Kolmogorov?Smirnov test under dependent and independent ranked set sampling based on single and double stage designs

The ranked set sampling (RSS) and its modifications, such as neoteric ranked set sampling (NRSS), double ranked set sampling (DRSS), and neoteric-neoteric ranked set sampling (NNRSS), have emerged as efficient alternatives to the commonly used simple random sampling (SRS), by leveraging auxiliary variables to enhance sampling precision. This study conducts a comparative analysis of the Kolmogorov?Smirnov (KS) test power under one-stage (RSS, NRSS) and two-stage (DRSS, NNRSS) designs in terms of dependent and independent sampling approaches. Using Monte Carlo simulations, we evaluate the performance of these methods against SRS across normal and non-symmetric distributions for various population sizes and varying correlation coefficients between auxiliary and target variables. The results indicate that NNRSS consistently outperforms other methods, achieving the highest efficiency, particularly under perfect correlation (? = 1.00) with larger set sizes. Moreover, NRSS and DRSS surpass RSS and SRS, though RSS exhibits lower efficiency, especially with small correlation coefficients (? = 0.50). Additionally, the study highlights the superior power of independent two-stage designs using NNRSS in goodness-of-fit testing, offering significant implications for cost-effective and precise statistical inference in finite populations. The main contribution of this study lies in assessing and highlighting the effectiveness of the recently developed and modified ranked set sampling designs?NRSS, DRSS, and NNRSS?for goodness-of-fit tests. By systematically comparing dependent and independent designs across one- and two-stage frameworks, this work offers new insights into improving ranking mechanisms to boost the power and efficiency of statistical inference.