Karl Pearson and David Heron 
293 
These instances will suffice, and now let us sum them in a table with their 
probable errors. 
Index 
Number 
Values of q 
Probable 
Error 
Mr Yule's Judgment on the Table 
(i), q» 
(-0, q h 
(3) , q„ 
(*), qo 
(*), qn 
(5), q u 
(4) , q h 
(4) , qo 
(5) , qh 
0-317 
0-877 
2-809 
6- 714 
7- 840 
10-882 
33-528 
36-457 
36-570 
36-951 
+ 0-163 
+ 0-029 
+ 0-093 
+ 3-40 
+ 5-77 
+ 7-93 
+ 0-68 
+ 2-05 
+ 2-05 
+ 0-73 
" Distinct positive Association " 
" High degree of Association " 
" High degree of Association " 
" Distinct positive Association " 
" No Association " 
" No Association " 
" Very high indeed " 
" Shows the tendency to resemblance " 
" Shows the tendency to resemblance " 
" Very high indeed " 
Now Mr Yule has used the method of percentages in a curious manner; some- 
times he compares a/(a + c) with b/(b + d) but at other times with (a + b)jN; 
sometimes he uses the percentages found both ways, sometimes only found one 
way. He has throughout failed to give the probable errors of the differences 
of the percentages, which might have influenced his judgment, but he leaves his 
readers to believe that some inference as to the intensity of association can be 
founded merely upon such relative percentage differences. He indeed tells us (loc. 
cit. p. 651) to distinguish between the intensity of an association and the reliability 
of that intensity, so that we must presume that in speaking of the grade of the 
association, he does not form his judgment in relation to the probable error. 
Now in this table we find percentage differences of 7*8 and 109 belong to 
tables which in Mr Yule's judgment exhibit no association, but tables with 
differences of 0'3 have "distinct positive association" and of 0'8 have "high degree 
of association." One table with a difference of 36 merely shows the "tendency" 
to association; another with the same percentage difference has association "very 
high indeed." For any given table there are six ways in which the difference of 
percentages can be enumerated, namely 
a + c b + d' 
a 
a + c 
a + b 
a + c 
a+b c+d 
a + b N 
b+d 
c 
c + d 
a + b 
a + c 
Mr Yule sometimes uses one, sometimes another of these methods to reach 
his judgment of the degree of association in a table. He has given us his 
judgment with regard to the association of developmental defects and dullness 
for the partial universe of those without nerve signs (loc. cit. pp. 45 — 46), he says 
the association is " very high indeed." It may according to the percentage differ- 
ence chosen be either 2 - 92 or 36'96. He has further given us his judgment on the 
association of developmental defects and dullness for those with nerve signs, he 
