This article addresses a seemingly trivial question-"Based on theological measurements, when are two samples different beyond experimental error?"-and proceeds to give a non trivial answer. The preferred answer requires the application of t statistics to multiple measurements on each sample. The larger the number of multiple measurements made, the lower is the uncertainty in conclusively discriminating between two samples. However, such multiple measurements on every sample are seldom feasible in real life and then it becomes necessary to resort to the use of Z statistics. A stepwise procedure for the application of both, t and Z statistics is given. Knowledge of the measurement precision is a prerequisite for scientifically answering this seemingly trivial question. Hence, the precision of capillary rheometry measurements (apparent viscosity, extrudate swell ratio, and entrance pressure loss) is discussed in detail. The precision of these capillary rheometry measurements improves as the magnitude of the variable measured (force/pressure or swell) increases. This implies that the precision of capillary rheometry measurements can be improved by lowering the experimental temperature. Extensive numerical data on various high-density polyethylenes generated using two different capillary rheometers are given and are compared with the ASTM round-robin data.