EFFICIENCY OF RATIO ESTIMATOR WITH RANDOM MISSING VALUES IN STRATIFIED TWO-STAGE SAMPLING USING DOUBLE SAMPLING FOR AUXILIARY INFORMATION

Abstract

Accurate estimation of population parameters in stratified two-stage sampling is often challenged by missing data, which can reduce the efficiency of estimators. Existing approaches, such as the Bahl and Saini (2011) ratio and difference estimators, do not explicitly account for missing observations, limiting their applicability in practical survey contexts. To address this gap, this study formulated and evaluated a ratio-type estimator of population mean in stratified two-stage sampling. Two populations were considered: a synthetically generated dataset from an exponential distribution and a field survey on school attendance and pupils’ mathematics scores. Sample sizes of 25, 40, 70, and 100 were drawn to assess estimator’s performance. To investigate efficiency under missing data, 20% of the observations were assumed Missing Completely at Random (MCAR) so that regression and ratio imputation methods were implemented. The developed estimator compared well with other results with efficiency assessed in terms of variance, standard error, coefficient of variation, and confidence intervals. Findings showed that the developed estimator consistently outperformed other estimators across all sample sizes, achieving lower coefficients of variation and narrower confidence intervals. Efficiency improved steadily with increasing sample size, and regression imputation provided superior recovery of efficiency compared to ratio imputation, particularly when strong correlations between auxiliary and study variables were present. The developed estimator demonstrated efficiency in both controlled and real-world survey conditions, making it a reliable alternative to existing estimators, especially in the presence of missing data, and highlighting its strong potential for application in practical survey contexts.