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

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. 351 Similarly, to express the standard error of the standard-deviation we_ require to know, in the general case, the mean (deviation)? with respect to the mean. Either, then, we must find this quantity for the given distribution—and this would entail entering on a field of work which hitherto we have intentionally avoided—or we must, if that be possible, assume the distribution to be of such a form that we can express the mean (deviation) in terms of the mean (deviation)?. This can be done, as a fact, for the normal distribution, but the proof would again take us rather beyond the limits that we have set ourselves. To deal with the standard error of the correlation coefficient would take us still further afield, and the proof would be laborious and difficult, if not impossible, without the use of the differential and integral cal- culus. We must content ourselves, therefore, with a simple statement of the standard errors of some of the more important constants, Standard-deviation.—]If the distribution be normal, standard error of the o standard-deviation in \ = i (12) a normal distribution Van This is generally given as the standard error in all cases: it is, however, by no means exact : the general expression is standard error of the standard- 1 deviation in a dein = J fy 14 (13) of any form py. m where pu, is the mean (deviation)*—deviations being, of course, measured from the mean—and Py the mean (deviation)? or the square of the standard-deviation: n is assumed sufficiently large to make the errors in the standard-deviation small compared with that quantity itself. Equation (13) may in some cases give values considerably ‘oreater—twice as great or more—than (12). (Cf. ref. 17.) If, however, the distribution be normal, equation (12) gives the standard error not merely of standard-deviations of order zero, to use the terminology of Chap. XII, but of standard- deviations of any order (ref. 33). It will be noticed, on reference to equation (4) above, § 8, that the standard error of the standard. deviation is less than that of the semi-interquartile range for a normal distribution. For a normal distribution, again, we have— standard error of the co- 24 v \2)1# efficient of variation a Bo) 1+ (150) } - (14)

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