jan. 3,i 9 2i Correlation and Causation 581 



We now have eight equations from which to find eight unknown path 

 coefficients. 



(1) W = 0.28 = w + tc. 



( 2 ) *br — .48 — ts + bw + ah. 



(3) >'bt = .59 = t + dh + wc 



(4) ^= — .01 = 6. 



(5) %i = — .02 = c. 



(6) r RT = .47 = ^- 



(7) w 2 + h 2 + t 2 + 2wtc+2htd= 1. 



(8) 5.01 14 = 5.2204.24- 1.1 i6iw. 



Equations (4), (5), and (6) give b, c, and s directly. Solution of (1) and 

 (8) gives 2 = 0.8963, its— 0.2979. 



From (2) ah= 0.0617 



From (7) h 2 = .6570, fe= — 0.8105, a = — 0.0761 

 From (3) dh = — .3003, d= .3706 

 r BU = h + td= — 0.4784. 



The coefficients of determination, the path coefficients, and the corre- 

 lations are thus as follows : 



d B . T = 0.8034 ^ B " T = °-^9^3 rBT = °-59°° 



^b-h = -657° ^b-h= — -8105 r Bn = — .4784 



d B .^ = .0888 p B -w= -2979 *W= .2800 

 ^ B -ii= — .5384 



^B-^= — -OI07 *H E = — .O761 



I. OOOI 



r H T= .37°6 



r RT = .47OO. 



It turns out that the differences between different days in wet-bulb 

 depressions are due to a somewhat greater extent to differences in tem- 

 perature (0.80) than to absolute humidity (0.66). The variation in wet- 

 bulb depression would be much greater were it not that these factors 

 vary together but act on wet-bulb depression in opposite directions and 

 so tend to balance each other (d B .^=— 0.54). Temperature shows a 

 rather strong positive correlation with absolute humidity (0.37) as well 

 as with radiation (0.47), but the various paths of influence between 

 radiation and absolute humidity almost balance each other (r HE = — 0.08). 



These results can now be used in finding the relative importance of 

 the various factors which determine evaporation or transpiration. In 

 figure 16, X may represent either evaporation or the transpiration of 

 any plant. Radiation must be considered as a direct causal factor in 

 these cases. 



