Four researchers at the Educational Testing Service describe what they consider some of the most vexing research problems they face. While these problems are not completely statistical, they all have major statistical components. Following the introduction (section 1), in section 2, "Problems with the Simultaneous Estimation of Many True Scores," Charles Lewis describes a technical problem that occurs in taking a Bayesian approach to traditional test theory. In the third section, "Test Theory Reconceived," Robert J. Mislevy explains problems involved in reconceiving old approaches and new theories. Section 4, "Allowing Examinee Choice in Exams" by Howard Wainer, discusses the general problem of nonignorable nonresponse in the circumstance in which examinees choose to answer only a small number of test items from a larger sample. The fifth section, "Some Statistical Issues Facing NAEP," by Eugene G. Johnson, describes the inferences that are occurring within the National Assessment of Educational Progress due to nonignorable response. (Contains 28 references.) (SLD)