THEORY OF STATISTICS. 
The expression in the bracket is usually very nearly unity, for 
a normal distribution, and in that case may be neglected. 
Correlation coefficient.—If the distribution be normal, 
standard error of the cor- | Te 
relation coefficient for Se : (15) 
a normal distribution ad 
This is the value always given: the use of a more general formula 
which would entail the use of higher moments does not appear 
to have been attempted. As regards the case of small samples, 
cf. refs. 10, 28, and 31. Equation (15) gives the standard error 
of a coeflicient of any order, total or partial (ref. 33). For the 
standard error of the correlation-coefficient for a fourfold table 
(Chap. XI., § 10), see ref. 34: the formula (15) does not apply. 
Coefficient of regression.—If the distribution be normal, 
standard error of the co- EE 
efficient of regression 4, » =T2LN- "Tie T12_ (16) 
for a normal distribution 0) Jn 0, Nn 
This formula again applies to a regression coefficient of any order, 
total or partial: ¢.e. in terms of our general notation, £ denoting 
any collection of secondary subscripts other than 1 or 2, 
standard error of by, for | im 
a normal distribution | =o, A/n. 
Correlation ratio.—The general expression for the standard 
error of the correlation-ratio is a somewhat complex expression 
(¢f. Professor Pearson’s original memoir on the correlation-ratio, 
ref. 18, Chap. X.). In general, however, it may be taken as 
given sufficiently closely by the above expression for the standard 
error of the correlation coefficient, that is to say, 
standard error of correlation- | _ 1-7? (17) 
ratio approximately dey : 
As was pointed out in Chap. X,, § 21, the value of {=72—-1%is a 
test for linearity of regression. Very approximately (Blakeman, 
ref. 1), 
standard error of {= Wi JA -p2)2-(1-r22+1. (18) 
n 
For rough work the value of the second square root may be 
taken as nearly unity, and we have then the simple expression, 
standard error of { roughly = 2 a 19) 
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