THE CORRELATIONS OF AREAS OF MATURED CROP AND THE RAINFALL. 377 

 Thus 



This gives the relative standard deviations of the array of the old and new 

 systems in terms of each other. 



To find the new standard deviations of the whole distribution 



w= i * 3 



= 5 \ N m (y^+eyji+tf (yV+V)) I 



m = i v 3 



m= I * 3 





thus we have r' = 



which is the same result as before for the case r = i . 



r 



We may write it r = 



%/!+**(!+>•) 



y ioo 

 where *■ = — = — , where v is the coefficient of variation of the whole group of y 



characters. 



Again since r'a-/ =r<* y and v x is unaltered, the regression coefficient of v on x is 

 unaltered, and consequently so far as errors of this type are concerned the regression 

 equation of y on x is unaffected. But the regression coefficient of x on y is now 



V i_ mi+"*(i+ t *)) 



and the regression coefficient of x on y is increased by the factor i +&* i+ T *) 



To express the value of the true coefficient of correlation in terms of the erro- 

 neously estimated values of r' and «y , we have 



y=y / {i+£ a (i + T *)} 1 / 2 



__ t f f(i+£*(i+r*)) 



]\lOW T a = ^-=i-l _ LL 



