Editorial 
, „ , ^ I 0^-40,- 3/9./ - 24^ + 1 2/ 3, + 96/3, - 6 ^ ^, 
""'"'^ vv^^-3 = rf ^I^TJ^^ — ^ (l^D), 
reducing with a Gaussian distribution to* 
12 
It will be observed that the approach to the normal curve is by no means close 
for fairly small samples. For example, if ilf = 24, we might easily have mB,' = "3 
and mB.J = 3"5. In other words the distribution of /x., in samples of size M is far 
from as close to a normal curve as the distribution of means /a/. 
We should anticipate accordingly that the distribution of the second moment- 
coefficient in the array of a sample JSf would be even further removed. 
We find by replacing l/il/*' by S (^^^ that 
dfi,y] 0,-1 \f^_l\ I (3,-3 
'l _ 1 1 3/3, - 5 \ 
nlj^V] _ (ft -If _ i 1 ft - 4ft - 6ft^ - 24/3;, + 30ft + 96^^ - 2 1 
Jij\~ Tip' \ N'^ Vp (ft-1)^ 
(EE) 
Hence 
lft-3ft -6ft+ 2r ._ 3 ^ 1/ 3 (ft - 3) ^ _ 8 (3ft- 5) 
' (ft-1? 1 ^ "iA ft-1 /3^_3ft-6ft + 2 
(FF). 
giving for a Gaussian distribution 
and . 5; - 3 = i ^^rA^.-24ft+6ft4-9Gft-3 _ 3 
^ " (ft-l)= ^ 
giving for a Gaussian distribution 
Thus for a small array of, say, 2-5 we might easily have upBi = '37 and 
npB-i' = 3"6, values very remote from a Gaussian distribution. 
It is clear therefore that the " probable error " of a second moment-coefficient 
has no very illuminating meaning in the case of the arrays of small or even 
moderate size- in the case of a sample of size JV. It may, however, be remarked 
that the distribution of /j., is one thing and that of cr„^ which is what we usually 
require is another. In order to obtain this we must raise the expression in (U) 
* See the second footnote on preceding page. 
