Jan. 3,i92i Correlation and Causation 577 



INDIRECT METHOD 



Six equations can be formed, expressing the six known correlations in 

 terms of the unknown path coefficients. A seventh equation represents 

 the complete determination of B by W, R, T, and O. 



(i) r B w = o.2& = w + t(c+bs) + ub. 



(2) ?-br= .4& = wb + ts + u. 



(3) rm= .59 = w(c + bs) + t + us. 



(4) r WR =- .01 = 6. 



(5) Twt= — .02 = c+bs. 



(6) r RT = 47 = s. 



(7) o 2 + w 2 + f + u 2 + 2wt(c + bs) + 2wub + 2Uts = I . 



The values of b and s are given directly from equations (4) and (6) , 

 and the value of c (=—0.0153) can then be obtained from (5). The 

 solution of (1), (2), and (3) gives w = 0.2921, t = 0.4735, and 14 = 0.2604. 

 Finally, from (7) we obtain o 2 = 0.5138 as the degree of determination by 

 outst anding factors. 



= 0.5138 



p B . Vf =W =0.2921 

 p B . T =t = .4735 

 p B . R = u = .2604 



1. 0000 



DIRECT METHODS 



According to the formulae given in part I we have 



${BWRT) 



d R . = 



d n .p = 



(J>(WRT) 



4>{BRT)-d B .MRT) 



4>{WRT) 

 4>(BWT)-d B . cj>(WT) 



4>{WRT) 

 cj>(BRW)-d B . ct>(RW) 



where 



B ' T 4>{WRT) 



4>{BWRT) = 1 - r 2 BW + 2r BVf r WR r RB - 2r Byf r yfR r KT r T B + r 2 BW r 2 R T 



— r2 BR+ 2r Bw r W T^TB— 2r B wTwT»'TRJ' E B'+y 2 BR^ 2 WT 



— r 2 BT + 2r BR r UT r T B— 2r BR r RW r vrT rT:B+r 2 BTr 2 vrR 



— r 2 WR + 2r yrR r RT r TW 



— r^wT 



— r 2 RT 



<t>(WRT) = 1 — r 2 WR — r 2 wT — ^rt + 2r W B.rHTr T w 



<j>(BWR), etc., are analogous to 4>{WRT) 



<t>(RT) -i-f 8 ,, 4>(WT), etc., are analogous to 4>(RT). 



