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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SUPPLEMENTS—GOODNESS OF FIT. R75 1 success, and the frequency of 12 successes with that of 11 successes. In the second place, the proof outlined assumes that the theoretical law is known a priorz. In a large number, perhaps almost the majority, of practical cases in which the test is ap- plied this condition is not fulfilled. We determine, for example, the constants of a frequency curve from the observations them- selves, not from a priori considerations: we determine the “independence values” of the frequencies for a contingency table from the given row and column totals, again not from a priori considerations. This general case is dealt with below, in the section headed * Comparison Frequencies based on the Observations.” Finally, attention should be paid to the run of the signs of the differences m’—m. The method used pays no attention to the order of these signs, and it may happen that x* has quite a moderate value and P is not small when all the positive differences are on one side of the mode and all the negative differences on the other, so that the mean shows a deviation from the expected value that is quite outside the limits of sampling, or that the differences are negative in both tails so that the standard deviation shows an almost impossible divergence from expectation. In the first example on the preceding page all the differences are negative up to 5 successes, positive from 6 to 10 successes, and negative again for 11 and 12 successes. This is almost the first case supposed, and in fact we have already found (p. 267) that the mean deviates from the expected value by 5°1 (more precisely 5:13) times its stan- dard error. From Table II. of Tables for Statisticians we have :— Greater fraction of the area of a normal curve for a deviation 5°13 . : . "9999998551 Area in the tail of the curve . . *01)00001449 Area in both tails . : . '0000002898 so that the probability of getting such a deviation (+ or —) on random sampling is only about 3 in 10,000,000. The value found for P (0015) by the grouping used is therefore in some degree misleading. If we regroup the distribution according to the signs of m"— m, we find m—— sgt ved Expected requency Frequency. 0-5 1426 1586 6-10 2659 2497 11-12 1 13 Total. 28 1095 - (aAet al(3Qv a

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