The agricultural output of England and Wales 1925

The agricultural output of England and Wales 1925

Bibliographic data

Monograph

Identifikator:: 1757028552

URN:: urn:nbn:de:zbw-retromon-135495

Document type:: Monograph

Title:: The agricultural output of England and Wales 1925

Place of publication:: London

Publisher:: Stat. Off.

Year of publication:: 1927

Scope:: XV, 152 Seiten; graph. Darst., Kt.

Digitisation:: 2021

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Chapter III. The production of crops

Collection:: Economics Books

Full text

XIV.—REMOVING LIMITATIONS OF SIMPLE SAMPLING. 281 7. Such an examination may be of service, however, as indicating one possible source of bias, viz. great heterogeneity in the original material. If, for example, in the first illustration, the hair-colours of the children differed largely in the different schools—much more largely than would be accounted for by fluctuations of simple sampling—it would be obvious that one school would tend to give an unrepresentative sample, and questionable therefore whether the five, ten or fifteen schools observed might not also have given an unrepresentative sample. Similarly, if the herrings in different catches varied largely, it would, again, be difficult to get a representative sample for a large area. But while the dissimilarity of subsamples would then be evidence as to the difficulty of obtaining a representative sample, the similarity of subsamples would, of course, be no evidence that the sample was representative, for some very different material which should have been represented might have been missed or overlooked. 8. The student must therefore be very careful to remember that even if some observed difference exceed the limits of fluctua- tion in simple sampling, it does not follow that it exceeds the limits of fluctuation due to what the practical man would regard — and quite rightly regard—as the chances of sampling. Further, he must remember that if the standard error be small, it by no means follows that the result is necessarily trustworthy: the smallness of the standard error only indicates that it is not untrustworthy owing to the magnitude of fluctuations of simple sampling. It may be quite untrustworthy for other reasons: owing to bias in taking the sample, for instance, or owing to definite errors in classifying the 4’s and o’s. On the other hand, of course, it should also be borne in mind that an observed proportion is not necessarily incorrect, but merely to a greater or less extent untrustworthy if the standard error be large. Similarly, if an observed proportion =, in a sample drawn from one universe be greater than an observed proportion =, in a sample drawn from another universe, but m, — , is considerably less than three times the standard error of the difference, it does not, of course, follow that the true proportion for the given universes, p, and p,, are most probably equal. On the contrary, py most likely exceeds p, ; the standard error only warns us that this conclusion is more or less uncertain, and that possibly p, may even exceed p,. 9. Let us now consider the effect, on the standard-deviation of sampling, of divergences from the conditions of simple sampling which were laid down in § 8 of Chap. XIII. First suppose the condition (a) to break down, so that there is some essential difference between the localities from which, or the

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