380) 
THEORY OF STATISTICS. 
4295/7350 0, 5°33 
3844/633 . .  . 6°07 
9/583 02 
1225/653 ! T:83 
4356/527 . 827 
961/486 ea 1:98 
900/570 . 158 
16/460 yy. 03 
1156/423 273 
Total x2 27°94 
n' 5 
iP 000012 
The results are shown in the preceding table, the upper figure in 
each compartment of the table being the observed frequency of 
the corresponding pair of names. Below the observed frequency 
are given the independence frequency (4,,B,), and the difference 
dmn. It will be seen that the observed figures are not very close 
to the independence-values, there being apparently a marked 
tendency to give the same names to the two tints on any card, so 
that all the diagonal frequencies are in excess of the independence- 
values and all the others in defect. 
Working out x2 as shown, the total comes to 27-94, or practically 
28. Since r and ¢ are both 3, #»’ must be taken as (2 x 2) +1— 
that is, 5. Turning up the tables in the column »’=>5, we find 
P=-000012—that is to say, we would only expect to find so great 
a divergence from independence, in random sampling, a little 
more than once in 100,000 trials, so the result is certainly 
significant. 
Association Tables.— When we are dealing with an association 
table there are only two rows and two columns, and consequently 
n’ must be taken as (2—1)(2—1)+ 1—that is, 2. But no column 
for n’ = 2 is given in Tables for Statisticians and Biometricians, the 
lowest value taken being n’= 3, and a supplementary table (XV. c) 
is not sufficiently detailed: the necessary table, reprinted by 
permission from the Journal of the Royal Statistical Society 
(ref. 77), will be found at the end of this Supplement. As will 
be seen from the following illustrations, the required probability 
can also be determined from the table of areas of the normal 
curve, but it is very convenient to keep the arithmetic in the 
usual form. 
Example i.— (Data from Chapter III, p. 37.) The following 
data are there cited for colour of flower and prickliness of fruit in 
Datura: the independence-frequencies have been entered below 
the numbers of observations.