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

342 THEORY OF STATISTICS. percentiles in the same distribution, the student must be care- ful to note that the errors in two such percentiles are not independent. Consider the two percentiles, for which the values of p and ¢ are p, q,, p, 9, respectively, the first-named being the lower of the two percentiles. These two percentiles divide the whole area of the frequency curve inte three parts, the areas of which are proportional to ¢;, 1 — ¢; —p,, and p,. Further, since the errors in the first percentile are directly proportional to the crrors in ¢,, and the errors in the second percentile are directly proportional but of opposite sign to the errors in p,, the corre- lation between errors in the two percentiles will be the same as the correlation between errors in ¢; and p, but of opposite sign. But if there be a deficiency of observations below the lower percentile, producing an error §, in ¢;, the missing observations will tend to be spread over the two other sections of the curve in proportion to their respective areas, and will therefore tend to produce an error 3,= 2%, 5, in p,. If then » be the correlation between errors in ¢, and p,, ¢ and e, their respective standard errors, we have r2= _P2 & py Or, inserting the values of the standard errors, 8 al 991 The correlation between the percentiles is the same in magni- tude but opposite in sign : it is obviously positive, and consequently correlation between errors | _ z NL Poth ; } - 3) in two percentiles Gol If the two percentiles approach very close together, ¢, and g,, p; and p, become sensibly equal to one another, and the correla- tion becomes unity, as we should expect. 8. Let us apply the above value of the correlation between percentiles to find the standard error of the semi-interquartile range for the normal curve. Inserting ¢;=p,=%, ¢,=p,=4%, we find r=1. Hence the standard error of the interquartile range is, applying the ordinary formula for the standard-deviation of a difference, 2/,/3 times the standard error of either quartile, or “wy

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