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Journal ArticleDOI

The Teacher's Corner

01 Oct 1967-The American Statistician (Taylor & Francis Group)-Vol. 21, Iss: 4, pp 26-28
TL;DR: In this paper, the general impression that the precision of an estimator increases with increasing sample size is scrutinized and it is demonstrated that if the estimator under consideration is an average function, the statement does not hold good when the population elements are drawn with varying probabilities of selection at each draw.
Abstract: The general impression that precision of an estimator increases with increasing sample size is scrutinized. It is demonstrated that, if the estimator under consideration is an average function, the statement does not hold good when the population elements are drawn with varying probabilities of selection at each draw. An example is presented to illustrate the point.
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TL;DR: In this paper, the problem of extending a given sampling design, when additional resources are available, is considered and some existing methods of improving an initial sampling strategy, so that the use of the additional resources is justified, are critically reviewed.

Additional excerpts

  • ...Cochran (1963), Ajgaonkar (1967), Chaudhuri (1977) and -3- Chaudhuri and Mukhopadhayay (1978) considered the properties of the sample mean and/or the Horiwitz-Thompson estimator (HTE) under different sampling designs Pn and Pm· It was observed that the sampling strategies (Pm' HTE) and (Pm' Ym) are…...

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References
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Journal ArticleDOI
TL;DR: In this paper, two sampling schemes are discussed in connection with the problem of determining optimum selection probabilities according to the information available in a supplementary variable, which is a general technique for the treatment of samples drawn without replacement from finite universes when unequal selection probabilities are used.
Abstract: This paper presents a general technique for the treatment of samples drawn without replacement from finite universes when unequal selection probabilities are used. Two sampling schemes are discussed in connection with the problem of determining optimum selection probabilities according to the information available in a supplementary variable. Admittedly, these two schemes have limited application. They should prove useful, however, for the first stage of sampling with multi-stage designs, since both permit unbiased estimation of the sampling variance without resorting to additional assumptions. * Journal Paper No. J2139 of the Iowa Agricultural Experiment Station, Ames, Iowa, Project 1005. Presented to the Institute of Mathematical Statistics, March 17, 1951.

3,990 citations

Book
01 Jan 1954
TL;DR: The delphi method as a research tool an example design as mentioned in this paper is used for mold testing is it beneficial or snake oil, mould testing is beneficial, snake oil is snake oil.
Abstract: chapter 111 subchapter c texas education agency. the delphi method as a research tool an example design. mould testing is it beneficial or snake oil. mathematics tacoma. indoor air quality forensic applications consulting. welcome · distancesampling org. u s smartphone use in 2015 pew research center. web site for perfectly random sampling with markov chains. sampling statistics wikipedia. communication courses department of communication. guidelines for education and training at the masters level. sampling theory and applications will yancey. evaluation theory design and methods – tei the. questionnaire design and surveys sampling ubalt edu. research amp theory air university. cluster sampling wikipedia. rbi 2018 exam dates syllabus application form pattern. dr arsham s statistics site home ubalt edu

506 citations

Journal ArticleDOI
TL;DR: In this paper, the bias in the estimation of the total of a variate y derived by weighting the units by weights proportional to 1/x is investigated, and it is shown that the amount of bias is usually quite trivial.
Abstract: In selection with probability proportional to size x from within strata without replacement, the usual method of selection gives rise to bias in the estimate of the total of a variate y derived by weighting the units by weights proportional to 1/x. By means of numerical examples it is shown that the amount of this bias is usually quite trivial. If, however, unbiased estimates are required, the true total probabilities of selection of the different units can be calculated easily for samples of 2, and with considerably more labour for samples of 3. The bias in the ordinary formula for the estimation of error is also investigated, and the formula is shown to be reasonably accurate. Horvitz and Thompson have given an unbiased estimator of the error variance, but this is shown to be inefficient and a new unbiased estimator is given. A method of revising the size measures so that with the usual method of selection the true total probabilities of selection are proportional to the original size measures is given for samples of 2. Horvitz and Thompson's solution of this problem does not appear to give satisfactory approximations in the cases met with in practice. The selection of successive members of a sample with arbitrary sets of probabilities chosen solely so that the total probabilities shall be proportional to the original size measures, which has been advocated in various quarters, is criticized.

390 citations