THEORY OF STATISTICS. 
AX to the sum S. The total value of S is accordingly ¢V, and the 
value of C— 
t—1 
o=y/ So 
This is the greatest possible value of C' for a symmetrical ¢ x z-fold 
classification, and therefore, in such a table, for— 
- 7 “7 cannot exceed 0-707 
: 316 
: +366 
. 0894 
0913 
1-926 
D035 
2943 
t= 10 »y 0949 
It is as well, therefore, to restrict the use of the “coefficient of 
contingency ” to 5 x 5-fold or finer classifications. At the same 
time the classification must not be made too fine, or else the value 
of the coefficient is largely affected by casual irregularities of no 
physical significance in the class-frequencies (cf. the remarks: in 
Chap. III. §§ 7-8). 
TasLE III. —Independence- Values of the Frequencies for Table IT. 
Eye-colour. Fair. | Brown. Black. | Red. 
Blue. | 2a or a SL TOM 1028 506 | 48°0 
Grey or Green . ; . . - IR1303 | 1212 | 563 534 
Brown . 2 v : I. 357 332 154 | 14+6 
8. As the classification of Table II. is only 3 x 4-fold, it is rather 
crude for the purpose of calculating the coefficient, but will serve 
simply as an illustration of the form of the arithmetic. In Table 
ITI. are given the values of the independence frequencies, 2829 x 
2811/6800=1169 and so on. The value of x2 is more readily 
calculated from equation (5) than from (3) :— 
66