.\\VII-X\\ 



I ittrntlttrlnni 



Wo shall .suppose m lt w,, S 1( 2,, p to bo tho IM.-.UIS, st;iinl;inl deviation* 

 coefficient of convl;it,ion of tho two variatus in tin: p.m-nl population; x, y, tr lt 

 r-q, to be the corresponding <ju<iiitii random sample of *\. 



Then the distribution curves are for N samples as follows: 

 For the distribution of x : 



For the distribution of 



For the distribution of ^2,0 = 



The constants of equations (ii) and (iii) are discussed in another section (pp. ciii 

 civ). Equation (i) is a normal curve and needs no discussion. The consideration of 

 the distribution of correlation coefficients, r^, is also dealt with in another section 

 (pp.cxlvii cxlviii). a; and y have a correlation p with each other but are not correlated 

 with 0-j, er a or r^. The correlation surface of a; and y is normal and of the form 



Nn 



_ e 



o 



~ 2,* 



this equation requires only the theory of the normal surface for its discussion. 



2. Correlation Surface of Standard Deviations. 



If we write si S t Vl p 2 /V/i, 2 = S 2 Vl p 2 /*/n, the correlation surface for 

 <r% is given by 





-2) 





If we write 



n - 2) (2/i + 2) . . . (2n + 4jo - 6) 



+ " (v). 



72 2 (2w-2)(2n-f-2) 



+ " 



pl (2n - 2) (2ri + 2) ... (2 + 4p-6) 



* The notation bero is not the same as that used on p. ciii. 







B. IL 



