We address the problem of selecting the best of a set of units based on a criterion variable, when its value is recorded for every unit subject to estimation, measurement, or another source of error. The solution is constructed in a decision-theoretical framework, incorporating the consequences (ramifications) of the various kinds of error that…

Issues of equity and fairness across subgroups of the population (e.g., gender or ethnicity) must be seriously considered in any standardized testing program. For this reason, many testing programs require some means for assessing test characteristics, such as reliability, for subgroups of the population. However, often only small sample sizes are…