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 III. Theory of sampling

Collection:: Economics Books

THEORY OF STATISTICS. the same way, which renders many statistical results based on samples so dubious. 5. Thus in collecting returns as to family income and expendi- ure from working-class households, the families with lower a are almost certain to be under-represented ; they largel ‘“ escape the sampler’s fingers” from their simple lack of abilit o keep the necessary accounts. It is almost impossible to say, however, to what extent they are under-represented, or to for any estimate as to the possible error when two such samples aken by different persons at different times, or in different places, are compared. Again, if estimates as to crop-production are formed on the basis of a limited number of voluntary returns, the estimates are likely to err in excess, as the persons who make the returns will probably include an undue proportio of the more intelligent farmers whose crops will tend to be above average. Whilst voluntary returns are in this way liable to lead to more or less unrepresentative samples, compulsor sampling does not evade the difficulty. Compulsion could not en- sure equally accurate and trustworthy returns from illiterate and well-educated workmen, from intelligent and unintelligent armers. The following of some definite rule in drawing the sample may also produce unrepresentative samples: if samples of fruit were taken solely from the top layers of baskets expose or sale, the results might be unduly favourable; if from th ottom layer, unduly unfavourable. 6. In such cases we can see that any sample, taken in the way supposed, is likely to be definitely biassed, in the sens hat it will not tend to include, even in the long run, equa roportions of the 4’s and o’s in the original material. In othe ases there may be no obvious reason for presuming such bas, ut, on the other hand, no certainty that it does not exist. Thus if we noted the hair-colours of the children in, say, one ol in ten in a large town, the question would arise whethe his method would tend to give an unbiassed sample of all th hildren. No assured answer could be given: conjectures o he matter would be based in part on the way in which the chools were selected, e.g. the volunteering of teachers for the work might in itself introduce an element of bias. Again, if say 0,000 herrings were measured as landed at various North Se ports, and the question were raised whether the sample was likely to be an unbiassed sample of North Sea herrings, no assured answer could be given. There may be no definite reaso for expecting definite bias in either case, but it may exist, an no mere examination of the sample itself can give any informa WE to whether it exists or no. 280)

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