XXVII XXX] IntrwhH'tn,,, 



not, however, -signify that there is no correlation b.-i \\.-.-n /,', md a,, lor the 

 standard deviation of R\ for a constant GI bring given by 



Vn <*' 



the scedastic curve is a rectangular hyperbola. This is well illustrated by taking 

 the regression of <r a on RI. The curve of frequency of a, for a given R t may be 

 written 



, , 



where a = 



The curve is therefore of the same nature as the distribution curve of any standard 

 deviation sampled from a normal population. Hence the mean value Hl a t and the 

 modal value Rl <r 2 arc given by 





(xxvl! 



The standard deviation R^^ is given by the equation 



p2 _ -*v- r, /!_r* v?A^_-). ...(xxviii). 



Thus the regression curves of either mode or mean, and the scedastic curve of oj 

 on RI are given by quartic curves, showing that the frequency surface of RI and cr t has 

 a zero correlation coefficient with heteroscedasticity both ways; while for regression 

 curves we have a horizontal line one way and a quartic curve the other. It is an 

 instructive example for the student to ponder upon, if he has been taught to think 

 solely of linear regression and homoscedasticity both ways, as in normal correlation 

 surfaces. 



9. Distribution for Samples of the Standard Deviations of Arrays. 



Let us take in the next place the standard deviation of an array in a sample of 

 size n; we will denote it by <r fll . Its value in the parent population is ^ l = -i v 1 p*. 

 We will use a fll for the mean value of <r fll in samples and ov ai for its standard 

 deviation. 



