cliv Tables for Statisticians and Biometricians [XX VII XXXIV 



/ 2 d- 2 Y\ 



3(7i-3)| n n\ n) , .... 



Hence &=- =-*\l r* / ( xln )- 



n 5 > <f> I 



It is accordingly possible to fit a Type VII curve 



= 

 ~ 



to the frequency of y x which will have the same first four moments as that frequency. 

 But as a rule '2/n will be small as compared to $ 2 , in which case the appropriate 

 Type VII curve reduces to 



2 

 where the term - may be neglected. Such a curve approximately represents the 



distribution of y x found in samples, i.e. the mean of the array of y's for a given x 

 in samples determined in each case by the regression line of the sample. y x is 

 the deviation of y x from its mean as given by the regression line of the parent 

 population, i.e. 



yx=yx-m z -p^(x-m l ) (xliv). 



i 



We may note that the correlation of R z and y x is given by 



x mi 



/I 



V J 



This is independent of p, the parental population correlation, and is a function of the 

 distance from the mode of the parent population at which we require y x . 



TABLES XXXII XXXIV. 



Tables for determining the Distribution of the Correlation Coefficient in small 

 Samples drawn from a Population assumed to be normal or approximately normal. 

 (Biometrika, Vol. XL pp. 328413.) 



9 



"Small" samples are usually taken to be those of which the number n is less 

 than 50, but up to w = 100 some results for "large" samples i.e. those in which 

 statistical differentials have been treated as mathematical differentials have only 

 rough approximation. This is peculiarly the case with the distribution of the corre- 

 lation coefficient. For n = 100, and even for n 400, the mean correlation coefficient 

 in samples is appreciably less than the correlation coefficient in the parent popu- 

 lation, while the /3i and /3 2 of the distributions show sensible deviations from 

 normality when the correlation is '6 or higher. 



