Effectiveness of Takahasi's Ranked Set Sampling

Author

Prof. Arun Kumar Sinha

Co-author

• Vijay Kumar, Dept. of Statistics, TM Bhagalpur University, Bhagalpur- 812007, Bi

Conference

Format: CPS Abstract

Abstract

Ranked Set Sampling (RSS) has been introduced by McIntyre (1952) with the aim of estimating agricultural characteristics. It is a cost-effective sampling technique when the variable of interest is expensive or difficult to measure but it could be ranked easily at a negligible cost. Under equal allocation RSS performs better than simple random sampling (SRS). The performance of RSS further improves when appropriate unequal allocation is used instead of equal allocation. In Takahasi's RSS method, after selecting m2 (m squared) units randomly from an infinite population and arranged them into m sets with m units each, a unit is randomly selected from each set. Each so obtained unit is then quantified and a rank between 1 and m (both inclusive) is given to its quantification. Obviously, one may not get the same frequency for each rank order as in the case of McIntyre’s RSS method and also there is a possibility of zero frequency for a rank order even after selecting r times m-squared units from the population.
To deal with these difficulties, Takahasi (1970) suggested the McIntyre’s method for collecting samples in one cycle. This ensures that every rank order gets at least one quantification. This method performs well when one is interested only to estimate the population mean. But this does not help while estimating the variance of the estimator because in this case the variance of each rank order is needed. In view of these facts Norris, Patil and Sinha (1995) suggested to use McIntyre’s method in two cycles while using TRSS and referred to it as modified TRSS (MTRSS). These procedures are illustrated using a real data set regarding the yield of potato. The technique is more useful to those who look for cost-effective technique for estimating agricultural products that are grown underground such as potato, ginger, turmeric, garlic, onion, beetroot, peanut, etc. These methods are quite useful when a population of interest may not be stratified, and this is a general scenario in many real-life scenarios.