CHAPTER IIL 
ASSOCIATION. 
1-4. The criterion of independence.—5-10. The conception of association and 
testing for the same by the comparison of percentages—11-12. 
Numerical equality of the differences between the four second-order 
frequencies and their independence values—13. Coefficients of associa- 
tion—14. Necessity for an investigation into the causation of an 
attribute 4 being extended to include non-4’s. 
I. Ir there is no sort of relationship, of any kind, between two 
attributes 4 and B, we expect to find the same proportion of 4’s 
amongst the B’s as amongst the non-A’s. We may anticipate, 
for instance, the same proportion of abnormally wet seasons in 
leap years as in ordinary years, the same proportion of male to 
total births when the moon is waxing as when it is waning, the 
same proportion of heads whether a coin be tossed with the right 
hand or the left. 
Two such unrelated attributes may be termed independent, and 
we have accordingly as the criterion of independence for 4 and B— 
(4B) _ (46) Cw 
(B)  (B) 
If this relation hold good, the corresponding relations 
(a5) (a5) 
8B) (B) 
(4B) _(aB) 
4) (a) 
(4B) _(aB) 
(4) (a)° 
must also hold. Tor it follows at once from (1) that— 
(Br-(45) _(B) (Af) 
F2) = CON TY 
! (B) 
Fh