Der österreichische Exporteur

An Introduction to the theory of statistics

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Monograph

Identifikator:: 1758074884

URN:: urn:nbn:de:zbw-retromon-135614

Document type:: Monograph

Title:: Der österreichische Exporteur

Edition:: [2. Aufl]

Place of publication:: Wien

Publisher:: [Kammer für Handel, Gewerbe und Industrie]

Year of publication:: 1927

Scope:: 240 S.

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Abkürzungen - Abbreviations - Abréviations - Abreviaturas

Collection:: Economics Books

XVIL.—SIMPLER CASES OF SAMPLING FOR VARIABLES. 343 the standard error of the semi-interquartile range 1/,/3 times the standard error of a quartile. Taking the value of the standard error of a quartile from the table in § 4, we have, finally, standard error of the semi- | 7 interquartile range in a - =0-78672——=, (4) normal distribution J X# Of course the standard-deviation of the inter-quartile, or semi- interquartile, range can readily be worked out in any particular case, using equation (2) and the value of the correlation given above: it is best to work out such standard errors from first principles, applying the usual formula for the standard deviation of the difference of two correlated variables (Chap. XI. § 2, equation (1)). 9. If there is any failure of the conditions of simple sampling, the formule of the preceding sections cease, of course, to hold good. We need not, however, enter again into a discussion of the effect of removing the several restrictions, for the effect on the standard error of p was considered in detail in § 9-14 of Chap. XIV., and the standard error of any percentile is directly proportional to the standard error of p (¢f. § 3). Further, the student may be reminded that the standard error of any per- centile measures solely the fluctuations that may be expected in that percentile owing to the errors of simple sampling alone: it has no bearing, therefore, save on the one question, whether an observed divergence of the percentile, from a certain value that might be expected to be yielded by a more extended series of observations or that had actually been observed in some other series, might or might not be due to fluctuations of simple sampling alone. It cannot and does not give any indication of the possibility of the sample being biassed or unrepresentative of the material from which it has been drawn, nor can it give any indication of the magnitude or influence of definite errors of observation—errors which may conceivably be of greater im- portance than errors of sampling. In the case of the distribution of statures, for instance, the standard error almost certainly gives quite a misleading idea as to the accuracy attained in determining the average stature for the United Kingdom : the sample is not representative, the several parts of the kingdom not contributing in their true proportions. The student should refer again to the discussion of these points in §§ 4-8 of Chap. XIV. Finally, we may note that the standard error of a percentile cannot be evaluated unless the number of observations is fairly large—large enough to determine f, (eqn. 2) with reasonable accuracy, or

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