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

THEORY OF STATISTICS. were discussed very fully for the case of attributes (Chap. XIII § 8), and we would refer the student to the discussion then given. ere it is sufficient to state the assumptions briefly, using the etters (a), (6) and (c) to denote the corresponding assumption indicated by the same letters in the section cited. (a) We assume that we are drawing from precisely the same record throughout the experiment, so that the chance of drawin a card with any given value of X, or a value within any assigned limits, is the same at each sampling. (6) We assume not only that we are drawing from the same record throughout, but that each of our cards at each drawin ay be regarded quite strictly as drawn from the same record (or rom identically similar records): e.g. if our card-record is con- ained in a series of bundles, we must not make it a practice to ake the first card from bundle number 1, the second card from undle number 2, and so on, or else the chance of drawing card with a given value of X, or a value within assigned limits may not be the same for each individual card at each drawing. (c) We assume that the drawing of each card is entirely independent of that of every other, so that the value of X recorde on card 1, at each drawing, is uncorrelated with the value of recorded on card 2, 3, 4, and so on. It is for this reason that w spoke of the record, in § 1, as containing a practically infinit umber of cards, for otherwise the successive drawings at each sampling would not be independent: if the bag contain te ickets only, bearing the numbers 1 to 10, and we draw the car bearing 1, the average of the following cards drawn will be higher han the mean of all cards drawn ; if, on the other hand, we dra he 10, the average of the following cards will be lower than the mea f all cards—.e. there will be a negative correlation between th umber on the card taken at any one drawing and the card taken at any other drawing. Without making the number of cards i he bag indefinitely large, we can, as already pointed out for th ase of attributes (Chap. XIII. § 3), eliminate this correlation b replacing each card before drawing the next. Sampling conducted under these conditions we shall, as before speak of as simple sampling. We do not, it should be noticed make the further assumption that the sample is unbiassed, 7.e. hat the chance of inclusion in the sample is independent of the value of X recorded on the card (cf. the last paragraph in § 8, hap. XIII, and the discussion in §§ 4-8, Chap. XIV.). This assumption is unnecessary. If it be true, the interpretation o our results becomes simpler and more straightforward, for we can substitute for such phrases as ‘the standard-deviation of 'n a very large sample,” “the form of the frequency-distributio 236

Access restriction

Copyright

fullscreen: An Introduction to the theory of statistics

Monograph

Chapter

Table of contents

Download

Monograph

Chapter

This page

Image fragment

Citation links

Citation recommendation