An Introduction to the theory of statistics

Bibliographic data

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

Usage license:: Get license information via the feedback formular.

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Theory of sampling

Collection:: Economics Books

XVIL—SIMPLER CASES OF SAMPLING FOR VARIABLES. 345 the two standard errors, viz. 126, assumes almost exactly the theo- retical magnitude. In the case of the asymmetrical distribution of rates of pauperism, also used as an illustration in § 6, the standard error of the median was found to be 00655 per cent. The standard error of the mean is only 0:0493 per cent., which bears to the standard error of the median a ratio of 1 to 1°33. As such cases as these seem on the whole to be the more common and typical, we stated in Chap. VII. § 18 that the mean is in general less affected than the median by errors of sampling. At the same time we also indicated the exceptional cases in which the median might be the more stable—cases in which the mean might, for example, be affected considerably by small groups of widely outlying observations, or in which the frequency-distri- bution assumed a form resembling fig. 53, but even more exaggerated as regards the height of the central “peak ” and the relative length of the “tails.” Such distributions are not un- common in some economic statistics, and they might be expected to characterise some forms of experimental error. If, in these cases, the greater stability of the median is sufficiently marked to outweigh its disadvantages in other respects, the median may be the better form of average to use. Fig. 53 represents a distribution in which the standard errors of the mean and of the median are the same. Further, in some experimental cases it is conceivable that the median may be less affected by definite experimental errors, the average of which does not tend to be zero, than is the mean, —this is, of course, a point quite distinct from that of errors of sampling. 12. If two quite independent samples of n, and n, observations respectively be drawn from a record, evidently €,5 the standard error of the difference of their means is given by Lio) €la = s + 2) (5) If an observed difference exceed three times the value of €19 given by this formula it can hardly be ascribed to fluctuations of sampling. If, in a practical case, the value of o is not known a priory, we must substitute an observed value, and it would seem natural to take as this value the standard-deviation in the two samples thrown together. If, however, the standard-deviations of the two samples themselves differ more than can be accounted for on the basis of fluctuations of sampling alone (see below, § 15), we evidently cannot assume that both samples have been drawn from the same record: the one sample must have been drawn from a record or a universe exhibiting a greater standard-deviation ~

Access restriction

Copyright

fullscreen: An Introduction to the theory of statistics

Monograph

Chapter

Table of contents

Download

Monograph

This page

Image fragment

Citation links

Citation recommendation