THEORY OF STATISTICS. 
(3) Yurz, G. U., “On the Methods of Measuring the Association between Two 
Attributes,” Jour. Roy. Siat. Soc., vol. 1xxv., 1912, pp. 579-642. (A 
critical survey of the various coefficients that have been suggested for 
measuring association and their properties: a modified form of the 
coefficient of § 13 given which possesses marked advantages.) 
(4) PEARSON, KARL, “On the Correlation of Characters not Quantitatively 
Measurable,” Phil. Trans. Roy. Soc., Series A, vol. cxev., 1900, p. 1. 
(Deals with the problem of measurement of intensity of association 
from the standpoint of the theory of variables, giving a method which 
has since been largely used : only the advanced student will be able to 
follow the work. For a criticism see ref. 3.) 
(5) PEARSON, Kary, and DAvip Heron, “On Theories of Association,” 
Biometrika, vol. ix., 1913, pp. 159-832. (A reply to criticisms in ref. 3.) 
(6) GREENWOOD, M., and G. U. YuLg, “The Statistics of Anti-typhoid and 
Anti-cholera Inoculations, and the interpretation of such statistics in 
general,” Proc. Roy. Soc. of Medicine, vol. viii., 1915, p. 118. (Cited 
for the discussion of association coefficients in § 4, and the conclusion 
that none of these coefficients are of much value for comparative pur- 
poses in interpreting statistics of the type considered.) 
(7) Lipps, G. F., “Die Bestimmung der Abhiingigkeit zwischen den Merkmalen 
eines Gegenstandes,” Berichte d. math. -phys. Klasse d. kgl. sdchsischen 
Gesellschaft d. Wissenschaften, Leipzig, Feb. 1905. (Deals with the 
general theory of the dependence between two characters, however 
classified ; the coefficient of association of § 13 is again suggested inde- 
pendently.) 
EXERCISES. 
1. At the census of England and Wales in 1901 there were (to the nearest 
1000) 15,729,000 males and 16,799,000 females; 3497 males were returned 
as deaf-mutes from childhood, and 3072 females. 
State proportions exhibiting the association between deaf-mutism from 
childhood and sex. How many of each sex for the same total number would 
have been deaf-mutes if there had been no association ? 
2. Show, as briefly as possible, whether 4 and B are independent, posi- 
tively associated, or negatively associated in each of the following cases :— 
(@) N =5000 (4) =2350 (B) =3100 (4B)=1600 
©) (4) = 490 (4B)= 294 («) = 570 (aB)= 380 
(c) (4B)= 256 (aB) = 768 (4B)= 48 (af) ="144 
3. (Figures derived from Darwin’s Cross- and Self-fertilisation of Plants, 
¢f. ref. 1, p. 294.) The table below gives the numbers of plants of certain 
species that were above or below us average height, stating separately those 
that were derived from cross-fertilised and from self-fertilised parentage 
Investigate the association between height and cross-fertilisation of parentage, 
and draw attention to any special points you notice. 
Parentage Cross-fer- Parentage Self-fer- 
tilised. Height— tilised. Height— 
Species. 3 
Above | Below Above | Below 
Average. Average. | Average. | Average. 
Ipomaa purpurea . . . 63 10 18 b5 
Petunia violacea . . 61 16 13 64 
Reseda lutea =. . . 25 7 11 21 
Reseda odorata  . . . . 39 | 16 25 30 
Lobelia fulgens . : . 17 17 12 22 
4.0