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

£ THEORY OF STATISTICS. identically similar throughout the experiment, so that the chance of throwing “heads” with the coins or, say, “six” with the dice was the same throughout: we did not commence an experiment with dice loaded in one way and later on take a fresh set of dice loaded in another way. Consequently if formula (2) is to hold good in our practical case of sampling there must not be a difference in any essential respect—1.e. in any character that can affect the proportion observed—between the localities from which the observations are drawn, nor, if the observations have been made at different epochs, must any essential change have taken place during the period over which the observations are spread. Where the causation of the character observed is more or less unknown, it may, of course, be difficult or impossible to say what differences or changes are to be regarded as essential, but, where we have more knowledge, the condition laid down enables us to exclude certain cases at once from the possible applications of formula (1) or (2). Thus it is obvious that the theory of simple sampling cannot apply to the variations of the death-rate in localities with populations of different age and sex compositions, nor to death-rates in a mixture of healthy and unhealthy districts, nor to death-rates in successive years during a period of con- tinuously improving sanitation. In all such cases variations due to definite causes are superposed on the fluctuations of sampling. (6) In the second place, we have also tacitly assumed not only that we were using the same set of coins or dice throughout, so that the chances p and ¢ were the same at every trial, but also that all the coins and dice in the set used were identically similar, so that the chances p and ¢ were the same for every coin or die. Consequently, if our formule are to apply in the practical case of sampling, the conditions that regulate the appearance of the character observed must not only be the same for every sample, but also for every individual in every sample. This is again a very marked limitation. To revert to the case of death- rates, formule (1) and (2) would not apply to the numbers of persons dying in a series of samples of 1000 persons, even if these samples were all of the same age and sex composition, and living under the same sanitary conditions, unless, further, each sample only contained persons of one sex and one age. For if each sample included persons of both sexes and different ages, the condition would be broken, the chance of death during a given period not being the same for the two sexes, nor for the young and the old. The groups would not be homogeneous in the sense required by the conditions from which our formule have been deduced. Similarly, if we were observing hair-colours, our formule 7260

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