-In this paper the statistical consistency of the singlephase Admittance Matrix-Based State Estimator (AMB SE) originally proposed for distribution systems is for the first time assessed and compared to that of the widely used Traditional SE (TSE). The AMB SE is an interesting alternative for distribution systems given the use of a constant Gain matrix, thus simplifying its implementation and significantly reducing the computational time. However, it is crucial to statistically assess its consistency so as to ensure estimated values and variances (outputs) are in agreement with the specified measurements and variances (inputs). This is carried out using a Monte Carlo analysis and a generic 16-bus UK distribution system. Despite the conversion from actual to equivalent measurements required by the AMB SE, as well as the approximations regarding the variances of the equivalent measurements, the results demonstrate that the single-phase AMB SE is as consistent and precise as the TSE.