An efficient and easy to carry out sampling design in environmental studies

In survey sampling, finding an efficient sampling design, with both a logistically feasible sampling scheme and an efficient estimator is the ultimate goal. Some efficient estimators when used with complex sampling design have such complicated formula that calculations are impossible even by computers. This can be the case with the Murthy’s estimator (1957) when used in designs with unequal selection probabilities and without replacement. This complexity of the estimator often means that the designs are not used to field studies in environmental studies, ecological studies, biological studies, and so on. In this paper, Murthy’s estimator is approximated for sampling designs with unequal selection probabilities and without replacement. This approximation produces an estimator that is fairly simple to calculate. We use it for a real population, a contaminated area with arsenic in Kurdistan. The efficiency of the introduced sampling design is compared with other counterpart estimators. The auxiliary variable, arsenic concentration values in the soil are used to improve the efficiency of arsenic concentration estimator in plants.