Performance of a Predictive Ratio Estimator in Two-Stage Sampling with Auxiliary Inforation

This study examines the relative performance of a predictive ratio estimator against the conventional ratio estimator within a two-stage sampling design incorporating double sampling for the auxiliary variable. Fertilizer application quantity was used as the auxiliary characteristic, with crop yield as the study variable. Estimator performance was assessed through the mean squared error (MSE), standard error (SE), coefficient of variation (CV), and relative efficiency (RE). The predictive ratio estimator had a lower MSE of 0.1542, a SE of 0.3927 and a CV of 2.065% against the MSE of 0.1560, a SE of 0.3927 and a CV of 2.092% for the classical ratio estimator. The predictive ratio estimator also yielded a slightly higher relative efficiency of 101.17% compared with classical ratio estimator 100%. This efficiency gain is attributable to the estimator's capacity to exploit the strong auxiliary–study variable correlation captured in the first-phase sample. The study recommends the adoption of predictive ratio estimators in two-stage agricultural surveys with reliable auxiliary data.