L' Industrie cotonnière en Allemagne

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Monograph

Identifikator:: 84539584X

URN:: urn:nbn:de:zbw-retromon-36509

Document type:: Monograph

Author:: Koechlin, Armand

Title:: L' Industrie cotonnière en Allemagne

Place of publication:: Paris

Publisher:: Pelletier

Year of publication:: 1906

Scope:: 1 Online-Ressource (387 S)

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Conditions de la vie

Collection:: Economics Books

346 THEORY OF STATISTICS. than the other. If two samples be drawn quite independently from different universes, indefinitely large samples from which exhibit the standard-deviations o;, and o,, the standard error of the difference of their means will be given by oi 0% SR ot 1D This is, indeed, the formula usually employed for testing the significance of the difference between two means in any case: seeing that the standard error of the mean depends on the standard-deviation only, and not on the mean, of the distribution, we can inquire whether the two universes from which samples have been drawn differ in mean apart from any dyfference in dispersion. If two quite independent samples be drawn from the same universe, but instead of comparing the mean of the one with the mean of the other we compare the mean m, of the first with the mean m, of both samples together, the use of (6) or (7) is not justified, for errors in the mean of the one sample are correlated with errors in the mean of the two together. = Following precisely the lines of the similar problem in § 13, Chap. XIII, case IIL, we find that this correlation is Nn J(n, + ny), and hence ny 0 =10; (my + 7g) h : \ . (8) (For a complete treatment of this problem in the case of samples drawn from two different universes ¢f. ref. 22.) 13. The distribution of means of samples drawn under the conditions of simple sampling will always be more symmetrical than the distribution of the original record, and the symmetry will be the greater the greater the number of observations in the sample. Further, the distribution of means (and therefore also of the differences between means) tends to become not merely sym- metrical but normal. We can only illustrate, not prove, the point here ; but if the student will refer to§ 13, Chap. XV., he will see that the genesis of the normal curve in this case is in accord- ance with what we then stated, viz. that the distribution tends to be normal whenever the variable may be regarded as the sum (or some slightly more complex function) of a number of other variables. In the present instance this condition is strictly ful filled. The mean of the sample of n observations is the sum of the values in the sample each divided by n, and we should expect the distribution to be the more nearly normal the larger n. As an illustration of the approach to symmetry even for small values

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