Editorial 
3 
Next we want a^o-^r^, but this is known, or easily found to be p n /N. 
Returning to (x), squaring, summing for every possible sample and dividing by 
the number of samples, we have 
- 2qp q +l,q'Pq-l,q> ~ fy[Pq,4+lPq,t-* •••( xii )- 
We may now find the correlation between any pair of higher moment 
coefficients, 
W$pu,u- = 8 [8n S!f (x s - x) w (yj - Tj) w '} - n8xp u - ltU > - u'hyp u ,te-i ■ • .(xiii). 
Multiplying (x) and (xiii) together, summing for all possible samples and 
dividing by the number of samples and N, we have 
N tr PQ, i ' <J 'Pu, n ' r Pg,q'Pu, «' = ^9+".9'+«' ~ P'h'/P^ + qUpWpq-^q-pU-^vi + ?'4o,2ft^-l^,tf-l 
+ <l u 'PhlPq-hQ , Pu,u>-i + qup^pq^'-ipu-^u' 
MPq+iiQ'P"— i,' 4 ' u P'h f /+iP u , «'— i 
- qpu+^u'pq-l.q 1 - q'p u ,i,,'^lPq,</-i (xiv). 
(xii) and (xiv) contain all the requisite data for the probable errors of random 
sampling in the case of two variables. They, of course, contain implicitly the case 
of one variable, as we have only to put q and u zero in order to fall back upon the 
formulae (vii) and (viii) of the first part of this paper (Biometrika, Vol. II. 
pp. 276—7). 
(8) We may illustrate as follows : 
(a) Correlation of errors in means : 
r xy = r xy (xv). 
(/3) Correlation of errors in standard deviations* : 
.P22-pooP n -2 
_ lh* P>n Pn-2 
.(xvi). 
<r ' f(T '" ^ Pio - p\o V p oi - p\ 2 
This is the general value of the correlation between the standard deviations of two 
correlated variables. We may write it in the form 
r = PkKPzoPoz)-! 
V(ft-i)(&'-T) 
where /8 2 and /3. 2 ' are the second /3's for the two variables respectively 
We may now investigate p 22 , 
p-22 = ^-S [(a, - xf (y, - yf n^}, 
* We may safely write j>22 for p 2i 2 etc. when we leave the general formulae, but p, m '-\ for 2> ?>9 '_j is 
capable of misinterpretation. 
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