An Introduction to the theory of statistics

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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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Document type:: Monograph

Structure type:: Chapter

Title:: Part I. The theory of atributes

Collection:: Economics Books

THEORY OF STATISTICS. If we use 4 to denote “heads” in the first toss, B “heads” in the second, we have from the above (4)=44, (B)=53. Hence (4)(B)|N = th 23-32, while actually (4B) is 26. Hence there is a positive association, in the given record, between the result of the first throw and the result of the second. But it is fairly certain, from the nature of the case, that such association cannot indicate any real connection between the results of the two throws; it must therefore be due merely to such a complex system of causes, impossible to analyse, as leads, for example, to differences between small samples drawn from the same material. The conclusion is confirmed by the fact that, of a number of such records, some give a positive association (like the above), but others a negative association. 8. An event due, like the above occurrence of positive associa- tion, to an extremely complex system of causes of the general nature of which we are aware, but of the detailed operation of which we are ignorant, is sometimes said to be due to chance, or better to the chances or fluctuations of sampling. A little consideration will suggest that such associations due to the fluctuations of sampling must be met with in all classes of statistics. To quote, for instance, from § 1, the two illustrations there given of independent attributes, we know that in any actual record we would not be likely to find exactly the same proportion of abnormally wet seasons in leap years as in ordinary years, nor exactly the same proportion of male births when the moon is waxing as when it is waning. But so long as the diver- gence from independence is not well marked we must regard such attributes as practically independent, or dependence as at least unproved. The discussion of the question, how great the divergence must be before we can consider it as ““ well marked,” must be postponed to the chapters dealing with the theory of sampling. At present the attention of the student can only be directed to the existence of the difficulty, and to the serious risk of interpreting a ‘chance association ” as physically significant. 9. The definition of § 5 suggests that we are to test the existence or the intensity of association between two attributes by a comparison of the actual value of (4B) with its independence- value (as it may be termed) (4)(B)/N. The procedure is from the theoretical standpoint perhaps the most natural, but it is more usual, and is simplest and best in practice, to compare proportions, e.g. the proportion of 4’s amongst the B’s with the proportion amongst the ’s. Such proportions are usually expressed in the form of percentages or proportions per thousand. 30

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