A new data analysis framework with mathematical foundation and implementations: Its case studies in higher education and radiation sciences

Population proportion estimation is one of the main issues in survey sampling, especially when the characteristic of interest is qualitative and cannot be numerically quantified. In most real-life surveys, an auxiliary attribute is present and can be used effectively to enhance the precision of the estimate. The proposed study suggests a better estimator for the population proportion using auxiliary attribute information under simple random sampling without replacement. The recommended estimator uses the available population parameters of the auxiliary attribute to be more efficient than conventional estimators. Theoretical properties of the proposed estimator are obtained to the first degree of approximation. Bias and mean-squared error expressions are derived, and conditions for efficiency are established that determine when the proposed estimator will be better than the existing estimators. Analytical findings indicate that the proposed estimator will always achieve a lower mean square error, especially when the auxiliary attribute is positively related to the study attribute. Empirical studies on real data sets in radiation sciences and higher education are conducted to evaluate their practical performance. The theoretical findings are very strongly supported by the numerical findings and show that it is much more efficient than the conventional estimator. The paper outlines the role of auxiliary attributes in estimating population proportions and provides an easy yet effective alternative for researchers and practitioners dealing with attribute data. The presented estimator is highly appropriate for educational assessment, radiographic exposure research, and other practical applications because it delivers superior performance and is easy to implement.