This report presents results of several extensive empirical studies. Prior to these studies it was believed that errors in procedural skills such as multi-digit subtraction could be accurately modelled with two mechanisms: bugs ("competence" phenomena reflecting mistaken beliefs about subtraction which are stable over time) and slips ("performance" phenomena loosely related to subtraction which are unstable over time). A computational descriptive framework, the "Buggy" model and a diagnostic program (DEBUGGY) were developed wherein bugs and slips modelled performance, describing the content of wrong answers and the steps taken in producing them. Students (N=925) studying subtraction were tested using the diagnostic tests developed by DEBUGGY. Some students were retested two days later to measure short-term stability of bugs, while others were retested several months later to study long-term stability. All tests were analyzed by DEBUGGY, and by expert diagnosticians to assess DEBUGGY's diagnostic abilities. Findings indicate DEBUGGY was as good as or better than human diagnosticians at discovering bugs that explain students' errors. Other findings challenge the belief that bugs and slips alone account for procedural error data. In addition, predictions of Repair Theory (a theory that predicted which bugs would exist for a given procedural skill) were verified. (Author/JN)