IV.—PARTIAL ASSOCIATION. 51 
Male line. ~~ Female line. Mixed record. 
p RISIISWIRA Dirt 3d 25 percent. 1 per cent. 13 per cent. 
Parents with attribute and | 2% 17 
children without . a } ! = 
Parents without attribute | | 5 17 
and children with } f » B . . 
Parents without attribute 
and children without . 25 y Hl BS 
Here 13/30 =43 per cent. of the offspring of parents with the 
attribute possess the attribute themselves, but only 17/70 =24 
per cent. of the offspring of parents without the attribute. The 
association between attribute in parent and attribute in offspring 
is, however, due solely to the association of both with male sex. 
The student will see that if records for male-female and female- 
male lines were mixed, the illusory association would be negative, 
and that if all four lines were combined there would be no illusory 
association at all. 
8. Illusory associations may also arise in a different way 
through the personality of the observer or observers. If the 
observer’s attention fluctuates, he may be more likely to notice 
the presence of 4 when he notices the presence of B, and vice 
versa ; in such a case 4 and B (so far as the record goes) will both 
be associated with the observer's attention C, and consequently 
an illusory association will be created. Again, if the attributes 
are not well defined, one observer may be more generous than 
another in deciding when to record the presence of 4 and also 
the presence of 5, and even one observer may fluctuate in the 
generosity of his marking. In this case the recording of 4 and 
the recording of 2B will both be associated with the generosity 
of the observer in recording their presence, C, and an illusory 
association between 4 and 2 will consequently arise, as 
before. 
9. It is important to notice that, though we cannot actually 
determine the partial associations unless the third-order frequency 
(4BC) is given, we can make some conjecture as to their sign 
from the values of the second-order frequencies. 
Suppose, for instance, that— 
(dBc) = HOEY) 4 | 
(©) 16 =) 
(dy)(By) | 
ABy) = 3 
( y) (y) + 0g | 
(5