An Introduction to the theory of statistics

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Multivolume work

Identifikator:: 1895264332

Document type:: Multivolume work

Author:: Myers, Gustavus

Title:: Geschichte der großen amerikanischen Vermögen

Place of publication:: Berlin

Publisher:: Fischer

Year of publication:: 1916 -

Collection:: Economics Books

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Volume

Identifikator:: 1895266750

URN:: urn:nbn:de:zbw-retromon-242184

Document type:: Volume

Author:: Myers, Gustavus http://d-nb.info/gnd/10190651X

Title:: Geschichte der großen amerikanischen Vermögen

Volume count:: Bd. 1

Place of publication:: Berlin

Publisher:: Fischer

Year of publication:: 1916

Scope:: XL, 412 Seiten

Digitisation:: 2022

Collection:: Economics Books

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Chapter

Document type:: Multivolume work

Structure type:: Chapter

Title:: Erster Teil: Die Verhältnisse in der Niederlassungs- und Kolonialzeit

Collection:: Economics Books

2vn THEORY OF STATISTICS. sampling ”% The proportion of plants above average height in the two classes (cross- and selffertilised) together is 29/68. The standard-deviation of the differences due to simple sampling between the proportions of * tall” plants in two samples of 34 observations each is therefore 29139 1 aN c= 53 X 88 X 2) =0120, or 12:0 per cent. The actual proportions observed are 50 per cent. and 35 per cent.—difference 15 per cent. As this difference is only slightly in excess of the standard error of the difference, for samples of 34 observations drawn from identical material, no definite significance could be attached to it—if it stood alone. The student will notice, however, that all the other cases cited from Darwin in the question referred to show an association of the same sign, but rather more marked. Hence the difference observed may be a real one, or perhaps the real difference may be greater and may be partially masked by a fluctuation of sampling. If 50 per cent. and 35 per cent. were the true proportions in the two classes, the standard error of the percentage difference would be, by equation (6), 3 ar XO) 11 pr on, and consequently the actual difference might not infrequently be completely masked by fluctuations of sampling, so long as experi- ments were only conducted on the same small scale. Example iv.—(Data from J. Gray, Memoir on the Pigmentation Survey of Scotland, Jour. of the Royal Anthropological Institute, vol. xxxvii., 1907.) The following are extracted from the tables relating to hair-colour of girls at Edinburgh and Glasgow :— Of Medium Total Per cent. Hair-colour. observed. Medium. Edinburgh . ; 4,008 9,743 41'1 Glasgow : : 17,529 39,764 44-1 Can the difference observed in the percentage of girls of medium hair-colour have arisen solely through fluctuations of sampling * In the two towns together the percentage of girls with medium hair-colour is 43-5 per cent. If this were the true percentage, the standard error of sampling for the difference between per- centages observed in samples of the above sizes would be-— 1 ry cia = (435 x 560) x (ge + 57) =(0'56 per cent. ed

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