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 II. The theory of variables

Collection:: Economics Books

X.—CORRELATION : ILLUSTRATIONS AND METHODS. 203 found in various ways, for the most part dependent either (1) on the formule for the two regressions rot and vt, or (2) on v z the formule for the standard deviations of the arrays o, V1 - 12 and 0, v/T—72. Such approximate methods are not recommended for ordinary use, as they will lead to different results in different hands, but a few may be given here, as being occasionally useful for estimating the value of the correlation in cases where the data are not given in such a shape as to permit of the proper calculation of the coefficient. (1) The means of rows.and columns are plotted on a diagram, and lines fitted to the points by eye, say by shifting about a stretched black thread until it seems to run as near as may be to all the points. If ;, 4, be the slopes of these two lines to the vertical and the horizontal respectively, r= A/b,.5,. Hence the value of » may be estimated from any such diagram as figs. 36-40 in Chapter IX., in the absence of the original table. Further, if a correlation-table be not grouped by equal intervals, it may be difficult to calculate the product sum, but it may still be possible to plot approximately a diagram of the two lines of regression, and so determine roughly the value of 7. Similarly, if only the means of two rows and two columns, or of one row and one column in addition to the means of the two variables, are known, it will still be possible to estimate the slopes of RR and CC, and hence the correlation coefficient. (2) The means of one set of arrays only, say the rows, are calculated, and also the two standard-deviations 0, and o,. The means are then plotted on a diagram, using the standard-deviation of each variable as the unit of measurement, and a line fitted by eye. The slope of this line to the vertical is ». If the standard deviations be not used as the units of measurement in plotting, the slope of the line to the vertical is » o./o,, and hence » will be obtained by dividing the slope by the ratio of the standard- deviations, This method, or some variation of it, is often useful as a makeshift when the data are too incomplete to permit of the proper calculation of the correlation, only one line of regression and the ratio of the dispersions of the two variables being required : the ratio of the quartile deviations, or other simple measures of dispersion, will serve quite well for rough purposes in lieu of the ratio of standard-deviations. As a special case, we may note that

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