Kameralwissenschaften und vergleichende Betriebswirtschaftslehre

An Introduction to the theory of statistics

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Monograph

Identifikator:: 1752239113

URN:: urn:nbn:de:zbw-retromon-128654

Document type:: Monograph

Author:: Walb, Ernst http://d-nb.info/gnd/104056207

Title:: Kameralwissenschaften und vergleichende Betriebswirtschaftslehre

Place of publication:: Köln

Publisher:: Müller

Year of publication:: 1927

Scope:: 42 S.

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Kameralwissenschaften und vergleichende Betriebswirtschaftslehre

Collection:: Economics Books

XI.—CORRELATION : MISCELLANEOUS THEOREMS, 227 found for 36 small registration districts in which the number of births in a decade ranged between 1500 and 2500 :— Proportion of Male Births per 1000 of all Births. Decade, Mean Standard- : deviation. 1881-1890 . : 508-1 12°80 1891-1900 ; 5084 10-37 Both decades 50825 1165 It is believed, however, that a great part of the observed standard-deviation is due to mere ‘‘ fluctuations of sampling ” of no real significance. Given that the correlation between the proportions of male births in a district in the two decades is+ 036, estimate (1) the true standard-deviation freed from such fluctuations of sampling ; (2) the standard-deviation of fluctua- tions of sampling, 4.e, of the errors produced by such fluctuations in the observed proportions of male births, 4. (Data from Pearson, ref. 11.) The coefficients of variation for breadth, height, and length of certain skulls are 3°89, 3:50, and 324 per cent. respec- tively. Find the ‘spurious correlation ” between the breadth/length and height/length indices, absolute measures being combined at random so that they are uncorrelated. 5. (Data from Boas, communicated to Pearson : ¢f. Fawcett and Pearson, Proc. Roy. Soc., vol. Ixii. p. 413.) From short series of measurements on American Indians the mean coefficient of correlation found between father and son, and father and daughter, for cephalic index, is 0°14 ; between mother and son, and mother and daughter 0-33. Assuming these coefficients should be the same if it were not for the looseness of family relations, find the proportion of children not due to the reputed father. 6. Find the correlation between X, + X; and X,+ X;; X,, X, and X, being uncorrelated. 7. Find the correlation between X, and aX, +bX, X, and X, being uncorrelated. 8. (Referring to illustration iv., § 14, Chap. X.) Use the answer to question 7 to estimate, very roughly, the correlation that would be found between annual movements in infantile and general mortality if the mortality of those under and over 1 year of age were uncorrelated. Note that— pesos) brs } =infantile mortality per 1000 births x a + deaths over one year per 1000 of population. and treat the ratio of births to population as if it were constant at a rough average value, say 0°033. The standard-deviation of annual movements in infantile mortality is (loc. cit.) 9'6, and that of annual movements in mortality other than infantile may be taken as sensibly the same as that of general mortality, or say 1 unit. 9. If the relation az) +b.ag+ecxg=0

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