Optimal systematic sampling when sample size is odd in the presence of linear trend and two-way linear trend (Q2023831)

Earlier research showed that when there is a linear trend in the values of the study variable, balanced systematic sampling technique is optimum for the estimation of the population mean of the variate, when the sample size is even. Further, diagonal systematic sampling makes the sampling trend free when the population size is a perfect square of the sample size. In this paper, the authors suggest a modification to the balanced systematic sampling which is optimum when the population size is odd, under a population trend which is linear or two way linear. While in the theoretical derivations of the paper, it is assumed that perfect linear trend or perfect two way linear trend is present, in actual practice, this assumption does not hold. Hence data from 7 natural situations are considered and the efficiencies of various sampling methods are calculated and it is observed that the proposed modification fared better. Even for a small artificial population of size 10 units showing trend, the proposed method was efficient.