This paper describes a statistical positioning error analysis for two-line element (TLE) data of a set of medium earth orbiting (MEO) and geostationary earth orbiting (GEO) satellites over the past 20 years. The Joint Space Operations Center (JSpOC) provides spacecraft ephemerides in the form of TLEs, which represent the most comprehensive catalogue of space objects readily accessible to the public. Its utility as an initial estimate tool for space operations has made its limitations a topic of extensive study for many years. In this paper, we compare TLE data with precise ephemerides for tens of thousands of TLE sets, for representative space objects including Global Positioning System (GPS) and Wide Area Augmentation System (WAAS) satellites. Based on this data, we derive high-integrity error models using overbounding theory to determine probabilistic bounds on the radial, along-track, and cross-track positioning errors.