An Introduction to the theory of statistics

Bibliographic data

Monograph

Identifikator:: 175994050X

URN:: urn:nbn:de:zbw-retromon-137069

Document type:: Monograph

Author:: Gorter, Herman http://d-nb.info/gnd/118718207

Title:: Der historische Materialismus

Edition:: 3., bedeutend verm. Ausg.

Place of publication:: Berlin

Publisher:: Buchh. für Arbeiterliteratur

Year of publication:: 1928

Scope:: 137 S.

Digitisation:: 2021

Collection:: Economics Books

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

Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: V. Das gesellschaftliche Sein bestimmt den Geist

Collection:: Economics Books

XIII,—SIMPLE SAMPLING OF ATTRIBUTES. Co “standard-deviation of simple sampling” may be regarded as a measure of the magnitude of such errors, and may be called ac- cordingly the standard error, Three principal cases of comparison may be distinguished. Case I.—I¢t is desired to know whether the deviation of a certain observed number or proportion from an expected theoretical value is possibly due to errors of sampling. In this case the observed difference is to be compared with the standard error of the theoretical number or proportion, for the number of observations contained in the sample. Example i.—In the first illustration of § 7, 25,145 throws of a 4, 5, or 6 were made in lieu of the 24,576 expected (out of 49,152 throws altogether). The excess is 569 throws. Is this excess possibly due to mere fluctuations of sampling ? The standard error is o= 3x4 x49152 = 1109, The deviation observed is 5°1 times the standard error, and, practically speaking, could not occur as a fluctuation of simple sampling. It may perhaps indicate a slight bias in the dice. The problem might, of course, have been attacked equally well from the standpoint of the proportion in lieu of the absolute number of 4’s, 5s, or 6’s thrown. This proportion is 0-5116 instead of the theoretical 05000, difference in excess 0:0116. The standard error of the proportion is L sent X 4 X 49159 =0-00226, and the difference observed bears the same ratio to the standard error as before, as of course it must. Example ii.—(Data from the Second Report of the Evolution Committee of the Royal Society, 1905, p. 72.) Certain crosses of Pisum sativum gave 5321 yellow and 1804 green seeds. The expectation is 25 per cent. of green seeds, or 1781. Can the divergence from the exact theoretical result have arisen owing to errors of sampling only? The numerical difference from the expected result is 23. The standard error is o= 025x075 x T125 = 36-8. Hence the divergence from theory is only some 3/5 of the standard error, and may very well have arisen owing simply to fluctuations of sampling. 26"

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