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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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Theory of sampling

Collection:: Economics Books

PART III._THEORY OF SAMPLING. CHAPTER XIII SIMPLE SAMPLING OF ATTRIBUTES. 1. The problem of the present Part—2. The two chief divisions of the theory of sampling—3. Limitation of the discussion to the case of simple sampling—4. Definition of the chance of success or failure of a given event— 5. Determination of the mean and standard-deviation of the number of successes in n events—6. The same for the proportion of successes in n events: the standard-deviation of simple sampling as a measure of unreliability, or its reciprocal as a measure of precision—7. Verification of the theoretical results by experiment—8. More detailed discussion of the assumptions on which the formula for the standard- deviation of simple sampling is based—9-10. Biological cases to which the theory is directly applicable—11. Standard-deviation of simple sampling when the numbers of observations in the samples vary—12. Approximate value of the standard-deviation of simple sampling, and relation between mean and standard-deviation, when the chance of success or failure is very small—13. Use of the standard- deviation of simple sampling, or standard error, for checking and controlling the interpretation of statistical results. 1. ON several occasions in the preceding chapters it has been pointed out that small differences between statistical measures like percentages, averages, measures of dispersion and so forth cannot in general be assumed to indicate the action of definite and assign- able causes. Small differences may easily arise from indefinite and highly complex causation such as determines the fluctuating proportions of heads and tails in tossing a coin, of black balls in drawing samples from a bag containing a mixture of black and white balls, or of cards bearing measurements within some given class-interval in drawing cards, say, from an anthropometric record. In 100 throws of a coin, for example, we may have noted 56 heads and only 44 tails, but we cannot conclude that the coin is biassed : on repeating our throws we may get only 48 heads and 52 tails. Similarly, if on measuring the statures of 1000 men in each of two nations we find that the mean stature is slightly greater for IB 4

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