171 
On Theories of Association 
entirety to the 2 x 2-fold table " is wholly inconsistent with any validity in the 
coefficient of association. 
It is not only that we can give a vast range of values to for a constant Q, but 
equally we can give Q a whole range of values, starting at the symmetrical table 
value and proceeding up to unity for a constant </>. Examine for example the 
following series of fourfold tables. The first is the table as it actually occurred 
with Q = - 5078, the second is Mr Yule's "equivalent" symmetrical table with of 
course the same Q. 
(1) 
29600 
17300 
46900 
37200 
66600 
103800 
66800 
83900 
150700 
(2) 
47952 
27398 
75350 
27398 
47952 
75350 
75350 
75350 
150700 
Q = -5078, <£ = -2542. Q = '5078, <£ = -2728. 
We now proceed to adjust the latter table so that <j> remains stationary and 
Q rises. 
(3) 45452 
47103 
92555 
(4) 
43052 
56385 
99437 
12693 
45452 
58145 
8211 
43052 
51263 
58145 
92555 
150700 
51263 
99437 
150700 
Q=o511, <£ = -2728. 
(5) 
39852 
66467 
106319 
(6) 
37952 
71808 
109760 
4529 
39852 
44381 
2988 
37952 
40940 
44381 
106319 
150700 
40940 
109760 
150700 
Q 
= ■681! 
I 0 = 
2728. 
Q = -7407, </> = 
•2728. 
(7) 
35852 
77349 
113201 
(8) 
33552 
83090 
116642 
1647 
35852 
37499 
506 
33552 
34058 
37499 
113201 
150700 
34058 
116642 
150700 
Q 
- -8191 
3, <£ = 
2728. 
Q = -9288, <f> = 
•2728. 
(9) 
32952 
84541 
117493 
(10) 
32552 
85499 
118051 
255 
32952 
33207 
97 
32552 
32649 
33207 
117493 
150700 
32649 
118051 
150700 
Q 
= 9611, 0 = 
2728. 
Q = -984 
5, cf) = 
•2728. 
(11) 
32352 
85974 
118326 
(12) 
32327 
86035 
118362 
22 
32352 
32374 
11 
32327 
32338 
32374 
118326 
150700 
32338 
118362 
150700 
Q 
= •996^ 
K </> = ' 
2728. 
Q = -998: 
>, cf> = 
2728. 
(13) 
32302 
86095 
118397 
(14) 
32298 
86104 
118402 
1 
32302 
32303 
0 
32298 
32298 
32303 
118397 
150700 
32298 
118402 
150700 
Q = -9998, </> = -2728. 
Q= 10000, 0 = -2728. 
