Editorial 
(14), (15) and (16) give the magnitudes to be compared with (5), (10), and (8) 
respectively when results obtained by mean and standard deviation methods are to 
be compared for accuracy with those obtained by grade methods. 
We may now consider what these results reduce to when the frequency follows 
the simple normal distribution. 
We shall suppose 
1 {Xg - J) 2 
^.-tJ^""'^ (in 
and write Jig = (wg — x)jcr and — \^ e ~ "^''s', 
v27r 
thus Us = NHgja, and H,, may be found directly from the Tables for Statisticians, 
when hg is known, and Jig will be known when j),, is known. Again, X^a = Xg — x, 
and therefore As = 
We obtain the following results : 
For (5) : 
For (14) 
For (10) : 
= I ^- ^ A - J. 1_ ^ ^ _ M _ 4 ^ ^1 _ ^i'^l' 
(20), 
For (15)*: 
'^x,-x,^^^~(h,-h,) ; (21). 
For r^j^^ fi'om (13) : 
'^1^2= / r— rr (^^)- 
N\ n) 
n) 
N 
For r^j^^ from (18): 
We may illustrate (23) first. 
* The reader must bear in mind that with the present notation h-^>hn and n^^n.^. 
t hi and h., may be of opposite sign. 
