A test comprised of binary items has an associated theoretical structure (TS) Tp(D, R, E), which may be paired with any of a number of possible quantitative characterizations (QCs). The aim of test analysis is to examine whether a set of test items conforms to an appropriately chosen QC. In this article, the authors consider one of the most common TSs, Tp(D, R, E), in which D = 1 construct, R = monotone increasing item/construct regressions, and E = errors in variables. The authors then consider two QCs appropriate for this TS and review tests for each. Several examples are provided.
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