74 The Opsonic Index — A Medico-Statistical Enquiry 
Limits 
Normal Sera 
Test Sera 
•83 to -89 
oy to yo 
•95 to l^Ol 
l^Ol to 1-07 
1-07 to 1-13 
1-13 to 1-19 
2-95 7„ 
22-95 7° 
31-64 °f 
22-46 "U 
8-69 7, 
13- 0 
14- 8 7„ 
15- 8 7„ 
13-5 7„ 
9-4 7, 
Totals 
96-56 7„ 
74-0 7„ 
But the best comparison between the distributions is only made after the 
roughnesses associated with each individual observation are allowed for, that is to 
say, after we have determined the smooth curve Avhich shall represent the distri- 
butions with a minimum of error. 
Let I denote the normal serum distribution and II the test serum distribution; 
then the following are the equations and constants of the curves corresponding to 
them. Both curves come under the head of Pearson's Type IV, namely 
y = y^ 
I. y^m-i\ 
Standard Deviation 
1 + 
\ - 10-5796 ^ 
(5 -495077 
1-80, Mean = 1-0039, 
Mode = 1-0080. 
II 
y- 
131-71 1 
(7-9997)V 
Standard Deviation = 2-93, Mean = 1-0048, 
Mode = 0-9878. 
Curve I is represented by 610 observations while Curve II is based on 1000 ; 
therefore in order to compare them we must proportionately magnify the first to 
give an equal area with the second. Better still we may reduce Curve I so that 
the highest point upon it shall just touch the point corresponding to it in Curve II. 
The reduction is shown in Fig. 2. Then the area of Curve I as shown now in this 
reduced form will represent the degree of occurrence of as many indices out of the 
test sera indices as can possibly be considered normal, i.e. this area within the 
larger area I'epresents the maximum computation of normal serum indices. The 
method of reduction adopted gives a somewhat undue preponderance to the 
normals over and above that already given. We must keep this point in mind in 
drawing any deductions from the curves. It is taken for granted here that the 
curve of normal sera indices represents a true random sample. 
We may now examine our curves more particularly. Take the index 0'92 
as shown on the base line belonging to the two curves of Fig. 2 and we observe 
that the ordinate corresponding to this point would be nearly bisected by the 
