SUPPLEMENTS—GOODNESS OF FIT. ;
The ratio of the difference to its standard error is therefore
‘01853/-01025, or 1-808.
Greater fraction of normal curve for a deviation of 1-808 is 96470
Fraction in tail , . . "03530
Fraction in the two tails . 07060
As before, both methods must lead to the same result.
An Aggregate of Tables.—It may often happen that we have
formed a number of contingency or association tables—more
often the latter than the former—for similar data from different
fields. All may give, perhaps, a positive association, but the
values of P may run so high that we do not feel any great confidence
 even in the aggregate result. The question then arises
whether we cannot obtain a single value of P for the aggregate as
a whole, telling us what is the probability of getting by mere
random sampling a series of divergences from independence as
great as or greater than those observed. The question is usually
answered by pooling the tables; but, in view of the fallacies that
may be introduced by pooling (¢f. Chapter IV. §§ 6 and 7), this
method is not quite satisfactory. A better answer is given by the
application of the present general rule. Add up all the values of
x* for the different tables, thus obtaining the value of x for the
aggregate, and enter the P-tables with a value of #’ equal to the
total of algebraically independent frequencies increased by unity :
that is, take n” as given by
n'=1+3(r-1)(c-1).
For the association table there 1s only one algebraically independent
 value of 8. Hence if we are testing the divergence from
independence of an aggregate of association tables, we must add
together the values of x2 and enter the P-tables with #’ taken as
one more than the number of tables in the aggregate.
Thus from ref. 6 of Chapter IIL, from which the data of
Example ii. were cited, we take the following values of x? and of
P for six tables that include that example. They refer to six
different estates in the same group.
P
3 4 0022
6-08 014
251 11
3-27 071
561 018
1-59 21
Total 28°40

382