ON THE DISTRIBUTION OF THE STANDARD DEVIATIONS 
OF SMALL SAMPLES: APPENDIX L TO PAPERS BY 
"STUDENT" AND R. A. FISHER. 
(EDITORIAL.) 
Consider the population distributed according to the law 
"-^.^ " 
and let a sample of n represented by the variate values x^, ... ir„ be taken from 
it. Then the probability BP that this sample will lie between 
and Xi + Bxi, and x^ + Bx2 ... Xn and Xn + Bxn 
is hP = , — e BxiSx„...Bxn 
(V27r)»o-» 
, S (a;.,j-x)2 _ n{x- 
m) 
= const, xe ' <^'^ ^ '^'^ Bx^Bx^-.-Bx^ (ii), 
where x=-S(xs). If — - S (Xs — xY we may write: 
n n 
BP = const. X e ^ '^^ '^^ l Bx^Bx^ ... Bxn (iii). 
Changing as Mr Fisher does (see p. 510 above) to x and ^ as coordinates 
we have : 
8P = const, xe ^ ^ ^-^-^BxBt. 
We see at once from this* that the law of distribution of samples of means is 
the normal curve 
^ n (5 - to)^ 
y^y^e ■ (iv) 
* Of course the form reached above shows that for normal distributions there is no correlation 
between deviations in the mean and in the standard deviation of samples, a familiar fact. 
