An Introduction to the theory of statistics

Bibliographic data

Monograph

Identifikator:: 1751730271

URN:: urn:nbn:de:zbw-retromon-127610

Document type:: Monograph

Author:: Yule, George Udny http://d-nb.info/gnd/12910504X

Title:: An Introduction to the theory of statistics

Edition:: 8. ed. rev

Place of publication:: London

Publisher:: Griffin

Year of publication:: 1927

Scope:: XV, 422 S; Ill., Diagr

Digitisation:: 2021

Collection:: Economics Books

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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

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