IV.—PARTIAL ASSOCIATION, 
4 light-eye colour in husband, B in wife, C in son— 
N 1000 (4B) 358 
(4) 622 (40) 471 
(B) 558 (BC) 419 
(0) 617 
7. Show that if (4BC)=(aBy), (aBC)=(4Bv), and so on (the case of 
“complete equality of contrary frequencies” of Question 7, Chap. L), 4, B, 
and C are completely independent if 4 and 2, 4 and C, B and C are inde- 
pendent pair and pair. 
8. If, in the same case of complete equality of contraries, 
(4B)-N[4=38, 
(4C) - N/4=35, 
(BC) -N/1=38; 
show that 
(40) BC) (AY)(By) |_s _ 48:3; 
2 (4 BOY — —f l= - =O = 
so that the partial associations between 4 and 5 in the universes C and + are 
positive or negative according as 
43,8 
52 -~ 
9. In the simple contests of a general election (contests in which one 
Conservative opposed one Liberal and there were no other candidates) 66 per 
cent. of the winning candidates (according to the returns) spent more money 
than their opponents. Given that 63 per cent. of the winners were Con- 
servatives, and that the Conservative expenditure exceeded the Liberal in 80 
per cent. of the contests, find the percentages of elections won by Conservatives 
(1) when they spent more and (2) when they spent less than their opponents, 
and hence say whether you consider the above figures evidence of the influence 
of expenditure on election results or no. (Note that if the one candidate in a 
contest be a Conservative-winner-who spends more than his opponent—the 
other must necessarily be a Liberal-loser-who spends less — and so forth. 
Hence the case is one of complete equality of contraries.) 
10. Given that (4)/N=(B)/N=(C)/N==, and that (4B)/N=(4C)/N=y, 
find the major and minor limits to y that enable one to infer positive associa- 
tion between B and C, 7.e. (BC)/N>z?2. 
Draw a diagram on squared paper to illustrate your answer, taking 2 and y 
as co-ordinates, and shading the limits within which # must lie in order to 
perwit of the above inference. Point out the peculiarities in the case of in- 
ferring a positive association from two negative associations. 
11. Discuss similarly the more complex case (4)/N=z, (B)/N=2z, (C)/N= 
3x: — 
(1) for inferring positive association between B and C given (4B)/N= 
(4C)/N=y. 
(2) for inferring positive association between 4 and C given (4B)/N= 
(BC)/N=y. 
(8) for inferring positive association between 4 and B given (4C)/N= 
(BC)/N=y. 
59