correlation with absolute humidity can probably be neglected without 

 serious error. The relations between radiation, temperature, and abso- 

 lute humidity are undoubtedly very complex. Radiation has a direct 

 positive influence on temperature. Both radiation and temperature have 

 positive effects on absolute humidity by increasing evaporation. Cor- 

 relation between absolute humidity and temperature would be expected, 

 because with reduced temperature the saturation point is reached at a 

 lower absolute humidity and the excess moisture is precipitated. In- 

 crease in humidity, on the other hand, tends to reduce the radiation 

 which reaches the earth, and directly or indirectly this has a negative 

 influence on all three of the correlations. 



There are not enough data to estimate the importance of all of these 

 paths of influence. Even if we represent the complex of paths connecting 

 H, R, and T merely by three correlations, the diagram has eight paths to 

 solve. The six correlations between B, W , R, and T and the statement 



FlG. 13. — Relations between factors of figure 14 

 and absolute humidity (II) expressing causal 

 relations better than figure 14 but adapted only 

 to indirect analysis. 



