ITI.—ASSOCIATION. 7 
Datura (W. Bateson and Miss Saunders, Report to the Evolution 
Committee of the Royal Society, 1902) :— 
Flowers violet, fruits prickly (4.8) : dT 
ov yy, smooth (43) : 3 
Flowers white, ,, prickly (aB) . 2] 
. yy smooth (af) : £8 
Investigate the association between colour of flower and char- 
acter of fruit. 
Since 3 x 47=141, 12x 21=252, de. (4B) (aff)<(aB) (4B), 
there is clearly a negative association; 252 - 141=111, and at 
first sight this considerable difference is apt to suggest a consider- 
able association. But 6=111/83=1'3 only, so that in point of 
fact the association is small, so small that no stress can be laid 
on it as indicating anything but a fluctuation of sampling. 
Working out the percentages we have— 
Percentage of violet-flowered plants with 80 per ort, 
prickly fruits : 
Percentage of white-flowered plants with | 87 
prickly fruits . : : : 23 
13. While the methods used in the preceding pages suffice for 
nearly all practical purposes, it may be convenient to measure 
the intensities of association in different cases by means of some 
formula or “ coefficient,” so devised as to be zero when the attri- 
butes are independent, +1 when they are completely associated, 
and —1 when they are completely disassociated, in the sense of 
§ 6. If we use the term “complete association” in the wider 
sense there defined, we have, grouping the frequencies in fourfold 
tables, the three cases of complete association :— 
| 
(4 J @B)| 
(a? ® | (a8) | @ 
® | ® ® | (BB) |B) fv 
In the first case all 4’s are B, and so (4B8)=0; in the second 
all B’s are 4 and so (aB)=0; and in the third case we have (4)= 
5 
= (3)