Positioning errors of robots used for material handling and assembly can be sufficiently large to cause problems. These errors are due to imperfect repeatability of the robots, and their effects can be ameliorated or exacerbated by tolerances on the workpieces and on the jigs and fixtures. In this paper, a model for characterizing the positioning errors of robots is developed. A statistical analysis of positioning error data is performed to make inferences about the stochastic nature of the robotic system. The basic issue is whether the positioning errors of the robot are state dependent or state invariant.