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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HN THEORY OF STATISTICS. say, when we fulfil the conditions of simple sampling, is uniform over the whole range from 0 to 1. Thus for a rough grouping into four classes the above series of trials gave :— Number of Tables giving a Value of P lying between the Limits on the Left. Expected. Observed. 1:00-075 25 23 075-050 25 30 0°50-0°25 25 22 025-0 25 : 25 The value of x? for this comparison is 1:52, giving P=068, or we should expect a worse fit roughly twice in every three trials. COMPARISON FREQUENCIES BASED ON THE OBSERVATIONS. Contingency Tables.— Attention was specially directed above to the fact that the theoretical frequencies were assumed to be given a priori. The theory of the more general case, in which comparison is made with frequencies determined by the aid of the observations themselves, has only recently been fully worked out (Fisher, ref. 76). The most important practical case of the kind is that of association or contingency tables in which the observed frequenciescare compared with the independence-values obtained from the totals of rows and columns—that is, the values A4,.)(B (AmBp)y = AmB) of Chapter V. § 6, p. 64, and in which the differences Smn= (Am Br) i (Am Bn) are used as an indication of the divergence from independence. The rule to which the theory leads is a very simple one: the x? method is still applicable, but the tables must be entered with 2’ equal to the number of algebraically independent frequencies (or values of 8) increased by unity, and not with »’ equal to the number of compartments in the table. Now, if in any column of the contingency table we are given all the values of 6 but one— say, the marginal value at the bottom,—the remaining one can be determined. because the sum of the &'s for every column must be “78 p

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