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 III. Theory of sampling

Collection:: Economics Books

XIIL.—SIMPLE SAMPLING OF ATTRIBUTES. 245] would not apply if the samples were compounded by always taking one person from district 4, another from district B, and so on, these districts not being similar as regards the distribution of hair-colour. The above conditions were only tacitly assumed in our previous work, and consequently it has been necessary to emphasise them specially. The third condition was explicitly stated: (c) The individual *‘events,” or appearances of the character observed, must be completely independent of one another, like the throws of a die, or sensibly so, like the drawings of balls from a bag containing a number of balls that is very large compared with the number drawn. Reverting to the illustration of a death-rate, our formule would not apply even if the sample populations were composed of persons of one age and one sex, if we were dealing, for example, with deaths from an infectious or contagious disease. For if one person in a certain sample has contracted the disease in question, he has increased the possibility of others doing so, and hence of dying from the disease. The same thing holds good for certain classes of deaths from accident, e.g. railway accidents due to derailment, and explosions in mines: if such an accident is fatal to one person it is probably fatal to others also, and consequently the annual returns show large and more or less erratic variations. When we speak of simple sampling in the following pages, the term is intended to imply the fulfilment of all the conditions (a), (8), and (ec), all the samples and all the individual contributions to each sample being taken under precisely the same conditions, and the individual “events” or appearances of the character being quite independent. It may be as well expressly to note that we need not make any assumption as to the conditions that determine p unless we have to estimate i/mpg a priori. If we draw a sample and observe in it the actual proportion of, say, 4’s: draw another sample under precisely the same conditions, and observe the proportion of 4’s in the two samples together: add to these a third sample, and so on, we will find that p approaches —not continuously, but with some fluctuations—closer and closer to some limiting value. Tt is this limiting value which is to be used in our formulee—the value of » that would be observed in a very large sample. The standard-deviation of the number of sixes thrown with » dice, on this understanding, may be «/npg, even if the dice be out of truth or loaded so that pis no longer 1/6. Similarly, the standard-deviation of the number of black balls in samples of » drawn from an infinitely large mixture of black and white balls in equal proportions may be «npg even at

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