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 con-
fidence 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 inde-
pendent 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
