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

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THEORY OF STATISTICS. For this comparison n’ is 8, x2 is 26:96, or practically 27, and P is about *000001—a value much more nearly in accordance with that suggested by the mean. Such a regrouping of the frequency distribution by the runs of classes that are in excess and in defect of expectation would appear often to afford a useful and severe test of the real extent of agree- ment between observation and theory. In the second example the signs are fairly well scattered, and the regrouping has a com- paratively small effect ; the mean being in almost precise agreement with expectation. The regrouped distribution is :— SITCOREeE, a Expected requency. Frequency. 0 447 459 1 1145 1108 2-3 1977 2022 4 380 364 5-6 139 143 7-8 8 5 Total. . : E Here nn’ is 6, x*is 5°52, and P 0°36, so that the deviations from expectation are still well within the range of fluctuations of sampling. The value of P is the probability that a set of observations will occur giving a group of deviations from theory, s.e. a value of x, which is more improbable than that observed. If, to take the second illustration above, we were to repeat 4096 throws of twelve dice a large number of times, noting the throws of sixes, we should expect to get a worse fit to theory, z.e. a value of x? greater than 5 81, roughly speaking 56 times in every hundred trials. , The value of P corresponding to ¥2=0 ig necessarily unity, for it is certain that all values of x2 must exceed zero. If the value of P corresponding to x2=1 is P,, then 1-2, is ithe frequency of values of y2 between 0 and 1. Similarly, if the value of P corresponding to x2=2 is P, then the frequency of values of x? between 1 and 2 is P,— P,, and so on. Thus, for 16 classes (n”=16), we find in the tables :(— 376 4096 4096

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