An Introduction to the theory of statistics

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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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Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

IX.—CORRELATION. re asymmetrical, the skewness being positive for the rows at the top of the table (the mode being lower than the mean), and negative for the rows at the foot, the more central rows being, nearly symmetrical. The maximum frequency lies towards th upper end of the table in the compartment under the row an olumn headed “30-”. The frequency falls off very rapidly, wards the lower ages, and slowly in the direction of old age. utside these two forms, it seems impossible to delimit empirically; ny simple types. Tables V. and VI. are given simply as illus- rations of two very divergent forms. Fig. 31 gives a graphical representation of the former by the method corresponding to the histogram of Chapter VI., the frequency in each compartment eing represented by a square piliar. The distribution o requency is very characteristic, and quite different from that of any of the Tables I., IIL, III, or IV. 6. It is clear that such tables may be treated by any of the ethods discussed in Chapter V., which are applicable to al ontingency-tables, however formed. The distribution may be investigated in detail by such methods as those of § 4, or tested or isotropy (§ 11), or the coefficient of contingency can be calculated (§§ 5-8). In applying any of these methods, however, it is desirable to use a coarser classification than is suited to the methods to be presently discussed, and it is not necessary to retain the constancy of the class-interval. The classification should, on the contrary, be arranged simply with a view to avoidin many scattered units or very small frequencies. A few examples should be worked as exercises by the student (Question 3). 7. But the coefficient of contingency merely tells us whether, nd if so, how closely, the two variables are related, and muc more information than this can be obtained from the correlation- ble, seeing that the measures of Chapters VII. and VIII. can be pplied to the arrays as well as to the total distributions. If the wo variables are independent, the distributions of all paralle rrays are similar (Chap. V. § 13); hence their averages an ispersions, e.g. means and standard deviations, must be the same, n general they are not the same, and the relation between the mean or standard deviation of the array and its type require investigation. Of the two constants, the mean is, in general, the more important, and our attention will for the present be con- fined to it. The majority of the questions of practical statistic relate solely to averages: the most important and fundamental question is whether, on an average, high values of the one variable show any tendency to be associated with high (or with low) values of the other. If possible, we also desire to know how great divergence of the one variable from its average value is associate

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