298 
Ori the Probable Error of Biserial -q 
The functions ^sj' = ''^^ ( ^ 
^^■ 
= i(l 
where x, | (1 + a) and z are the values given in the tables of the probability 
function, have been calculated by my colleagues Miss Ethel M. Elderton and 
Miss B. M. Cave in the table given on p. 302 below. The labour was considerable 
as owing to the smallness of z for high values of x, the quantities involved 
had to be calculated to many places of decimals, 
put (xix) in the form : 
If this table be used we can 
N [l + y'f 
1 2 I 
N 
1_ (Y 
2 ) ]\[2, 
.2^ Y 
S 
XX . 
I propose to illustrate this on the following example correlating nature of 
vaccination and severity of attack in the case of smallpox. 
Severity of Attach. 
Nature of 
Vaccination 
(1) 
Haemoirliagic 
(2) 
Confluent 
(3) 
Abundant 
(4) 
Sparse 
(5) 
Very sparse 
Totals 
0 to 25 yrs. since 
5 
38 
120 
176 
148 
487 
Over 25 yrs. or 
44 
251 
388 
308 
211 
1202 
not at all 
Totals 
49 
289 
508 
484 
359 
1689 
Positions of 
means 
= + 1-2700 
•<Vo-2 = 72 
= + M194 
•'Vo-3 = 73 
= + ^7185 
■'^'Jo-i = 74 
= + ^3488 
■*'Jo-5 = 75 
= -2218 
■'7o"x = 7 
- -5583 
Ordinates at 
3i = -17810 
z^ = -21321 
Zs = •30818 
z^ = ^37540 
35 = -38925 
z = ^34137 
dichotomic line 
-10204 
-13149 
•23622 
•36364 
-41226 
^ = ^28834 
N 
njn. 
-89796 
•86851 
•76378 
•63636 
•58774 
= -71166 
N 
nJN 
-02901 
•17111 
•30077 
•28656 
•21255 
Sum = 1^00000 
nJN 
ys' 
-00296 
•02250 
•07105 
•10420 
•08763 
Sum = •28834=ri/iV 
1-61290 
r25306 
•51624 
•12166 
•04920 
y2= -31170 
7-13083 
5^25022 
233143 
•92914 
•56981 
y/z = 1-63547 
50-84867 
27^56489 
5^43556 
•86331 
•32469 
{y/zf = 2-67476 
thy i- IN 
n,y//N 
•04679 
•21441 
•1.5527 
•03486 
•01046 
k2= -46179 
-07.547 
•26867 
•06812 
•00424 
•00051 
7* = -09716 
nuys"/N 
-00477 
•02819 
•03668 
•01268 
•00431 
Sum = -08663 
w, N Zg 
•018955 
•102594 
' ^126515 
•061613 
-029346 
Sum = -339023 
n, 77, N \zj 
-135162 
•538639 
•294961 
•057247 
-016722 
Sum = 1-042731 
