A Novel Mixed Sampling Design Under the Existence of A Linear Trend

In almost every field of social sciences, data is obtained from a small part drawn from a large population. Two common procedures to draw a sample from a population of interest are stratified random sampling and systematic random sampling. Each sampling procedure has been designed to be used in particular sample surveys. In real-world surveys, researchers may face a situation in which the simultaneous use of two or more sampling designs may be feasible to precisely estimate the population parameter rather than simply relying on a single sampling design. We propose a novel mixed-mode sampling scheme for real-world sample surveys in which the population units exhibit some sort of linear trend. Our proposed mixed sampling design combines the diagonal and linear systematic sampling with stratified random sampling. In real-world circumstances in which some sort of linear trend exists in the population units, we prove that our proposed mixed sampling design performs more efficiently than the available sampling designs. Additionally, unlike the systematic sampling design, the suggested sampling scheme can be applied practically for any sample and population size.