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Two-stage cluster sampling with unequal probability sampling in the first stage and ranked set sampling in the second stage

100%
Ugwu M. C., Madukaife M. S.
Statistics in Transition new series
|
2022
|
vol. 23
|
issue 3
199-214
EN
In this research work we introduce a new sampling design, namely a two-stage cluster sampling, where probability proportional to size with replacement is used in the first stage unit and ranked set sampling in the second in order to address the issue of marked variability in the sizes of population units concerned with first stage sampling. We obtained an unbiased estimator of the population mean and total, as well as the variance of the mean estimator. We calculated the relative efficiency of the new sampling design to the two-stage cluster sampling with simple random sampling in the first stage and ranked set sampling in the second stage. The results demonstrated that the new sampling design is more efficient than the competing design when a significant variation is observed in the first stage units.
2

Intracluster Homogeneity Selection Problem in a Business Survey

72%
Žmuk B.
Business Systems Research Journal
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2016
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vol. 7
|
issue 2
91-103
EN
Background: In the cluster sampling approach many parameters have influence on lowering the survey costs and one of the most important is the intracluster homogeneity. Objectives: The goal of the paper is to find the most optimal value of intracluster homogeneity in case when two or more questions or variables have a key role in the research. Methods/Approach: Five key variables have been selected from a business survey conducted in Croatia and results for the two-stage cluster sampling design approach were simulated. The calculated intracluster homogeneity values were compared among all the five observed questions and survey costs and precision levels were inspected. Results: In the new cluster sampling design, for the fixed precision level, the lowest survey costs would be achieved by using the intracluster homogeneity value which is the closest to the average intracluster homogeneity value among all the key questions. Similar results were obtained when survey costs were held fixed. Conclusions: If there is more than one key question in the survey, then the best solution would be to use an average intracluster homogeneity value. However, one should notice that in that case minimum survey costs would not be reached, but the precision levels would increase at all key questions.
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