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

XIII.—SIMPLE SAMPLING OF ATTRIBUTES. ) nation 4 than for nation B, we cannot necessarily conclude that the real mean stature is greater in the case of nation 4 : possibly if the observations were repeated on different samples of 1000 men the ratio might be reversed. 2. The theory of such fluctuations may be termed the theory of sampling, and there are two chief sections of the theory corre- sponding to the theory of attributes and the theory of variables respectively. In tossing a coin we only classify the results of the tosses as heads or tails; in drawing balls from a mixture of black and white balls, we only classify the balls drawn as black or as white. These cases correspond to the theory of attributes, and the general case may be represented as the drawing of a sample from a universe containing both 4’s and o’s, the number or proportion of 4’s in successive samples being observed. If, on the other hand, we put in a bag a number of cards bearing different values of some variable X and draw sample batches of cards, we can form averages and measures of dispersion for the successive batches, and these averages and measures of dispersion will vary slightly from one batch to another. If associated measures of two variables X and Y are recorded on each card, we can also form correlation-coefficients for the different batches, and these will vary in a similar manner. These cases correspond to the theory of variables, and it is the function of the theory of sampling for such cases to inform us as to the fluctuations to be expected in the averages, measures of dispersion, correlation-coefficients, ete, in successive samples. In the present and the three following chapters the theory of sampling is dealt with for the case of attributes alone. The theory is of great importance and interest, not only from its applications to the checking and control of statistical results, but also from the theoretical forms of frequency- distribution to which it leads. Finally, in Chapter XVII. one or two of the more important cases of the theory of sampling for variables are briefly treated, the greater part of the theory, owing to its difficulty, lying somewhat outside the limits of this work. 3. The theory of sampling attains its greatest simplicity if every observation contributed to the sample may be regarded as independent of every other. This condition of independence holds good, e.g., for the tossing of a coin or the throwing of a die : the result of any one throw or toss does not affect, and is un- affected by, the results of the preceding and following tosses. It does not hold good, on the other hand, for the drawing of balls from a bag: if a ball be drawn from a bag containing 3 black and 3 white balls, the remainder may be either 2 black and 3 white, or 2 white and 3 black, according as the first ball was black or white. The result of drawing a second ball is therefore 25F

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