A new estimator under the simple random sampling framework with statistical properties: Its applications in physical education and radiation

Estimating the population mean is one of the primary goals of survey sampling. The inclusion of ancillary data has been identified as an effective way to improve the accuracy of estimates when using the simple random sampling model. Nonetheless, traditional estimators usually do not make the most of the auxiliary information available, especially in cases where information of the auxiliary variable is available to rank it. To overcome this shortcoming, the current study proposes a novel family of estimators that combine the sample mean of the variable of interest with the sample mean of the auxiliary variable, using ranking information for the auxiliary variable in simple random sampling. The proposed estimators will enhance the accuracy of population mean estimation while remaining simple and cost-effective in data collection. The statistical characteristics of the proposed estimator family are obtained analytically, including the formulations of bias and mean squared error, and the theoretical conditions under which the proposed estimators have an advantage over traditional estimators. The effectiveness of the suggested estimators is tested on real-world datasets from physical education and radiation studies. Experimental results consistently show that the proposed estimators are more efficient and more accurate than the current classical estimators. The results indicate the importance of the theory and the usefulness of integrating auxiliary-variable rankings into survey sampling, which can provide a strong and effective population-mean estimator across various fields of applied research.