Test scores are commonly reported in a small number of ordered categories. Examples of such reporting include state accountability testing, Advanced Placement tests, and English proficiency tests. This paper introduces and evaluates methods for estimating achievement gaps on a familiar standard-deviation-unit metric using data from these ordered categories alone. These methods hold two practical advantages over alternative achievement gap metrics. First, they require only categorical proficiency data, which are often available where means and standard deviations are not. Second, they result in gap estimates that are invariant to score scale transformations, providing a stronger basis for achievement gap comparisons over time and across jurisdictions. We find three candidate estimation methods that recover full-distribution gap estimates well when only censored data are available. [This paper is published in "Journal of Educational and Behavioral Statistics" v37 n4 p489-517 Aug 2012 (EJ973866).]