Appropriateness measurement is a general approach to the problem caused by multiple choice tests failing to measure accurately the ability of atypical examinees. The conceptual framework of appropriateness measurement is presented, and several statistical indices of the appropriateness of a multiple choice test for an examinee are noted. A series of interrelated experiments is used to demonstrate that appropriateness measurement is robust to errors in parameter estimation and to the presence of unidentified aberrant examinees in the test norming sample. Finally, studies with actual data are used to show that the three-parameter logistic model is sufficiently valid to support effective appropriateness measurement in applications with real examinees. (Author)