Volume IX 
MARCH, 1913 
NOS. 1 AND 2 
BIOMETBIKA. 
ON THE PEOBABLE ERRORS OF FREQUENCY 
CONSTANTS. 
PART II. 
EDITORIAL. 
(1) The probable errors of frequency constants for a single variable have been 
discussed in an elementary manner in Vol. II. pp. 273 — 281 of this Journal. The 
following notes on the probable errors of frequency constants of distributions with 
two variables have been provided at the request of certain of our readers*. 
All the constants of a frequency distribution of two variates are expressible in 
terms of the higher product moments defined by 
p q , g ' = S{n ss .x s «y s ,v'}/N (i), 
where the origin is at fixed values of x and y. Transferred to the mean x, y, we 
have : 
p 8 , i = S {ra ss . {at, - x)z (y, - y)*}/N (ii), 
where x and y will vary from sample to sample. Here n ss < is the frequency of 
individuals with characters x s and y S ' t and N is the total population. 
Throughout r a p will denote the correlation between two quantities a and /3 ; 
era, will denote the standard deviations of a and /3. 
The following results are well known : 
= «^(1--^J (iii), 
T n tv r n ss ,n tt , ~ N \ ly h 
Biometrika ix 
* Eeproduced from Lecture Notes. 
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