The multiple‐matrix item sampling designs that provide information about population characteristics most efficiently administer too few responses to students to estimate their proficiencies individually. Marginal estimation procedures, which estimate population characteristics directly from item responses, must be employed to realize the benefits of such a sampling design. Numerical approximations of the appropriate marginal estimation procedures for a broad variety of analyses can be obtained by constructing, from the results of a comprehensive extensive marginal solution, files of plausible values of student proficiencies. This article develops the concepts behind plausible values in a simplified setting, sketches their use in the National Assessment of Educational Progress (NAEP), and illustrates the approach with data from the Scholastic Aptitude Test (SA T).