IIL.—ASSOCIATION, 41 
4. (Figures from same source as Example vii. p. 33, but material differently 
grouped ; classes 7 and 8 of the memoir treated as *° dark.”) Investigate the 
association between darkness of eye-colour in father and son from the following 
data: — 
Fathers with dark eyes and sons with dark eyes (4B). 50 
ry > 5 not-dark eyes (48). 79 
Fathers with not-dark eyes and sons with dark eyes (eB) . 89 
" » 32 not-dark eyes (af) . 782 
Also tabulate for comparison the frequencies that would have been observed 
had there been no heredity, 7.e. the values of (4B)y, (AB), ete. (811). 
5. (Figures from same source as above.) Investigate the association between 
eye colour of husband and eye colour of wife (‘‘assortative mating”) from 
the data given below. 
Husbands with light eyes and wives with light eyes (4B). 309 
3 . ’ not-light eyes (48). 214 
Husbands with not-light eyes and wives with light eyes (aB). 132 
2 ”, » not-light eyes (a8) . 119 
Also tabulate for comparison the frequencies that would have been observed 
had there been strict independence between eye colour of husband and eye 
colour of wife, 7.e. the values of (4B),, ete., as in question 4. 
6. (Figures from the Census of England and Wales, 1891, vol. iii. : the data 
cannot be regarded as trustworthy.) The figures given below show the 
number of males in successive age groups, together with the number of the 
blind (4), of the mentally-deranged (5), and the blind mentally-deranged 
(AB). Trace the association between blindness and mental derangement 
from childhood to old age, tabulating the proportions of insane amongst the 
whole population and amongst the blind, and also the association coefficient 
Q of § 13. Give a short verbal statement of your results. 
CT ee ea 
N 3,304,230 2,712,521 2,089,010 1,611,077 1,191,789 770,124 444,896 161,692 
(A) 844 1,184 1,165 1,501 1752 1,905 1,932; 1701 
| (2) 2,820 6,225 8,482 9,214 8,187 | 5,799 3,412 1,008 
(4B) 17 | 1 19 | 81 | 32 34 22 9 
7. Show that if 
(4B), (aB), (4B), (aB) 
(4B); (aB); (4B); (aB), 
be two aggregates corresponding to the same values of (4), (B), (a), and (8), 
(4B), -(4B),= (aB), — (aB), =(4B)y- (4B) = (aB), — (aB)a 
8. Show that if 
3=(4B)- (4B), 
(4B)+ (eB) ~ (aB) - (4B8)2=[(d) - (a)][(B) - (8)] + 2IV. 5. 
9. The existence of association may be tested either by comparison of pro- 
portions (e.g. (4B)/(B) with (4B)/(B)), as in §§ 9, 10, or by the value of 3, us 
in §§ 11, 12. Show that 
s=2NB (4D) (5) 
NU 
=a) (45) el 
(Fy Lid) {a}